Fatigue time-varying reliability calculation method and device, equipment, storage medium and product

Abstract

The invention relates to the technical field of fatigue time-varying reliability analysis, in particular to a fatigue time-varying reliability calculation method and device, equipment, a storage medium and a product. The method comprises the following steps: performing crack propagation simulation on a three-dimensional plate shell structure based on a random propagation finite element method, and establishing a geometric model of a crack propagation path; based on the geometric model, calculating a stress intensity factor of the crack tip by adopting an interaction integral method, and determining change data of the stress intensity factor in the crack propagation process; based on the stress intensity factor of the crack tip and the change data of the stress intensity factor in the crack propagation process, performing numerical simulation on the crack propagation process by adopting an propagation finite element method; and based on a numerical simulation result, optimizing the crack propagation process by adopting an HLRF-BFGS optimization algorithm, and determining the reliability of fatigue crack propagation. According to the method, the fatigue reliability evaluation effect is improved.

Description

Technical Field

[0001] The present application relates to the technical field of fatigue time-varying reliability analysis, and in particular to a fatigue time-varying reliability calculation method, device, equipment, storage medium and product. Background Art

[0002] In engineering structures, crack propagation is an important factor affecting structural fatigue failure, especially in complex three-dimensional plate and shell structures such as aviation and ships, where the crack propagation path and speed are highly random. Traditional fatigue reliability analysis methods are mostly based on two-dimensional models, mainly using fixed stress intensity factors and simplified crack propagation path assumptions, which are difficult to accurately simulate the true propagation behavior of cracks in three-dimensional structures. In the prior art, the finite element method is often used for crack propagation analysis, but it often requires frequent re-gridding, has low computational efficiency and is difficult to handle the discontinuity of the crack path. In addition, reliability analysis usually relies on random simulation methods such as the Monte Carlo method, which has the problems of large computational complexity and slow convergence speed, and cannot meet the needs of high-precision and efficient fatigue assessment. Therefore, the development of new methods that can accurately simulate the crack propagation process and optimize the calculation of fatigue reliability has become a technical problem that needs to be solved urgently in the engineering field. Summary of the invention

[0003] The main purpose of this application is to provide a fatigue time-varying reliability calculation method, device, equipment, storage medium and product, aiming to solve the technical problem of how to improve the evaluation effect of the fatigue reliability of the structure.

[0004] To achieve the above object, the present application provides a fatigue time-varying reliability calculation method, the method comprising the following steps:

[0005] Based on the random expansion finite element method, the crack propagation of the three-dimensional plate and shell structure is simulated and the geometric model of the crack propagation path is established;

[0006] Based on the geometric model, the stress intensity factor at the crack tip is calculated by using the interaction integral method, and the change data of the stress intensity factor during the crack propagation process is determined;

[0007] Based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process, the extended finite element method is used to perform numerical simulation on the crack propagation process;

[0008] Based on the results of numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack growth process and determine the reliability of fatigue crack growth.

[0009] In one embodiment, before the step of simulating crack propagation of a three-dimensional plate-shell structure based on the random expansion finite element method and establishing a geometric model of the crack propagation path, the method further includes:

[0010] Obtaining the initial crack parameters of the structure, including crack formation time, crack location, and initial crack length;

[0011] Based on the initial crack parameters of the structure, random variables in the crack growth process are defined, including crack growth rate, crack growth direction, and stress intensity factor.

[0012] In one embodiment, after the step of defining random variables in the crack propagation process based on the initial crack parameters of the structure, including crack propagation speed, crack propagation direction, and stress intensity factor, the following step is further included:

[0013] Performing statistical distribution analysis on the crack formation time, the crack position, and the initial length of the crack to obtain an input vector;

[0014] Based on the input vector, fatigue load is taken as a random variable, and the change of the random variable is described by a probability distribution function;

[0015] Dynamically generating a crack length, a crack angle, and a stress intensity factor that are dependent on the random variables during crack propagation;

[0016] Based on the crack length, the crack angle and the stress intensity factor, a random change of non-initial variables during each crack propagation process is determined.

[0017] In one embodiment, the step of calculating the stress intensity factor at the crack tip based on the geometric model using the interaction integral method and determining the change data of the stress intensity factor during the crack propagation process includes:

[0018] Based on the geometric model, the stress and displacement data at the crack tip are extracted using the finite element method;

[0019] Obtaining a coverage path of the crack tip, and determining a J-integral value based on the coverage path and the stress and displacement data by using the interaction integration method;

[0020] Determining the stress intensity factor according to the J-integral value and preset material mechanical parameters, wherein different crack extension modes correspond to different stress intensity factors;

[0021] A numerical difference analysis is performed on the stress intensity factor to determine a change in the stress intensity factor.

[0022] In one embodiment, the step of numerically simulating the crack propagation process using an extended finite element method based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process includes:

[0023] Based on the geometric model, establishing an XFEM model;

[0024] Inputting the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process into the XFEM model to determine the propagation path and morphology of the crack;

[0025] According to the change of stress intensity factor at the crack tip, numerical iteration update is performed to simulate the step-by-step expansion behavior during crack propagation and determine the stress field change under each step of expansion. In the process of crack propagation, the local stress field and displacement field at the crack tip are calculated in real time to dynamically adjust the stress intensity factor and path of crack propagation.

[0026] The crack propagation path and morphology, the stress field change, the stress intensity factor and the change data of the stress intensity factor are used as numerical simulation results.

[0027] In one embodiment, the step of optimizing the crack propagation process based on the results of numerical simulation using the HLRF-BFGS optimization algorithm to determine the reliability of fatigue crack propagation includes:

[0028] Based on the results of numerical simulation, a reliability optimization model is constructed and the objective function is defined;

[0029] Converting the random variables in the crack propagation process into a standard normal distribution space, and determining the limit state equation according to the objective function;

[0030] The result of the numerical simulation is applied to the limit state equation, and the limit state equation is solved using the HLRF-BFGS optimization algorithm to obtain a reliability index of fatigue crack growth.

[0031] In addition, to achieve the above purpose, the present application also proposes a fatigue time-varying reliability calculation device, the fatigue time-varying reliability calculation device comprising:

[0032] The geometric model building module is used to simulate the crack propagation of three-dimensional plate and shell structures based on the random expansion finite element method and establish a geometric model of the crack propagation path;

[0033] An intensity factor determination module is used to calculate the stress intensity factor at the crack tip based on the geometric model by using an interaction integral method, and to determine the change data of the stress intensity factor during the crack propagation process;

[0034] A numerical simulation module, used for numerically simulating the crack propagation process by using an extended finite element method based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process;

[0035] The target module is used to optimize the crack growth process based on the results of numerical simulation using the HLRF-BFGS optimization algorithm to determine the reliability of fatigue crack growth.

[0036] In addition, to achieve the above-mentioned purpose, the present application also proposes a fatigue time-varying reliability calculation device, which includes: a memory, a processor, and a fatigue time-varying reliability calculation program stored in the memory and executable on the processor, and the fatigue time-varying reliability calculation program is configured to implement the steps of the fatigue time-varying reliability calculation method described above.

[0037] In addition, to achieve the above purpose, the present application also proposes a storage medium, on which a fatigue time-varying reliability calculation program is stored. When the fatigue time-varying reliability calculation program is executed by a processor, the steps of the fatigue time-varying reliability calculation method described above are implemented.

[0038] In addition, to achieve the above-mentioned purpose, the present application also proposes a computer program product, which includes a computer program. When the computer program is executed by a processor, the steps of the fatigue time-varying reliability calculation method described above are implemented.

[0039] This application uses the random extended finite element method to simulate the crack propagation of a three-dimensional plate-shell structure and establishes a geometric model of the crack propagation path; based on the geometric model, the interaction integral method is used to calculate the stress intensity factor at the crack tip, and the change data of the stress intensity factor during the crack propagation process is determined; based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process, the extended finite element method is used to numerically simulate the crack propagation process; based on the results of the numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack propagation process and determine the reliability of fatigue crack propagation. This application uses the random extended finite element method to establish a geometric model of the crack propagation path of a three-dimensional plate-shell structure, and uses the interaction integral method to dynamically calculate the stress intensity factor at the crack tip and its change data, combined with the extended finite element method to efficiently simulate the crack propagation process, without the need to redraw the grid, significantly improving the simulation accuracy and efficiency; based on the numerical simulation results, the HLRF-BFGS optimization algorithm is used for reliability optimization calculation, which can quickly solve the limit state equation compared to traditional methods and improve the accuracy and efficiency of fatigue reliability assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of the first embodiment of the fatigue time-varying reliability calculation method of the present application;

[0041] Figure 2 This is a schematic diagram of a sub-process in the second embodiment of the fatigue time-varying reliability calculation method of the present application;

[0042] Figure 3 This is a schematic diagram of a sub-process in the third embodiment of the fatigue time-varying reliability calculation method of the present application;

[0043] Figure 4 This is a schematic diagram of the module structure of the fatigue time-varying reliability calculation device according to an embodiment of the present application;

[0044] Figure 5 Schematic diagram of the equipment structure of the hardware operating environment involved in the fatigue time-varying reliability calculation method in the embodiment of the present application.

[0045] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0046] It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0047] In order to better understand the technical solution of the present application, a detailed description will be given below in conjunction with the accompanying drawings and specific implementation methods.

[0048] It should be noted that in engineering structures, crack propagation is an important factor affecting structural fatigue failure, especially in complex three-dimensional plate and shell structures such as aviation and ships, where the crack propagation path and speed are highly random. Traditional fatigue reliability analysis methods are mostly based on two-dimensional models, mainly using fixed stress intensity factors and simplified crack propagation path assumptions, which are difficult to accurately simulate the true propagation behavior of cracks in three-dimensional structures. In the prior art, the finite element method is often used for crack propagation analysis, but it often requires frequent re-gridding, has low computational efficiency and is difficult to handle the discontinuity of the crack path. In addition, reliability analysis usually relies on random simulation methods such as the Monte Carlo method, which has the problems of large computational complexity and slow convergence speed, and cannot meet the needs of high-precision and efficient fatigue assessment. Therefore, the development of new methods that can accurately simulate the crack propagation process and optimize the calculation of fatigue reliability has become a technical problem that needs to be urgently solved in the engineering field.

[0049] The main solution of this application is: based on the random extended finite element method, this application simulates the crack propagation of three-dimensional plate and shell structures and establishes a geometric model of the crack propagation path; based on the geometric model, the interaction integral method is used to calculate the stress intensity factor at the crack tip, and the change data of the stress intensity factor during the crack propagation process is determined; based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process, the extended finite element method is used to numerically simulate the crack propagation process; based on the results of the numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack propagation process and determine the reliability of fatigue crack propagation.

[0050] This application establishes a geometric model of the crack propagation path of a three-dimensional plate and shell structure through the random extended finite element method, and uses the interaction integral method to dynamically calculate the stress intensity factor at the crack tip and its change data. The extended finite element method is combined to efficiently simulate the crack propagation process without the need for re-meshing, which significantly improves the simulation accuracy and efficiency. Based on the numerical simulation results, the HLRF-BFGS optimization algorithm is used for reliability optimization calculation. Compared with traditional methods, it can quickly solve the limit state equation and improve the accuracy and efficiency of fatigue reliability assessment.

[0051] It should be noted that the execution subject of the method of this embodiment can be a computing service device with data processing, network communication and program running functions, or it can be the above fatigue time-varying reliability calculation device with the same or similar functions. This embodiment and the following embodiments will be described by taking the fatigue time-varying reliability calculation device as an example.

[0052] Based on this, the first embodiment of the fatigue time-varying reliability calculation method of this application is proposed, please refer to Figure 1 , Figure 1 This is a flow chart of the first embodiment of the fatigue time-varying reliability calculation method of the present application.

[0053] In this embodiment, the fatigue time-varying reliability calculation method includes the following steps:

[0054] S1: Based on the random expansion finite element method, the crack propagation of the three-dimensional plate and shell structure is simulated and the geometric model of the crack propagation path is established;

[0055] It should be noted that the random extended finite element method is an improved version of the extended finite element method (XFEM), which is specifically used to simulate the evolution process of discontinuous phenomena such as cracks. It combines randomness analysis, so that the random changes in structural material properties, loads and geometric shapes can be considered when simulating crack propagation, and is suitable for crack propagation processes in complex stress fields. Plate and shell structures refer to structural forms with thickness much smaller than other dimensions, such as aircraft wings and hull shells. Three-dimensional plate and shell structures are more complex geometries, including plates (thin plane structures) and shells (curved structures), requiring accurate stress and crack behavior simulation. The geometric model of the crack propagation path is a geometric description of the position, morphology and evolution process of the crack in the structure obtained through finite element simulation. It contains parameters such as the starting point, extension direction, and extension speed of the crack, and is an important basis for subsequent crack behavior analysis and reliability assessment.

[0056] Specifically, obtain the geometric model of the three-dimensional plate and shell structure and the parameters of the initial crack (such as crack location, length and direction). Define material properties and boundary conditions, including material parameters such as the elastic modulus and Poisson's ratio of the structure, as well as the load type and distribution. Determine the random variables in the crack propagation process, such as crack propagation speed, direction, initial position, etc. Perform statistical distribution analysis on these random variables, use probability density functions (such as normal distribution, uniform distribution, etc.) to describe the randomness of the variables, and generate random samples for input into the model.

[0057] Furthermore, the stochastic expansion finite element method (SXFEM) is used to numerically simulate crack propagation and generate the crack propagation path in the structure. SXFEM describes the propagation of the crack tip through an enhanced shape function, and can dynamically simulate the crack propagation without re-meshing. During the simulation, the geometric information of the crack path is continuously updated according to the changes in the stress field, and a three-dimensional crack propagation path geometric model is gradually established. According to the simulated crack propagation trajectory, a complete crack geometry model is formed, which includes information such as the crack propagation starting point, path, branching, and crack tip position. The model can dynamically reflect the changes in geometric morphology during crack propagation, and provide basic data for subsequent stress analysis and reliability assessment.

[0058] By considering the random factors in the crack propagation process, SXFEM can simulate the actual behavior of cracks in complex stress fields, more accurately describe the crack propagation path and its evolution law, and improve the authenticity and accuracy of the simulation compared with the traditional deterministic model. SXFEM does not need to re-divide the grid during the crack propagation process. By introducing enhanced shape functions to achieve dynamic tracking of cracks, it significantly simplifies the complexity of grid processing and improves the computational efficiency. Through the simulation of three-dimensional plate and shell structures, SXFEM can handle crack propagation problems under complex geometry and load conditions, with a wider range of applications, and can effectively analyze the crack behavior in actual engineering structures (such as aviation and ships). The established crack propagation path geometry model provides accurate geometric basic data for subsequent stress intensity factor calculation, numerical simulation and reliability optimization, which helps to achieve more accurate fatigue assessment and reliability analysis. In summary, this step effectively solves the randomness problem in the crack propagation simulation of complex three-dimensional structures, improves the simulation accuracy and computational efficiency of the crack propagation path, and lays a solid foundation for fatigue time-varying reliability calculation.

[0059] S2: Based on the geometric model, the stress intensity factor at the crack tip is calculated by using the interaction integral method, and the change data of the stress intensity factor during the crack propagation process is determined;

[0060] It should be noted that the geometric model refers to the spatial description of the crack propagation path established during the crack propagation simulation process, including information such as the location, length, and direction of the crack, which is used to analyze the impact of crack propagation on the structural stress field. The interaction integral method is a numerical method for calculating the stress intensity factor at the crack tip. By integrating the stress and displacement fields in the area near the crack tip, the interaction integral method can accurately evaluate the changes in the stress intensity factor at the crack tip, which is especially suitable for complex stress fields and crack geometries. The stress intensity factor is an important parameter that describes the intensity of the stress field at the crack tip and is used to quantify the stress concentration at the crack tip. Different crack propagation modes (such as type I cracking, type II slip, and type III tearing) correspond to different types of stress intensity factors.

[0061] Specifically, based on the geometric model of the crack propagation path established in the previous step, the geometric data of the crack, including the crack tip position, path shape, etc., are imported. The stress field and displacement field data near the crack tip are extracted from the numerical simulation, which are the basis for calculating the stress intensity factor. The integral path surrounding the crack tip is determined, and a closed path (such as a ring or rectangular area) near the crack tip is usually selected as the integral area. Make sure that the integral path is close enough to the crack tip to capture the detailed changes in the stress field, while avoiding the path being too close to the crack tip to cause calculation instability.

[0062] Furthermore, the extracted stress and displacement data are used to calculate the stress intensity factor at the crack tip through the interaction integral method. The interaction integral method calculates the stress intensity factors of type I, type II and type III crack modes based on the stress and displacement field data at the crack tip, and accurately evaluates the concentration of the stress field at the crack tip. At different stages of crack propagation, the interaction integral calculation is repeated to obtain the stress intensity factor of each stage. By numerical difference or fitting methods, the changing trend of the stress intensity factor at different stages is analyzed, and the changing data of the stress intensity factor during crack propagation is determined.

[0063] The interaction integral method uses geometric models and extracted stress and displacement data to accurately calculate the stress intensity factor at the crack tip, overcoming the simplified assumptions of crack morphology and stress distribution in traditional methods, making the evaluation of stress intensity factors more realistic and reliable. By calculating and comparing the stress intensity factors at different stages of crack extension, the change process of the stress field at the crack tip can be dynamically reflected, providing accurate data support for the risk assessment of crack extension and fatigue life prediction. The interaction integral method is particularly suitable for the analysis of complex stress fields and irregular crack geometries. It can be directly applied to the actual crack extension path without changing the geometric model, greatly improving the applicability and flexibility of the calculation. The change data of the stress intensity factor at the crack tip is an important input for crack extension simulation and reliability analysis. Accurate stress intensity factor data provides a reliable basis for subsequent expansion finite element simulation and optimization analysis, ensuring the rigor and accuracy of the overall calculation process. In summary, this step improves the ability to evaluate the stress state of the crack extension process through accurate calculation and change analysis of the stress intensity factor, and provides high-quality data support for the subsequent steps of fatigue reliability calculation.

[0064] S3: Based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process, the extended finite element method is used to perform numerical simulation on the crack propagation process;

[0065] It should be noted that the stress intensity factor (SIF) is a key parameter to measure the intensity of the stress field at the crack tip, reflecting the degree of stress concentration of the crack under load. Different crack propagation modes (type I, type II, type III) correspond to different stress intensity factors, which directly affect the crack propagation behavior and path. The change data reflects the dynamic characteristics of the crack tip stress intensity factor as the crack propagation path, morphology and external load change during the crack propagation process. It is an important input for numerical simulation and is used to reflect the changes in the stress field of the crack at different propagation stages. The Extended Finite Element Method (XFEM) is an improved finite element method that can simulate the crack propagation process without re-meshing. By introducing special shape functions, XFEM can handle the dynamic changes of the crack path and the complexity of the crack tip stress field, and is an effective tool for simulating complex crack propagation behavior.

[0066] Specifically, an XFEM model of crack propagation is established based on the existing geometric model and stress intensity factor data. The material properties, boundary conditions and external loads of the structure are defined. The crack location and propagation path are controlled by the geometric model, and meshing is not required to accurately capture the crack location. The crack is embedded in the model through the shape function of XFEM. The stress intensity factor at the crack tip calculated by the interaction integral method and its change data are input into the XFEM model. These data will be used to guide the crack propagation direction, speed and morphological changes. The changes in the stress intensity factor during crack propagation are dynamically input, so that the model can update the crack propagation path and stress field in real time.

[0067] Furthermore, XFEM uses the input stress intensity factor and change data to simulate the gradual expansion of cracks under load. The dynamic change of the crack path does not require re-meshing, which greatly simplifies the simulation calculation process. The shape and expansion direction of the crack are controlled by the stress intensity factor. The model recalculates the stress field and displacement field at the crack tip in each expansion step to ensure that the simulation can accurately capture the dynamic expansion behavior of the crack. In each expansion step, XFEM adjusts the crack path and stress distribution according to the current stress intensity factor changes, and performs numerical iterative calculations. Through gradual expansion and updating, the stress field changes, path morphology, and possible branching and stagnation phenomena of the crack during the entire expansion process are simulated. Output numerical simulation results such as crack expansion path, changes in stress intensity factor, local stress field and displacement field. These results provide basic data for subsequent fatigue reliability evaluation and optimization calculations, and are used to verify the accuracy and reliability of the model.

[0068] The extended finite element method can directly simulate the crack propagation process without re-meshing, and use shape functions to accurately track the changes in the crack tip, reducing the complexity and time of calculations and improving the accuracy and efficiency of simulation. Using the stress intensity factor and its change data, XFEM can adjust the crack propagation path and stress field distribution in real time, accurately capture the crack propagation trend and stress field changes, and enhance the simulation ability of complex crack propagation behavior. This method does not require excessive geometric simplification of complex three-dimensional plate and shell structures, can handle complex stress fields and multi-mode crack propagation, and is suitable for crack propagation analysis of actual structures in engineering. The simulation results provide accurate stress field and crack path data for subsequent fatigue reliability analysis, providing a solid basis for fatigue life prediction and reliability assessment. In summary, the numerical simulation of the crack propagation process through XFEM can dynamically and accurately capture the stress changes and propagation behavior of the crack tip, providing an efficient and accurate numerical tool for fatigue reliability analysis of complex structures.

[0069] S4: Based on the results of numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack propagation process and determine the reliability of fatigue crack propagation.

[0070] It should be noted that the numerical simulation results are the crack propagation path, stress intensity factor change, stress field distribution, displacement field and other data obtained by calculating the crack propagation process through the extended finite element method (XFEM). These results reflect the dynamic behavior of the crack at different stages and provide input data for subsequent reliability calculations. The HLRF (Hasofer-Lind-Rackwitz-Fiessler)-BFGS (Broyden-Fletcher-Goldfarb-Shanno) optimization algorithm is an optimization algorithm for reliability analysis. The HLRF algorithm is used to construct the limit state equation of reliability, while BFGS is a quasi-Newton iterative optimization algorithm for solving complex optimization problems. The algorithm combines the advantages of optimization and reliability analysis and can efficiently solve reliability indicators. The reliability of fatigue crack propagation refers to the probability that a structure or component remains functionally intact at a specific crack propagation stage under given use conditions. By calculating the reliability, the safety and failure risk of the structure during fatigue crack propagation can be evaluated.

[0071] Specifically, the crack propagation path, stress intensity factor change, stress field distribution and other data obtained by numerical simulation are used to construct the limit state equation for reliability analysis and define the failure criteria of the structure. The random variables involved in the crack propagation process (such as stress intensity factor, crack length, load amplitude, etc.) are input into the optimization model to describe the statistical characteristics of the random variables. The random variables in the crack propagation process are converted to the standard normal space to eliminate the correlation between variables and simplify the optimization solution. Commonly used conversion methods are Rosenblatt transformation or Nataf transformation. Through the conversion of the standard normal space, it is ensured that the solution of the reliability index has better numerical stability.

[0072] Furthermore, the HLRF-BFGS algorithm is used to solve the limit state equation and gradually approach the failure boundary. The HLRF algorithm finds the solution closest to the failure point through iterative optimization and determines the minimum reliability index point. The BFGS optimization algorithm adjusts the iteration direction and step size during the solution process to ensure rapid convergence of the algorithm and improve the solution efficiency. During the optimization solution process, iterative calculations are repeated to update the stress intensity factor, path and stress field data of crack extension until the limit state equation converges. The reliability index of fatigue crack extension (such as reliability index or failure probability) is calculated, and the fatigue life and failure risk of the structure are evaluated based on the index. The optimized reliability index is output to provide an evaluation result on the reliability of the crack extension process. According to the reliability analysis results, a basis is provided for structural design, service life prediction and maintenance decisions.

[0073] Compared with the traditional Monte Carlo simulation, the HLRF-BFGS optimization algorithm directly approaches the failure point through gradient optimization, which significantly improves the computational efficiency and can quickly solve complex reliability problems. By combining the numerical simulation results with the optimization algorithm, the randomness and uncertainty in the crack propagation process can be accurately described, making the reliability calculation results closer to the actual situation and improving the accuracy of failure risk assessment. This method can handle multi-variable and high-dimensional complex fatigue reliability problems, and is suitable for the evaluation of crack propagation in actual engineering structures, solving the problem of poor applicability of traditional methods in complex structures. The reliability analysis results provide a scientific basis for structural design optimization, maintenance decisions and life prediction, which helps to identify potential fatigue failure risks in advance and improve the safety and service life of the structure. In summary, by optimizing the crack propagation process through the HLRF-BFGS optimization algorithm, the reliability of the structure in the fatigue crack propagation process can be quickly and accurately determined, providing an efficient calculation tool for fatigue assessment of complex three-dimensional structures.

[0074] This embodiment uses the random extended finite element method to simulate the crack propagation of a three-dimensional plate-shell structure and establishes a geometric model of the crack propagation path; based on the geometric model, the interaction integral method is used to calculate the stress intensity factor at the crack tip, and the change data of the stress intensity factor during the crack propagation process is determined; based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process, the extended finite element method is used to numerically simulate the crack propagation process; based on the results of the numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack propagation process and determine the reliability of fatigue crack propagation. This embodiment uses the random extended finite element method to establish a geometric model of the crack propagation path of a three-dimensional plate-shell structure, and uses the interaction integral method to dynamically calculate the stress intensity factor at the crack tip and its change data, and combines the extended finite element method to efficiently simulate the crack propagation process without redrawing the grid, which significantly improves the simulation accuracy and efficiency; based on the numerical simulation results, the HLRF-BFGS optimization algorithm is used to perform reliability optimization calculations, which can quickly solve the limit state equation compared to traditional methods, and improve the accuracy and efficiency of fatigue reliability assessment.

[0075] Based on the above first embodiment, a second embodiment of the fatigue time-varying reliability calculation method of the present application is proposed. Figure 2 , Figure 2 This is a schematic diagram of a sub-process in the second embodiment of the fatigue time-varying reliability calculation method of the present application.

[0076] like Figure 2 As shown, in this embodiment, before step S1, the following is further included:

[0077] S1a: Obtain the initial crack parameters of the structure, including crack formation time, crack location, and initial crack length;

[0078] S1b: Based on the initial crack parameters of the structure, random variables in the crack propagation process are defined, including crack propagation speed, crack propagation direction, and stress intensity factor.

[0079] It should be noted that the initial crack parameters of the structure refer to the relevant parameters of the known or assumed crack initiation state in the structure, including the formation time, position and initial length of the crack. The initial crack parameters are the basis of crack propagation analysis and affect how the crack propagates and develops during the subsequent loading process. The crack formation time refers to the time point when the crack first appears or is detected in the structure. This time point marks the starting point of the structural fatigue process and is the key reference time for fatigue analysis. The crack position refers to the specific location of the crack in the structure, usually expressed in a coordinate system. The position parameters determine the orientation of the crack relative to the external load and the stress concentration area at the crack tip. The initial crack length refers to the initial length of the crack when it is formed, which is the starting state of the crack propagation analysis. The initial length affects the stress concentration of the crack and the path and speed of subsequent propagation. Random variables refer to the fact that during the crack propagation process, due to the randomness of factors such as materials, geometry, loads and environment, the crack propagation parameters (such as speed, direction, stress intensity factor, etc.) at different stages will have different values. These parameters are defined as random variables. The crack growth rate refers to the speed at which a crack grows in a structure with the increase of time or load. It is usually random and related to factors such as the stress intensity factor of the crack, material properties and external environment. The crack growth direction refers to the direction of the crack tip during the crack growth process. It is also affected by factors such as material properties, crack morphology and external loads, and is usually random and uncertain. The stress intensity factor (SIF) is a parameter that quantifies the degree of stress concentration at the crack tip and is the driving force of crack growth behavior. The stress intensity factor will change with the crack growth path and load conditions.

[0080] Specifically, the crack formation time, crack location and initial crack length are obtained from the design documents, test reports or fatigue test data of the structure. The crack formation time can be calculated through historical load data and fatigue properties of the material or obtained through monitoring of the test equipment. The crack location is usually determined by non-destructive testing technology (such as ultrasonic testing, X-ray testing), and the initial position of the crack is represented by a coordinate system. The initial crack length can be determined by measurement or image processing technology as the starting point data for crack propagation analysis.

[0081] Furthermore, according to the initial crack parameters, the random variables in the crack propagation process are determined, and these variables are used to describe the crack propagation behavior. Based on the material properties of the structure, the characteristics of the stress field, and the environmental conditions (such as temperature, humidity, etc.), the probability distribution of the crack propagation rate (such as normal distribution, lognormal distribution, etc.) is defined. The probability distribution of the crack propagation direction is defined in combination with the initial crack position and the direction of the external load. Considering the anisotropy of the material and the uncertainty of the external load, the crack propagation direction may change randomly. The stress intensity factor is related to the stress field at the crack tip, and its change law and probability distribution during the crack propagation process are defined. The randomness of the stress intensity factor reflects the uncertainty of the crack under actual loading conditions. By statistically analyzing the random variables in the crack propagation process, the corresponding probability distribution model is established. Common distribution types include normal distribution, lognormal distribution, Weibull distribution, etc. The statistical characteristics such as the mean and variance of each random variable are determined for subsequent numerical simulation and reliability analysis.

[0082] By obtaining the initial crack parameters of the structure, the initial state of crack propagation can be accurately described, providing real and reliable initial conditions for subsequent analysis. Defining random variables in the crack propagation process, taking into account the uncertainty of materials and external environment, makes the crack propagation analysis more in line with the actual situation. By defining and establishing a statistical model of random variables, the uncertainty and randomness in the crack propagation process can be quantified, which helps to better predict the speed and direction of crack propagation and improve the accuracy of fatigue life prediction. The determined initial crack parameters and random variables can be used as the basic input for numerical simulation and reliability analysis, ensuring that the simulation process takes into account all relevant uncertainty factors and enhancing the practical applicability and reliability of the model. In summary, by obtaining the initial crack parameters and defining random variables in the crack propagation process, accurate basic data can be provided for the numerical simulation and reliability analysis of crack propagation, improving the accuracy and reliability of the analysis, and providing a more scientific basis for the fatigue life prediction of engineering structures.

[0083] Based on the first embodiment above, in this embodiment, after step S1b, the following is further included:

[0084] S1c: performing statistical distribution analysis on the crack formation time, the crack position, and the initial length of the crack to obtain an input vector;

[0085] S1d: Based on the input vector, the fatigue load is taken as a random variable, and the change of the random variable is described by a probability distribution function;

[0086] S1e: dynamically generating a crack length, a crack angle and a stress intensity factor dependent on the random variables during crack propagation;

[0087] S1f: Based on the crack length, the crack angle and the stress intensity factor, determine the random changes of non-initial variables during each crack propagation process.

[0088] It should be noted that statistical distribution analysis is a mathematical analysis method used to determine the statistical characteristics of a set of data (such as crack formation time, position, initial length), including its probability distribution, mean, variance, etc. Through statistical distribution analysis, the randomness and uncertainty of data can be quantified. In crack growth simulation, the input vector is a set of values ​​formed by the initial crack parameters (crack formation time, position, initial length) through statistical distribution analysis, which is used to describe the initial state and possibility of crack growth. Fatigue load refers to the external load repeatedly applied to the structure during service. Its amplitude and frequency change over time and may cause fatigue failure of the material. In crack growth analysis, fatigue load is usually regarded as a random variable because its variation characteristics affect the crack growth speed and direction. Probability distribution function is used to describe the probability distribution of random variables (such as fatigue load, crack growth speed, etc.). Commonly used probability distribution functions include normal distribution, lognormal distribution, Weibull distribution, etc. Through probability distribution function, the variation characteristics of random variables can be quantitatively described. Non-initial variables refer to variables (such as crack length, crack angle, stress intensity factor, etc.) that are dynamically generated with time or load changes during the crack propagation process, in addition to the initial crack parameters (such as crack formation time, position, and initial length). These variables are a direct description of the crack propagation state.

[0089] Specifically, the data of crack formation time, crack location, and initial crack length are collected and sorted, and statistical analysis is performed to determine the probability distribution type of these data (such as normal distribution, lognormal distribution, Weibull distribution, etc.). The statistical characteristics of these data (such as mean, variance, skewness, kurtosis, etc.) are calculated, and these parameters are used to form an input vector to describe the initial state of the crack and its random characteristics. Based on the input vector, the random characteristics of the fatigue load are defined and introduced as a random variable into the crack growth analysis model. The variation characteristics of the fatigue load are described by probability distribution functions (such as normal distribution, Poisson distribution, etc.), and the load fluctuations under actual use conditions are simulated to ensure that the crack growth process takes into account the randomness of the load.

[0090] Furthermore, during the crack propagation simulation, the changes in the length, angle, and stress intensity factor of the crack are dynamically calculated through numerical simulation methods based on the random variables of the input vector and fatigue load. In each simulation step, the crack length is updated according to the changes in fatigue load and stress intensity factor; the crack angle is adjusted according to the stress state and material properties at the crack tip; and the stress intensity factor is recalculated according to the changes in crack length and angle. Based on the real-time calculated crack length, crack angle, and stress intensity factor, the changes in non-initial variables during each crack propagation process are determined. The Monte Carlo method or other numerical iterative algorithms are used to simulate multiple changes in non-initial variables to obtain the range and distribution of random variables.

[0091] By performing statistical distribution analysis on the initial crack parameters and treating fatigue load and other crack extension parameters as random variables, the uncertainty in the crack extension process can be accurately described, and the accuracy and authenticity of crack extension simulation can be improved. By dynamically generating key variables such as crack length, crack angle and stress intensity factor, and adjusting them in real time according to the actual load and crack state during the simulation, the simulation process can better adapt to the crack extension behavior under actual use conditions, and enhance the dynamic and adaptability of numerical simulation. The dynamic changes of these variables reflect the actual situation of crack extension under different use conditions, which can provide more scientific and reliable data support for fatigue life prediction and improve the scientific nature of structural reliability analysis and design optimization. By treating fatigue load and crack extension parameters as random variables and performing numerical simulation, the influence of uncertainty factors on crack extension can be quantified, providing more targeted optimization decision-making basis for structural reliability assessment. In summary, this step can effectively improve the description accuracy of crack extension and the dynamic response capability of numerical simulation by statistically analyzing and dynamically simulating the initial and non-initial variables in the crack extension process, and provide more accurate and reliable basic data for fatigue life prediction and reliability analysis of the structure.

[0092] Based on the above first embodiment, in this embodiment, step S2 includes:

[0093] S21: Based on the geometric model, using a finite element method, extracting stress and displacement data at the crack tip;

[0094] S22: obtaining a coverage path of the crack tip, and determining a J-integral value based on the coverage path and the stress and displacement data by using the interaction integration method;

[0095] S23: determining the stress intensity factor according to the J-integral value and preset material mechanical parameters, wherein different crack extension modes correspond to different stress intensity factors;

[0096] S24: performing numerical differential analysis on the stress intensity factor to determine a change in the stress intensity factor.

[0097] It should be noted that the finite element method is a numerical calculation method used to solve the stress, strain and displacement field distribution of complex structures. By dividing the structure into a finite number of units and performing discretization analysis on them, the finite element method can accurately calculate the local stress and displacement data at the crack tip. The covering path refers to a closed integral path around the crack tip, which is usually used to calculate the stress field parameters at the crack tip. The covering path needs to be carefully selected to ensure that the critical area of ​​the crack tip is included and the changes in the stress field at the crack tip can be effectively captured. The interaction integral method is a numerical method for calculating the J-integral value at the crack tip. The interaction integral method can accurately evaluate the energy release rate at the crack tip by integrating the stress field and displacement field near the crack tip. The J-integral is a measure of the energy release rate and is used to quantify the stress intensity at the crack tip. It reflects the energy required for the growth of a unit crack surface during crack propagation and is related to the fracture toughness of the material. Numerical difference analysis is a numerical method used to determine the numerical derivative or difference of the change in variables. By numerical difference analysis of the stress intensity factor, the change in the stress intensity factor during crack propagation can be calculated.

[0098] Specifically, based on the geometric model of the crack, the finite element method (FEM) is used to perform stress analysis and displacement field solution on the structure. By refining the mesh and calculating the response of the structure under external loads, the stress and displacement data at the crack tip and its surrounding area are extracted. The extracted data include stress tensors (such as tensile stress, shear stress, etc.) and displacement vectors at the crack tip for further J-integral calculation. A closed covering path around the crack tip is determined, which should be as close to the crack tip as possible and cover the stress field change area at the crack tip. An annular or rectangular path is usually selected to ensure an accurate assessment of the stress intensity factor at the crack tip. Through the FEM model, stress and displacement data are sampled on the covering path to provide input data for the calculation of the J-integral. Using the interaction integral method, the stress and displacement data within the covering path are numerically integrated to calculate the J-integral value at the crack tip. The J-integral represents the energy release rate required for the growth of a unit crack surface during crack propagation. According to the mechanical properties of the material and the geometry of the crack, the J-integral value is calculated and applied to different crack propagation modes (type I, type II, type III).

[0099] Furthermore, the stress intensity factor (SIF) at the crack tip is determined based on the calculated J-integral value and the preset mechanical parameters of the material (such as elastic modulus, Poisson's ratio, etc.). There is a corresponding relationship between the stress intensity factor and the J-integral value, and different crack extension modes have different stress intensity factors. The stress intensity factors under different modes are calculated and distinguished to evaluate the crack extension behavior under each mode. Numerical differential analysis is performed on the stress intensity factors at different crack extension stages to calculate the rate of change of the stress intensity factor. The differential analysis can use the finite difference method to determine its change trend by comparing the stress intensity factors at different times. The obtained stress intensity factor change data is used for crack extension simulation and fatigue reliability analysis to predict the speed, direction and mode changes of crack extension.

[0100] By extracting the stress and displacement data at the crack tip through the finite element method based on the geometric model, and calculating the J integral value by the interaction integral method, the energy release rate and stress concentration at the crack tip can be accurately quantified. Compared with the traditional method, it can more accurately evaluate the driving force of crack extension and improve the reliability of the simulation. By analyzing the stress intensity factor under different crack extension modes, the direction and speed of crack extension can be dynamically evaluated, the complex behavior of the crack extension process can be accurately described, and the prediction ability of the crack extension trend can be enhanced. The numerical difference analysis is used to dynamically track the changes in the stress intensity factor, so that the crack extension simulation can reflect the real response of the structure under different loads and conditions in real time, and the simulation accuracy is improved. At the same time, this method is suitable for the analysis of complex stress fields and crack geometries, and has stronger adaptability. By accurately determining the change data of the stress intensity factor, it provides an important basic input for the reliability analysis of fatigue crack extension, ensuring the accuracy and reliability of subsequent reliability calculations. In summary, this step can better evaluate the driving force and behavior characteristics of crack extension by accurately calculating and analyzing the stress intensity factor at the crack tip, and provides scientific data support for fatigue life prediction and structural reliability analysis.

[0101] This embodiment uses the random extended finite element method to simulate the crack propagation of a three-dimensional plate-shell structure and establishes a geometric model of the crack propagation path; based on the geometric model, the interaction integral method is used to calculate the stress intensity factor at the crack tip, and the change data of the stress intensity factor during the crack propagation process is determined; based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process, the extended finite element method is used to numerically simulate the crack propagation process; based on the results of the numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack propagation process and determine the reliability of fatigue crack propagation. This embodiment uses the random extended finite element method to establish a geometric model of the crack propagation path of a three-dimensional plate-shell structure, and uses the interaction integral method to dynamically calculate the stress intensity factor at the crack tip and its change data, and combines the extended finite element method to efficiently simulate the crack propagation process without redrawing the grid, which significantly improves the simulation accuracy and efficiency; based on the numerical simulation results, the HLRF-BFGS optimization algorithm is used to perform reliability optimization calculations, which can quickly solve the limit state equation compared to traditional methods, and improve the accuracy and efficiency of fatigue reliability assessment.

[0102] Based on the above second embodiment, a third embodiment of the fatigue time-varying reliability calculation method of the present application is proposed. Figure 3 , Figure 3 This is a schematic diagram of a sub-process in the third embodiment of the fatigue time-varying reliability calculation method of the present application.

[0103] In this embodiment, step S3 includes:

[0104] S31: Establishing an XFEM model based on the geometric model;

[0105] S32: inputting the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process into the XFEM model to determine the propagation path and morphology of the crack;

[0106] S33: According to the change of the stress intensity factor at the crack tip, numerical iteration update is performed to simulate the step-by-step expansion behavior during the crack extension process and determine the stress field change under each step of expansion, wherein the local stress field and displacement field at the crack tip are calculated in real time during the crack extension process, and the stress intensity factor and path of the crack extension are dynamically adjusted;

[0107] S34: taking the crack propagation path and morphology, the stress field change, the stress intensity factor and the change data of the stress intensity factor as numerical simulation results.

[0108] It should be noted that the Extended Finite Element Method (XFEM) model: XFEM is an enhanced finite element method used to simulate discontinuous phenomena such as cracks. The XFEM model can describe the crack propagation process through special shape functions without re-meshing, and accurately capture the changes in stress and displacement fields near the crack tip. Numerical iterative update is a numerical calculation method that gradually approaches the solution of the problem through repeated iterative calculations. In crack propagation simulation, numerical iteration is used to update the stress field, displacement field and propagation path at the crack tip, so that the simulation can dynamically reflect the gradual propagation behavior of the crack. The local stress field and displacement field are the stress and displacement distribution near the crack tip, which directly affect the crack propagation path and speed. The real-time calculation of the local stress field and displacement field is the key link in the XFEM simulation to ensure the accurate simulation of the crack propagation process.

[0109] Specifically, based on the geometric model, an XFEM model suitable for crack propagation analysis is established. The XFEM model uses enhanced shape functions to capture the discontinuities in the crack location and propagation process, avoiding the re-meshing of the crack propagation process in the traditional finite element method. The material properties, boundary conditions, and loading conditions of the model are set to ensure that the XFEM model can truly reflect the physical properties and crack propagation behavior of the structure. The previously calculated stress intensity factor at the crack tip and its change data during the crack propagation process are input into the XFEM model. These data are used to guide the crack propagation direction, speed, and morphological changes. The XFEM model uses the input stress intensity factor data to dynamically adjust the crack propagation path and morphology to simulate the complex behavior during the actual crack propagation process.

[0110] Furthermore, according to the change of stress intensity factor at the crack tip, the XFEM model is numerically iterated and updated to gradually simulate the gradual expansion behavior during the crack propagation process. In each iteration, the XFEM model recalculates the local stress field and displacement field at the crack tip, and adjusts the crack propagation path and morphology according to the results of these real-time calculations to ensure that the simulation process can dynamically reflect the true behavior of crack propagation. Repeat the above process until the crack reaches the predetermined extension length or failure criterion, and complete the numerical simulation of the entire crack propagation. The crack propagation path and morphology, stress field changes, stress intensity factor, and stress intensity factor change data are output as the final results of the numerical simulation. These simulation results are used for subsequent fatigue reliability analysis and life prediction, providing a scientific basis for the design and safety assessment of engineering structures.

[0111] Through the numerical iteration update based on the XFEM model, the changes of stress field and displacement field near the crack tip can be accurately captured, and the gradual expansion behavior of the crack can be dynamically reflected. Compared with the traditional finite element method, the XFEM model does not require mesh re-division, which greatly improves the simulation accuracy and calculation efficiency. By inputting the stress intensity factor and its change data, the XFEM model can adjust the crack extension path and morphology in real time, accurately reflect the complex behavior in the actual crack extension process, and improve the dynamic response ability of crack extension prediction. The XFEM model is suitable for crack extension analysis of complex three-dimensional structures. It does not need to simplify the structure and can directly process complex geometric shapes and stress fields, which enhances the applicability and practicality of the model. The numerical simulation results contain detailed information on the crack extension path, stress field changes and stress intensity factors. These data provide reliable input for subsequent fatigue reliability analysis and improve the accuracy and reliability of fatigue life prediction. In summary, through the numerical iteration update process of the XFEM model, this step can accurately simulate the gradual behavior of the crack extension process, providing efficient and accurate tools and methods for fatigue assessment and safety analysis of engineering structures.

[0112] Based on the above second embodiment, in this embodiment, step S4 includes:

[0113] S41: Based on the results of numerical simulation, a reliability optimization model is constructed and the objective function is defined;

[0114] S42: converting the random variables in the crack propagation process into a standard normal distribution space, and determining a limit state equation according to the objective function;

[0115] S43: applying the result of the numerical simulation to the limit state equation, and using the HLRF-BFGS optimization algorithm to solve the limit state equation to obtain a reliability index of fatigue crack growth.

[0116] It should be noted that the numerical simulation results are based on the crack propagation process simulated by the extended finite element method (XFEM), and the crack propagation path, stress field changes, stress intensity factor and its changes are obtained. These results reflect the crack propagation behavior of the structure under actual loading conditions and are an important basis for reliability analysis. The reliability optimization model is a mathematical model used to evaluate the reliability of the structure during the crack propagation process. The model uses the numerical simulation results and the probability distribution of random variables to define the failure probability and reliability index of the structure. The goal is to obtain the solution closest to the failure boundary through optimization calculation. In the reliability optimization model, the objective function is used to describe the failure condition or state of the structure during the crack propagation process. Usually, the objective function is expressed by the limit state equation, which takes random variables (such as crack length, stress intensity factor, etc.) as input to reflect the safety state and failure risk of the structure. The standard normal distribution space of random variables refers to the process of converting the random variables involved in the crack propagation process (such as stress intensity factor, crack length, fatigue load, etc.) into the standard normal distribution form. Through this conversion, the correlation between variables is eliminated and the calculation process in reliability analysis is simplified. The limit state equation is a mathematical expression used to describe the structure under critical conditions, reflecting the boundary of the structure reaching failure conditions. The limit state equation usually takes the form of an objective function, with random variables in the standard normal distribution space as parameters, to represent the reliability boundary of the structure. The HLRF-BFGS optimization algorithm is an optimization algorithm for reliability analysis, which combines the iterative optimization algorithm of the BFGS (Broyden-Fletcher-Goldfarb-Shanno) quasi-Newton method to solve the minimum reliability index point in the limit state equation. It can quickly and efficiently approach the minimum value of the probability of structural failure.

[0117] Specifically, based on the results of numerical simulation, a reliability optimization model is constructed, and the crack propagation path, stress field changes, stress intensity factors and their change data are input. Define the objective function to describe the state or condition of structural failure. The objective function usually takes the form of a limit state equation, and takes the random variables in the crack propagation process (such as stress intensity factor, crack length, fatigue load, etc.) as input. The goal is to solve the failure probability of the structure. All random variables in the crack propagation process (such as stress intensity factor, crack length, etc.) are standardized and transformed, and they are mapped to the standard normal distribution space. Rosenblatt transformation or Nataf transformation is usually used for transformation to eliminate the correlation between variables. The converted standard normal random variables are used as input for the subsequent solution of the limit state equation.

[0118] Furthermore, the limit state equation is determined based on the converted random variables and the defined objective function. This equation represents the safety state boundary of the structure under given conditions, and the solution of the equation represents the failure state of the structure. The results of the numerical simulation (such as crack propagation path, stress intensity factor change, etc.) are substituted into the limit state equation as the boundary conditions and initial parameters for the solution. The HLRF-BFGS optimization algorithm is used to solve the limit state equation. The algorithm iteratively approximates through gradient optimization and quasi-Newton method to find the minimum reliability index point. According to the optimization results of the HLRF-BFGS algorithm, the reliability index of fatigue crack propagation (such as failure probability or reliability index) is calculated. The calculated reliability index is output to provide data support for fatigue life prediction and safety assessment of engineering structures.

[0119] By applying the numerical simulation results to the reliability optimization model, the stress field change and stress intensity factor change data during the actual crack propagation process can accurately describe the real failure state of the structure under fatigue load, and enhance the accuracy and reliability of reliability analysis. The random variables are converted into the standard normal distribution space, and the calculation process in the reliability analysis is simplified by eliminating the correlation between variables. The HLRF-BFGS optimization algorithm is used to solve the limit state equation, which can quickly approximate the minimum reliability index point, and greatly improves the solution efficiency compared with traditional methods such as the Monte Carlo method. By defining the objective function and the limit state equation, the reliability optimization model can identify the failure risk of the structure during the crack propagation process, providing a scientific basis for engineering design, structural improvement and safety assessment. The calculated fatigue crack propagation reliability index provides reliable data support for the fatigue life prediction of the structure, which helps to formulate effective maintenance and maintenance strategies and improve the service life and safety of the structure. In summary, through the reliability optimization model based on the numerical simulation results and the application of the HLRF-BFGS optimization algorithm, this step can efficiently and accurately determine the reliability of the structure during the crack propagation process, providing strong technical support for fatigue assessment and safety decision-making of engineering structures.

[0120] This embodiment uses the random extended finite element method to simulate the crack propagation of a three-dimensional plate-shell structure and establishes a geometric model of the crack propagation path; based on the geometric model, the interaction integral method is used to calculate the stress intensity factor at the crack tip, and the change data of the stress intensity factor during the crack propagation process is determined; based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process, the extended finite element method is used to numerically simulate the crack propagation process; based on the results of the numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack propagation process and determine the reliability of fatigue crack propagation. This embodiment uses the random extended finite element method to establish a geometric model of the crack propagation path of a three-dimensional plate-shell structure, and uses the interaction integral method to dynamically calculate the stress intensity factor at the crack tip and its change data, and combines the extended finite element method to efficiently simulate the crack propagation process without redrawing the grid, which significantly improves the simulation accuracy and efficiency; based on the numerical simulation results, the HLRF-BFGS optimization algorithm is used to perform reliability optimization calculations, which can quickly solve the limit state equation compared to traditional methods, and improve the accuracy and efficiency of fatigue reliability assessment.

[0121] Exemplarily, in order to help understand the technical concept or technical principle of the fatigue time-varying reliability calculation method of the above embodiment, the fatigue time-varying reliability calculation method of the above embodiment is further explained: this method is based on the existing calculation strategy, and four improvements are made. First, the stress intensity factor of the displacement method is replaced by the interaction integral calculation, which improves the calculation accuracy of the stress intensity factor; second, the grid coincidence method of the finite element calculation is replaced by the extended finite element method, which avoids the difficulty of grid division during crack propagation; third, the two-dimensional unit is replaced by the three-dimensional shell unit, thereby realizing the calculation capability of the three-dimensional plate and shell structure; fourth, the original gradient optimization algorithm is replaced by the HLRF-BFGS algorithm, which improves the calculation efficiency of the reliability. Through the above improvements, on the basis of the original two-dimensional calculation method, a fatigue time-varying reliability SXFEM calculation method suitable for three-dimensional plate and shell structures is proposed, which can simultaneously consider the randomness of the crack propagation direction and the expansion speed.

[0122] The present application also provides a fatigue time-varying reliability calculation device, please refer to Figure 4 , Figure 4 This is a schematic diagram of the module structure of a fatigue time-varying reliability calculation device according to an embodiment of the present application. The fatigue time-varying reliability calculation device includes:

[0123] A geometric model building module 401 is used to simulate crack propagation of a three-dimensional plate-shell structure based on a random expansion finite element method and to establish a geometric model of the crack propagation path;

[0124] The intensity factor determination module 402 is used to calculate the stress intensity factor at the crack tip based on the geometric model by using the interaction integral method, and determine the change data of the stress intensity factor during the crack propagation process;

[0125] A numerical simulation module 403 is used to perform numerical simulation on the crack propagation process by using an extended finite element method based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process;

[0126] The target module 404 is used to optimize the crack growth process based on the results of the numerical simulation using the HLRF-BFGS optimization algorithm to determine the reliability of fatigue crack growth.

[0127] The fatigue time-varying reliability calculation device provided in the embodiment of the present application adopts the fatigue time-varying reliability calculation method in the above embodiment, which can solve the technical problem of how to improve the evaluation effect of the fatigue reliability of the structure. Compared with the prior art, the beneficial effects of the fatigue time-varying reliability calculation device provided in the embodiment of the present application are the same as the beneficial effects of the fatigue time-varying reliability calculation method provided in the above embodiment, and the other technical features in the fatigue time-varying reliability calculation device are the same as the features disclosed in the above embodiment method, which will not be repeated here.

[0128] The present application provides a fatigue time-varying reliability calculation device, which includes: at least one processor; and a memory connected to the at least one processor in communication; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the fatigue time-varying reliability calculation method in the above-mentioned embodiment.

[0129] Reference below Figure 5 , which shows a schematic diagram of the structure of a fatigue time-varying reliability calculation device suitable for implementing the embodiment of the present application. The fatigue time-varying reliability calculation device in the embodiment of the present application may include but is not limited to mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Descriptions), PMPs (Portable Media Players), vehicle-mounted terminals (such as vehicle-mounted navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, etc. Figure 5 The fatigue time-varying reliability calculation device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present application.

[0130] like Figure 5As shown, the fatigue time-varying reliability calculation device may include a processing device 1001 (such as a central processing unit, a graphics processor, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM: Read Only Memory) 1002 or a program loaded from a storage device 1003 to a random access memory (RAM: Random Access Memory) 1004. Various programs and data required for the operation of the fatigue time-varying reliability calculation device are also stored in the RAM 1004. The processing device 1001, the ROM 1002, and the RAM 1004 are connected to each other via a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to the I / O interface 1006: input devices 1007 including, for example, a touch screen, a touchpad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, a gyroscope, etc.; output devices 1008 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; storage devices 1003 including, for example, a magnetic tape, a hard disk, etc.; and communication devices 1009. The communication device 1009 can allow the fatigue time-varying reliability calculation device to communicate with other devices wirelessly or by wire to exchange data. Although the figure shows a fatigue time-varying reliability calculation device with various systems, it should be understood that it is not required to implement or have all the systems shown. More or fewer systems may be implemented or have instead.

[0131] In particular, according to the embodiments disclosed in the present application, the process described above with reference to the flowchart can be implemented as a computer software program. For example, the embodiments disclosed in the present application include a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication device, or installed from a storage device 1003, or installed from a ROM 1002. When the computer program is executed by the processing device 1001, the above-mentioned functions defined in the method of the embodiment disclosed in the present application are executed.

[0132] The fatigue time-varying reliability calculation device provided by the present application adopts the fatigue time-varying reliability calculation method in the above embodiment, which can solve the technical problem of how to improve the evaluation effect of the fatigue reliability of the structure. Compared with the prior art, the beneficial effects of the fatigue time-varying reliability calculation device provided by the present application are the same as the beneficial effects of the fatigue time-varying reliability calculation method provided by the above embodiment, and the other technical features in the fatigue time-varying reliability calculation device are the same as the features disclosed in the method of the previous embodiment, which will not be repeated here.

[0133] It should be understood that the various parts disclosed in this application can be implemented by hardware, software, firmware or a combination thereof. In the description of the above embodiments, specific features, structures, materials or characteristics can be combined in any one or more embodiments or examples in a suitable manner.

[0134] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

[0135] The present application provides a computer-readable storage medium having computer-readable program instructions (ie, computer programs) stored thereon, and the computer-readable program instructions are used to execute the fatigue time-varying reliability calculation method in the above-mentioned embodiment.

[0136] The computer-readable storage medium provided in the present application may be, for example, a USB flash drive, but is not limited to electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, systems or devices, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, system or device. The program code contained on the computer-readable storage medium may be transmitted using any appropriate medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination of the above.

[0137] The computer-readable storage medium may be included in the fatigue time-varying reliability calculation device; or may exist independently without being assembled into the fatigue time-varying reliability calculation device.

[0138] The computer-readable storage medium carries one or more programs. When the one or more programs are executed by the fatigue time-varying reliability calculation device, the fatigue time-varying reliability calculation device: based on the random extended finite element method, simulates the crack propagation of the three-dimensional plate-shell structure and establishes a geometric model of the crack propagation path; based on the geometric model, the stress intensity factor at the crack tip is calculated by the interaction integral method, and the change data of the stress intensity factor during the crack propagation process is determined; based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process, the crack propagation process is numerically simulated by the extended finite element method; based on the result of the numerical simulation, the crack propagation process is optimized by the HLRF-BFGS optimization algorithm to determine the reliability of fatigue crack propagation. The computer program code for performing the operation of the present application can be written in one or more programming languages ​​or a combination thereof, and the programming language includes an object-oriented programming language such as Java, Smalltalk, C++, and a conventional procedural programming language such as "C" language or a similar programming language. The program code may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0139] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present application. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0140] The modules involved in the embodiments described in this application may be implemented by software or hardware, wherein the name of the module does not constitute a limitation on the unit itself in some cases.

[0141] The readable storage medium provided in the present application is a computer-readable storage medium, which stores computer-readable program instructions (i.e., computer programs) for executing the above fatigue time-varying reliability calculation method, and can solve the technical problem of how to improve the evaluation effect of the fatigue reliability of the structure. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in the present application are the same as the beneficial effects of the fatigue time-varying reliability calculation method provided in the above embodiment, and will not be repeated here.

[0142] An embodiment of the present application provides a computer program product, including a computer program, which implements the steps of the fatigue time-varying reliability calculation method as described above when the computer program is executed by a processor.

[0143] The computer program product provided in this application can solve the technical problem of how to improve the evaluation effect of the fatigue reliability of the structure. Compared with the prior art, the beneficial effects of the computer program product provided in the embodiment of this application are the same as the beneficial effects of the fatigue time-varying reliability calculation method provided in the above embodiment, which will not be repeated here.

[0144] The above are only preferred embodiments of the present application, and are not intended to limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent processing scope of the present application.

Claims

1. A fatigue time-varying reliability calculation method, characterized in that: The method comprises: Based on the random expansion finite element method, the crack propagation of the three-dimensional plate and shell structure is simulated and the geometric model of the crack propagation path is established; Based on the geometric model, the stress intensity factor at the crack tip is calculated by using the interaction integral method, and the change data of the stress intensity factor during the crack propagation process is determined; Based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process, the extended finite element method is used to perform numerical simulation on the crack propagation process; Based on the results of numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack growth process and determine the reliability of fatigue crack growth.

2. The method according to claim 1, characterized in that Before the step of simulating crack propagation of the three-dimensional plate-shell structure based on the random expansion finite element method and establishing a geometric model of the crack propagation path, the method further includes: Obtaining the initial crack parameters of the structure, including crack formation time, crack location, and initial crack length; Based on the initial crack parameters of the structure, random variables in the crack growth process are defined, including crack growth rate, crack growth direction, and stress intensity factor.

3. The method according to claim 2, characterized in that After the step of defining random variables in the crack propagation process based on the initial crack parameters of the structure, including crack propagation speed, crack propagation direction, and stress intensity factor, the method further includes: Performing statistical distribution analysis on the crack formation time, the crack position, and the initial length of the crack to obtain an input vector; Based on the input vector, fatigue load is taken as a random variable, and the change of the random variable is described by a probability distribution function; Dynamically generating a crack length, a crack angle, and a stress intensity factor that are dependent on the random variables during crack propagation; Based on the crack length, the crack angle and the stress intensity factor, a random change of non-initial variables during each crack propagation process is determined.

4. The method according to claim 1, characterized in that The step of calculating the stress intensity factor at the crack tip by using the interaction integral method based on the geometric model and determining the change data of the stress intensity factor during the crack propagation process includes: Based on the geometric model, the stress and displacement data at the crack tip are extracted using the finite element method; Obtaining a coverage path of the crack tip, and determining a J-integral value based on the coverage path and the stress and displacement data by using the interaction integration method; Determining the stress intensity factor according to the J-integral value and preset material mechanical parameters, wherein different crack extension modes correspond to different stress intensity factors; A numerical difference analysis is performed on the stress intensity factor to determine a change in the stress intensity factor.

5. The method according to claim 1, characterized in that The step of numerically simulating the crack propagation process using an extended finite element method based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process comprises: Based on the geometric model, establishing an XFEM model; Inputting the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process into the XFEM model to determine the propagation path and morphology of the crack; According to the change of stress intensity factor at the crack tip, numerical iteration update is performed to simulate the step-by-step expansion behavior during crack propagation and determine the stress field change under each step of expansion. In the process of crack propagation, the local stress field and displacement field at the crack tip are calculated in real time to dynamically adjust the stress intensity factor and path of crack propagation. The crack propagation path and morphology, the stress field change, the stress intensity factor and the change data of the stress intensity factor are used as numerical simulation results.

6. The method according to claim 2, characterized in that The step of optimizing the crack propagation process based on the result of numerical simulation by using the HLRF-BFGS optimization algorithm to determine the reliability of fatigue crack propagation includes: Based on the results of numerical simulation, a reliability optimization model is constructed and the objective function is defined; Converting the random variables in the crack propagation process into a standard normal distribution space, and determining the limit state equation according to the objective function; The result of the numerical simulation is applied to the limit state equation, and the limit state equation is solved using the HLRF-BFGS optimization algorithm to obtain a reliability index of fatigue crack growth.

7. A fatigue time-varying reliability calculation device, characterized in that: The device comprises: The geometric model building module is used to simulate the crack propagation of three-dimensional plate and shell structures based on the random expansion finite element method and establish a geometric model of the crack propagation path; An intensity factor determination module is used to calculate the stress intensity factor at the crack tip based on the geometric model by using an interaction integral method, and to determine the change data of the stress intensity factor during the crack propagation process; A numerical simulation module, used for numerically simulating the crack propagation process by using an extended finite element method based on the stress intensity factor at the crack tip and the change data of the stress intensity factor during the crack propagation process; The target module is used to optimize the crack growth process based on the results of numerical simulation using the HLRF-BFGS optimization algorithm to determine the reliability of fatigue crack growth.

8. A computer device, characterized in that: The device comprises: a memory, a processor, and a fatigue time-varying reliability calculation program stored in the memory and executable on the processor, wherein the fatigue time-varying reliability calculation program is configured to implement the steps of the fatigue time-varying reliability calculation method according to any one of claims 1 to 6.

9. A storage medium, characterized in that: The storage medium stores a fatigue time-varying reliability calculation program, and when the fatigue time-varying reliability calculation program is executed by the processor, the steps of the fatigue time-varying reliability calculation method according to any one of claims 1 to 6 are implemented.

10. A computer program product, characterized in that The computer program product comprises a computer program, and when the computer program is executed by a processor, the steps of the fatigue time-varying reliability calculation method according to any one of claims 1 to 6 are implemented.

Images