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

Abstract

The application relates to the technical field of fatigue time-varying reliability analysis, in particular to a fatigue time-varying reliability calculation method, device and equipment, a storage medium and a product. The method is based on a random extended finite element method, simulates crack propagation of a three-dimensional plate shell structure, and establishes a geometric model of a crack propagation path; based on the geometric model, the stress intensity factor of a crack tip is calculated by using an interaction integral method, and variation data of the stress intensity factor in a crack propagation process is determined; based on the stress intensity factor of the crack tip and the variation data of the stress intensity factor in the crack propagation process, the crack propagation process is numerically simulated by using an extended finite element method; based on the result of the numerical simulation, the crack propagation process is optimized by using an HLRF-BFGS optimization algorithm, and the reliability of fatigue crack propagation is determined. The method improves the effect of fatigue reliability evaluation.

Description

TECHNICAL FIELD

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

[0002] In engineering structures, crack propagation is an important factor affecting structural fatigue failure, especially in complex three-dimensional plate shell structures such as aviation and ships, the crack propagation path and speed have high randomness. The traditional fatigue reliability analysis method is mostly based on a two-dimensional model, mainly using a fixed stress intensity factor and a simplified crack propagation path assumption, which is difficult to accurately simulate the real crack propagation behavior in a three-dimensional structure. The finite element method in the prior art is mostly used for crack propagation analysis, but it often needs to frequently redraw the mesh, which is low in calculation efficiency and difficult to handle the discontinuity of the crack path. In addition, the reliability analysis usually relies on random simulation methods such as Monte Carlo method, which has the problems of large amount of calculation and slow convergence speed, and cannot meet the demand for high-precision and high-efficiency fatigue evaluation. Therefore, developing a new method that can accurately simulate the crack propagation process and optimize the calculation of fatigue reliability has become a technical problem to be solved in the engineering field. SUMMARY

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

[0004] To achieve the above-mentioned purpose, the present application provides a fatigue time-varying reliability calculation method, which comprises the following steps:

[0005] Based on the random propagation finite element method, the crack propagation of the three-dimensional plate shell structure is simulated, and a 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 variation data of the stress intensity factor in the crack propagation process is determined;

[0007] Based on the stress intensity factor at the crack tip and the variation data of the stress intensity factor in the crack propagation process, the crack propagation process is numerically simulated by using the extended finite element method;

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

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

[0010] obtaining 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, defining random variables in the crack propagation process, including crack propagation speed, crack propagation direction, and stress intensity factor.

[0012] In an 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 method further comprises:

[0013] statistically analyzing the crack formation time, the crack location, and the initial crack length to obtain an input vector;

[0014] based on the input vector, taking fatigue load as a random variable, and describing the change of the random variable through a probability distribution function;

[0015] dynamically generating crack length, crack angle, and stress intensity factor dependent on the random variable during the crack propagation process;

[0016] based on the crack length, the crack angle, and the stress intensity factor, determining the random variation of non-initial variables in each crack propagation process.

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

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

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

[0020] determining the stress intensity factor according to the J integral value and pre-set material mechanics parameters, wherein different crack propagation modes correspond to different stress intensity factors;

[0021] performing numerical difference analysis on the stress intensity factor to determine the change of the stress intensity factor.

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

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

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

[0025] According to the change of the stress intensity factor of the crack tip, numerical iteration is updated to simulate the step-by-step propagation behavior in the crack propagation process and determine the stress field change under each step of propagation, wherein the local stress field and displacement field of the crack tip are calculated in real time during the crack propagation process, and the stress intensity factor and path of the crack propagation are dynamically adjusted;

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

[0027] In an embodiment, based on the results of the numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack propagation process to determine the reliability of the fatigue crack propagation, comprising:

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

[0029] The random variables in the crack propagation process are converted into a standard normal distribution space, and a limit state equation is determined according to the target function;

[0030] The results of the numerical simulation are applied to the limit state equation, and the HLRF-BFGS optimization algorithm is used to solve the limit state equation to obtain the reliability index of the fatigue crack propagation.

[0031] In addition, in order to achieve the above-mentioned purpose, the application further provides a fatigue time-varying reliability calculation device, which comprises:

[0032] A geometric model construction module is configured to simulate crack propagation of a three-dimensional plate shell structure based on a random propagation finite element method, and to establish a geometric model of a crack propagation path;

[0033] A strength factor determination module is configured to calculate the stress intensity factor of the crack tip based on the geometric model and to determine change data of the stress intensity factor in the crack propagation process by using an interaction integral method;

[0034] A numerical simulation module is configured to perform numerical simulation of 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 by using an extended finite element method;

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

[0036] In addition, to achieve the above objectives, this application also proposes a fatigue time-varying reliability calculation device, the device comprising: a memory, a processor, and a fatigue time-varying reliability calculation program stored in the memory and executable on the processor, the fatigue time-varying reliability calculation program being configured to implement the steps of the fatigue time-varying reliability calculation method as described above.

[0037] In addition, to achieve the above objectives, this application also proposes a storage medium storing a fatigue time-varying reliability calculation program, which, when executed by a processor, implements the steps of the fatigue time-varying reliability calculation method described above.

[0038] In addition, to achieve the above objectives, this application also proposes a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the fatigue time-varying reliability calculation method described above.

[0039] This application uses the stochastic extended finite element method (SEP) to simulate crack propagation in a three-dimensional plate and shell structure, establishing a geometric model of the crack propagation path. Based on the geometric model, the stress intensity factor at the crack tip is calculated using the interaction integral method, and the variation data of the stress intensity factor during crack propagation is determined. Based on the stress intensity factor at the crack tip and the variation data of the stress intensity factor during crack propagation, 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 establishes a geometric model of the crack propagation path in a three-dimensional plate and shell structure using the stochastic extended finite element method and dynamically calculates the stress intensity factor at the crack tip and its variation data using the interaction integral method. Combined with the extended finite element method, it efficiently simulates the crack propagation process without re-meshing, significantly improving 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, improving the accuracy and efficiency of fatigue reliability assessment. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the first embodiment of the fatigue time-varying reliability calculation method of this 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 this application;

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

[0043] Figure 4 A module structure schematic diagram of the fatigue time-varying reliability calculation device in the embodiment of the application;

[0044] Figure 5 A device structure schematic diagram of the hardware running environment involved in the fatigue time-varying reliability calculation method in the embodiment of the application.

[0045] The implementation, functional features and advantages of the application will be further described with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

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

[0047] In order to better understand the technical solutions of the application, the specific embodiments will be described in detail below with reference to the accompanying drawings and specific embodiments.

[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 shell structures such as aviation and ships, the crack propagation path and speed have high randomness. The traditional fatigue reliability analysis method is mostly based on a two-dimensional model, mainly using a fixed stress intensity factor and a simplified crack propagation path assumption, which is difficult to accurately simulate the real crack propagation behavior in a three-dimensional structure. The finite element method in the prior art is mostly used for crack propagation analysis, but it often needs to frequently redraw the mesh, which is low in calculation efficiency and difficult to handle the discontinuity of the crack path. In addition, reliability analysis usually relies on random simulation methods such as Monte Carlo method, which has the problems of large amount of calculation and slow convergence speed, and cannot meet the demand for high-precision and high-efficiency fatigue evaluation. Therefore, developing a new method that can accurately simulate the crack propagation process and optimize the calculation of fatigue reliability has become a technical problem to be solved in the engineering field.

[0049] The main solution of the application is: based on the random propagation finite element method, the crack propagation of the three-dimensional plate shell structure is simulated, and a geometric model of the crack propagation path is established; 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 in 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 in the crack propagation process, the extended finite element method is used to numerically simulate the crack propagation process; based on the results of numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack propagation process, and the reliability of fatigue crack propagation is determined.

[0050] The application establishes a geometric model of the crack propagation path of a three-dimensional plate shell structure by a random extended finite element method, and dynamically calculates the stress intensity factor at the crack tip and its change data by an interaction integral method, combines the high-efficiency simulation of the crack propagation process by the extended finite element method, and does not need to redivide the grid, thereby significantly improving the simulation accuracy and efficiency; based on the numerical simulation result, the HLRF-BFGS optimization algorithm is used for reliability optimization calculation, compared with the traditional method, the limit state equation can be quickly solved, and the accuracy and efficiency of the fatigue reliability evaluation are improved.

[0051] It should be noted that the execution subject of the method of the embodiment can be a computing service device with data processing, network communication and program running functions, or a fatigue time-varying reliability calculation device with the same or similar functions. The embodiments and the following embodiments will be described 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 the application is proposed, please refer to Figure 1 , Figure 1 The flowchart of the first embodiment of the fatigue time-varying reliability calculation method of the application is shown in the figure.

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

[0054] S1: based on the random extended finite element method, simulating the crack propagation of a three-dimensional plate shell structure, and establishing a geometric model of the crack propagation path;

[0055] It should be noted that the random extended finite element method is an improved version of the extended finite element method (XFEM) and is specially used for simulating the evolution process of discontinuous phenomena such as cracks. It combines random analysis, so that the random changes of structural material properties, loads and geometric shapes can be considered when simulating crack propagation, and is suitable for crack propagation process in complex stress field. Plate shell structure refers to a structure form with a thickness much smaller than other dimensions, such as aircraft wings, ship hulls, etc. The three-dimensional plate shell structure is a more complex geometric body, which contains plate (thin planar structure) and shell (curved surface structure) parts, and requires accurate stress and crack behavior simulation. The geometric model of the crack propagation path is a geometric description of the position, shape and evolution process of the crack in the structure obtained by finite element simulation. It contains the starting point, propagation direction and expansion speed of the crack, and is an important basis for subsequent crack behavior analysis and reliability evaluation.

[0056] Specifically, the geometric model of the three-dimensional plate shell structure and the parameters of the initial crack (such as crack location, length, and direction) are obtained. Material properties and boundary conditions are defined, including material parameters such as the elastic modulus and Poisson's ratio of the structure, as well as load types and distribution conditions. Random variables during crack propagation are determined, such as crack propagation speed, direction, and initial position. Statistical distribution analysis is performed on these random variables, and probability density functions (such as normal distribution, uniform distribution, etc.) are used to describe the randomness of the variables, generating random sample inputs for the model.

[0057] Further, the random extended finite element method (SXFEM) is used to numerically simulate crack propagation, generating the crack propagation path in the structure. SXFEM uses enhanced shape functions to describe crack tip propagation, enabling dynamic simulation of crack propagation without re-meshing. During simulation, the geometric information of the crack path is continuously updated according to the stress field changes, gradually establishing a three-dimensional crack propagation path geometric model. Based on the simulated crack propagation trajectory, a complete crack geometric model is formed, containing information such as crack initiation point, path, branching, and crack tip location. This model can dynamically reflect the changes in the geometry during crack propagation, providing basic data for subsequent stress analysis and reliability assessment.

[0058] By considering the randomness 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 simulation accuracy and precision compared to traditional deterministic models. SXFEM does not require re-meshing during crack propagation, and uses enhanced shape functions to achieve dynamic tracking of cracks, significantly simplifying the complexity of mesh processing and improving computational efficiency. Through simulation of three-dimensional plate shell structures, SXFEM can handle crack propagation problems under complex geometric and load conditions, has a wider range of applications, and can effectively analyze crack behavior in actual engineering structures (such as aviation and shipping). The established crack propagation path geometric model provides accurate geometric basis data for subsequent stress intensity factor calculation, numerical simulation, and reliability optimization, contributing to more accurate fatigue assessment and reliability analysis. In summary, this step effectively solves the randomness problem in the simulation of crack propagation in complex three-dimensional structures, improves the simulation accuracy and computational efficiency of crack propagation paths, and lays a solid foundation for fatigue time-varying reliability calculation.

[0059] S2: 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 crack propagation 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 the position, length, direction and other information of the crack, which is used to analyze the influence of crack propagation on the stress field of the structure. The interaction integral method is a numerical method for calculating the stress intensity factor at the crack tip. By integrating the stress and displacement field near the crack tip, the interaction integral method can accurately evaluate the change of the stress intensity factor at the crack tip, especially suitable for complex stress fields and crack geometries. The stress intensity factor is an important parameter to describe the stress field intensity at the crack tip, which is used to quantify the stress concentration at the crack tip. Different crack propagation modes (such as I-type cracking, II-type sliding, III-type tearing) correspond to different types of stress intensity factors.

[0061] Specifically, based on the crack propagation path geometric model established in the previous step, the geometric data of the crack is imported, including the crack tip position, path shape, etc. 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, usually selecting a closed path (such as a ring or rectangular region) near the crack tip as the integral region. Ensure that the integral path is close enough to the crack tip to capture the detailed changes of the stress field, while avoiding the path being too close to the crack tip to cause unstable calculation.

[0062] Further, using the extracted stress and displacement data, the stress intensity factor at the crack tip is calculated by the interaction integral method. The interaction integral method calculates the stress intensity factors of I-type, II-type and III-type crack modes according to the stress and displacement field data at the crack tip, accurately evaluating the concentration degree of the stress field at the crack tip. In different stages of crack propagation, the interaction integral calculation is repeated to obtain the stress intensity factor at each stage. Through numerical differentiation or fitting method, the trend of the stress intensity factor at different stages is analyzed, and the change data of the stress intensity factor in the crack propagation process is determined.

[0063] The interaction integral method can accurately calculate the stress intensity factor at the crack tip using the geometric model and extracted stress and displacement data, overcoming the simplifying assumptions about crack shape and stress distribution in traditional methods, making the evaluation of stress intensity factor more realistic and reliable. By calculating and comparing the stress intensity factor at different stages of crack propagation, the dynamic changes in the stress field at the crack tip can be dynamically reflected, providing accurate data support for risk assessment and fatigue life prediction of crack propagation. The interaction integral method is particularly suitable for analyzing complex stress fields and irregular crack geometries, and can be directly applied to the actual propagation path of the crack 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 propagation simulation and reliability analysis, and accurate stress intensity factor data provide 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 stress state evaluation capability of the crack propagation process through accurate stress intensity factor calculation and change analysis, providing 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 numerically simulate the crack propagation process;

[0065] It should be noted that the stress intensity factor (SIF) is a key parameter for measuring the stress field intensity at the crack tip, reflecting the stress concentration degree of the crack under load. Different crack propagation modes (I, II, III) correspond to different stress intensity factors, directly affecting the crack propagation behavior and path. The change data reflects the dynamic characteristics of the stress intensity factor at the crack tip during crack propagation, which changes with the crack propagation path, shape and external load. It is an important input for numerical simulation, used to reflect the stress field changes of the crack at different expansion stages. The extended finite element method (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 crack path and the complexity of crack tip stress field, and is an effective tool for simulating complex crack propagation behavior.

[0066] Specifically, an XFEM model for crack propagation is established based on existing geometric models 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, eliminating the need for precise crack location capture via mesh generation; the crack is embedded into the model using XFEM shape functions. The stress intensity factor at the crack tip, calculated using the interaction integral method, and its variation data are input into the XFEM model. This data will guide the crack propagation direction, velocity, and morphological changes. Dynamically inputting the changes in the stress intensity factor during crack propagation allows the model to update the crack propagation path and stress field in real time.

[0067] Furthermore, XFEM utilizes the input stress intensity factor and its variation data to simulate the gradual propagation of cracks under load. The dynamic changes in the crack path do not require re-meshing, greatly simplifying the simulation process. The crack shape and propagation direction are controlled by the stress intensity factor; the model recalculates the stress and displacement fields at the crack tip in each propagation step, ensuring the simulation accurately captures the dynamic propagation behavior of the crack. In each propagation step, XFEM adjusts the crack path and stress distribution based on the current stress intensity factor variation, performing numerical iterative calculations. Through gradual propagation and updates, the simulation depicts the stress field changes, path morphology, and possible branching and stalling phenomena throughout the crack propagation process. The numerical simulation results, including the crack propagation path, stress intensity factor variation, local stress field, and displacement field, are output. These results provide fundamental data for subsequent fatigue reliability assessment and optimization calculations, and are used to verify the model's accuracy and reliability.

[0068] The Extended Finite Element Method (XFEM) can directly simulate crack propagation without re-meshing, accurately tracking crack tip changes using shape functions, reducing computational complexity and time, and improving simulation accuracy and efficiency. Utilizing stress intensity factors and their variation data, XFEM can adjust crack propagation paths and stress field distribution in real time, accurately capturing crack propagation trends and stress field changes, enhancing its ability to simulate complex crack propagation behavior. This method does not require excessive geometric simplification of complex 3D 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, numerical simulation of crack propagation processes using XFEM can dynamically and accurately capture stress changes and propagation behavior at crack tips, 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 the reliability of fatigue crack propagation is determined.

[0070] It should be noted that the numerical simulation results are the crack propagation path, stress intensity factor variation, stress field distribution and displacement field data obtained by the extended finite element method (XFEM) for crack propagation calculation. These results reflect the dynamic behavior of the crack at different stages, providing input data for subsequent reliability calculation. HLRF (Hasofer-Lind-Rackwitz-Fiessler) -BFGS (Broyden-Fletcher-Goldfarb-Shanno) optimization algorithm is an optimization algorithm for reliability analysis. 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. This algorithm combines the advantages of optimization and reliability analysis, and can efficiently solve the reliability index. The reliability of fatigue crack propagation refers to the probability that the structure or component remains functionally complete at a specific crack propagation stage under given service conditions. By calculating the reliability, the safety and failure risk of the structure during the fatigue crack propagation process can be evaluated.

[0071] Specifically, using the crack propagation path, stress intensity factor variation and stress field distribution data obtained by numerical simulation, the limit state equation for reliability analysis is constructed, and the failure criterion of the structure is defined. 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 standard normal space to eliminate the correlation between variables and simplify the optimization solution. The commonly used conversion method is Rosenblatt transformation or Nataf transformation. Through the conversion of the standard normal space, the solution of the reliability index has better numerical stability.

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

[0073] Compared with traditional Monte Carlo simulation, the HLRF-BFGS optimization algorithm directly approximates the failure point through gradient optimization, significantly improves the calculation 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 more close to the actual situation and improving the accuracy of failure risk assessment. This method can handle complex fatigue reliability problems with multiple variables and high dimensions, and is suitable for crack propagation assessment in actual engineering structures, solving the poor applicability problem of traditional methods in complex structures. The reliability analysis results provide a scientific basis for structure design optimization, maintenance decision and life prediction, and help to identify potential fatigue failure risks in advance and improve the safety and service life of the structure. In summary, by using the HLRF-BFGS optimization algorithm to optimize the crack propagation process, 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] The present embodiment is based on the random expanding finite element method to simulate the crack propagation of a three-dimensional plate shell structure and establish 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 determine the change data of the stress intensity factor during the crack propagation process. 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 expanding finite element method is used to numerically simulate the crack propagation process. Based on the results of numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack propagation process to determine the reliability of fatigue crack propagation. The present embodiment establishes a geometric model of the crack propagation path of a three-dimensional plate shell structure by using the random expanding finite element method, dynamically calculates the stress intensity factor at the crack tip and its change data by using the interaction integral method, and efficiently simulates the crack propagation process by using the expanding finite element method without the need to redraw the mesh, which significantly improves the simulation accuracy and efficiency. Based on the results of numerical simulation, the HLRF-BFGS optimization algorithm is used for reliability optimization calculation, which can quickly solve the limit state equation compared with traditional methods, and improve the accuracy and efficiency of fatigue reliability assessment.

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

[0076] As Figure 2 shown, in the present embodiment, before step S1, it also includes:

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

[0078] S1b: Define random variables during crack propagation based on the structure initial crack parameters, including crack propagation speed, crack propagation direction, stress intensity factor.

[0079] It should be noted that the structure initial crack parameters refer to the related parameters of the initial state of the crack 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 expands and develops in 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 structure fatigue process and is a key reference time for fatigue analysis. The crack position refers to the specific position of the crack in the structure, usually represented by a coordinate system. The position parameter determines the orientation of the crack relative to the external load and the stress concentration area at the crack tip. The initial length of the crack refers to the initial length of the crack when it is formed, which is the starting state of crack propagation analysis. The initial length affects the stress concentration degree of the crack and the path and speed of subsequent expansion. Random variables refer to the different values of crack propagation parameters (such as speed, direction, stress intensity factor, etc.) at different stages in the crack propagation process due to the randomness of material, geometry, load and environment, etc. These parameters are defined as random variables. Crack propagation speed refers to the speed at which the crack expands in the structure over time or with the increase of load, which is usually random and related to factors such as stress intensity factor, material properties and external environment. The crack propagation direction refers to the direction of the crack tip during crack propagation, which is also affected by material properties, crack morphology and external load, etc., and usually has randomness and uncertainty. Stress intensity factor (SIF, Stress Intensity Factor) is a parameter that quantifies the stress concentration at the crack tip and is the driving force for crack propagation behavior. The stress intensity factor will change with the crack propagation path and load conditions.

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

[0081] Further, based on the initial crack parameters, random variables in the crack propagation process are determined, which 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 speed (such as normal distribution, lognormal distribution, etc.) is defined. Combined with the initial crack position and the direction of external load, the probability distribution of the crack propagation direction is defined. 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 variation and probability distribution in the crack propagation process are defined. The randomness of the stress intensity factor reflects the uncertainty of the crack under actual loading conditions. Through statistical analysis of 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 mean, variance, and other statistical characteristics 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 a real and reliable initial condition for subsequent analysis. By defining random variables in the crack propagation process, the uncertainty of the material and external environment is considered, making the crack propagation analysis more consistent with the actual situation. By defining and establishing the 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 basis for numerical simulation and reliability analysis, ensuring that all relevant uncertainty factors are considered in the simulation process, enhancing the real applicability and reliability of the model. In summary, by obtaining the initial crack parameters and defining the random variables in the crack propagation process, accurate basic data can be provided for numerical simulation and reliability analysis of crack propagation, improving the accuracy and reliability of the analysis, and providing a more scientific basis for fatigue life prediction of engineering structures.

[0083] Based on the above first embodiment, in this embodiment, after step S1b, it further includes:

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

[0085] S1d: 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;

[0086] S1e: in the crack propagation process, the crack length, crack angle, and stress intensity factor dependent on the random variable are dynamically generated;

[0087] S1f: determining the random variation of non-initial variables in each crack propagation process based on the crack length, the crack angle, and the stress intensity factor.

[0088] It should be noted that statistical distribution analysis is a mathematical analysis method for determining 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 propagation simulation, the input vector is a numerical set formed by the initial crack parameters (crack formation time, position, initial length) after statistical distribution analysis, used to describe the initial state and the possibility of crack propagation. Fatigue load refers to the external load repeatedly applied to the structure during service, whose amplitude and frequency change over time, which may cause fatigue failure of the material. In crack propagation analysis, fatigue load is usually considered as a random variable because its variation characteristics affect the crack propagation speed and direction. The probability distribution function is used to describe the probability distribution of the value of a random variable (such as fatigue load, crack propagation speed, etc.), and commonly used probability distribution functions include normal distribution, lognormal distribution, Weibull distribution, etc. Through the probability distribution function, the variation characteristics of the random variable can be quantitatively described. Non-initial variables refer to variables (such as crack length, crack angle, stress intensity factor, etc.) that are dynamically generated over time or load changes in the crack propagation process, in addition to the initial crack parameters (such as crack formation time, position, initial length), which are direct descriptions of the crack propagation state.

[0089] Specifically, collect and organize data on crack formation time, crack position, and crack initial length, and perform statistical analysis to determine the probability distribution type of these data (such as normal distribution, lognormal distribution, Weibull distribution, etc.). Calculate the statistical characteristics (such as mean, variance, skewness, kurtosis, etc.) of these data, and use these parameters to form an input vector to describe the initial state of the crack and its random characteristics. Based on the input vector, define the random characteristics of the fatigue load and introduce it into the crack propagation analysis model as a random variable. Through the probability distribution function (such as normal distribution, Poisson distribution, etc.), describe the variation characteristics of the fatigue load, simulate the load fluctuation under actual use conditions, and ensure that the crack propagation process takes into account the randomness of the load.

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

[0091] By statistically analyzing the initial crack parameters and regarding the fatigue load and other crack propagation parameters as random variables, the uncertainty in the crack propagation process can be accurately described, and the accuracy and authenticity of the crack propagation 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 process, the simulation process can better adapt to the crack propagation behavior under actual use conditions, enhancing the dynamic and adaptability of numerical simulation. The dynamic changes of these variables reflect the real situation of crack propagation under different use conditions, providing more scientific and reliable data support for fatigue life prediction and improving the scientificity of structural reliability analysis and design optimization. By regarding the fatigue load and crack propagation parameters as random variables and performing numerical simulation, the influence of uncertainty factors on crack propagation can be quantified, providing more targeted optimization decision basis for structural reliability evaluation. In summary, this step can effectively improve the description accuracy of crack propagation and the dynamic response capability of numerical simulation by statistically analyzing and dynamically simulating the initial and non-initial variables in the crack propagation process, providing more accurate and reliable basic data for structural fatigue life prediction and reliability analysis.

[0092] Based on the first embodiment described above, in the present embodiment, step S2 comprises:

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

[0094] S22: obtaining the coverage path of the crack tip, based on the coverage path and the stress and displacement data, using the interaction integral method to determine the J integral value;

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

[0096] S24: Numerically differentiating the stress intensity factor to determine the change in the stress intensity factor.

[0097] It is noted that the finite element method is a numerical method for solving the stress, strain, and displacement field distribution of complex structures. By dividing the structure into a finite number of elements and analyzing them discretely, the finite element method can accurately calculate the local stress and displacement data at the crack tip. The path of coverage refers to a closed integration path around the crack tip, which is usually used to calculate the stress field parameters at the crack tip. The path of coverage needs to be carefully selected to ensure that it includes the key area of the crack tip and can effectively capture the changes in the stress field at the crack tip. 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 energy release rate, which is used to quantify the stress intensity at the crack tip. It reflects the energy required for unit crack surface growth during crack propagation, which is related to the fracture toughness of the material. Numerical differentiation analysis is a numerical method for determining the numerical derivative or difference of a variable change. By numerically differentiating 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 analyze the stress and solve the displacement field of the structure. By refining the grid division and calculating the response of the structure under external load, the stress and displacement data of the crack tip and its surrounding area are extracted. The extracted data includes the stress tensor (such as tensile stress, shear stress, etc.) and displacement vector at the crack tip, which are used for further J integral calculation. A closed coverage 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 of the crack tip. A ring or rectangular path is usually selected to ensure accurate evaluation of the stress intensity factor at the crack tip. By sampling the stress and displacement data on the coverage path using the FEM model, input data for J integral calculation is provided. Using the interaction integral method, the stress and displacement data within the coverage path are numerically integrated to calculate the J integral value at the crack tip. The J integral represents the energy release rate required for unit crack surface growth 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 (I, II, III).

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

[0100] By extracting the stress and displacement data at the crack tip based on the geometric model finite element method and using the interaction integral method to calculate the J-integral value, the energy release rate and stress concentration at the crack tip can be accurately quantified. Compared with traditional methods, the driving force of crack propagation can be more accurately evaluated, and the reliability of the simulation is improved. By analyzing the stress intensity factor under different crack propagation modes, the direction and speed of crack propagation can be dynamically evaluated, the complex behavior of the crack propagation process can be accurately described, and the prediction ability of the crack propagation trend is enhanced. Numerical difference analysis is used to dynamically track the change of the stress intensity factor, so that the crack propagation 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 field and crack geometry, and has stronger adaptability. By accurately determining the change data of the stress intensity factor, important input is provided for the reliability analysis of fatigue crack propagation, ensuring the accuracy and reliability of subsequent reliability calculation. In summary, this step can better evaluate the driving force and behavior characteristics of crack propagation by accurately calculating and analyzing the stress intensity factor at the crack tip, and provides scientific data support for fatigue life prediction and structure reliability analysis.

[0101] The embodiment is based on the random extended finite element method, simulates crack propagation of a three-dimensional plate shell structure, establishes a geometric model of a crack propagation path, calculates a stress intensity factor of a crack tip by using an interaction integral method based on the geometric model, and determines variation data of the stress intensity factor in a crack propagation process; based on the stress intensity factor of the crack tip and the variation data of the stress intensity factor in the crack propagation process, the crack propagation process is numerically simulated by using the extended finite element method; based on a result of the numerical simulation, the crack propagation process is optimized by using an HLRF-BFGS optimization algorithm, and reliability of fatigue crack propagation is determined. The embodiment establishes the geometric model of the crack propagation path of the three-dimensional plate shell structure by using the random extended finite element method, dynamically calculates the stress intensity factor of the crack tip and variation data thereof by using the interaction integral method, efficiently simulates the crack propagation process by using the extended finite element method, does not need to redivide a mesh, and significantly improves simulation accuracy and efficiency; based on the result of the numerical simulation, the reliability optimization calculation is performed by using the HLRF-BFGS optimization algorithm, compared with a traditional method, the limit state equation can be quickly solved, and accuracy and efficiency of fatigue reliability evaluation are improved.

[0102] Based on the second embodiment, a third embodiment of the fatigue time-varying reliability calculation method is provided. Figure 3 , Figure 3 FIG. 3 is a sub-process schematic diagram of the third embodiment of the fatigue time-varying reliability calculation method.

[0103] In the embodiment, step S3 includes:

[0104] S31: based on the geometric model, an XFEM model is established;

[0105] S32: the stress intensity factor of the crack tip and the variation data of the stress intensity factor in the crack propagation process are input into the XFEM model, and an extension path and a form of the crack are determined;

[0106] S33: according to the variation of the stress intensity factor of the crack tip, numerical iteration is updated to simulate step-by-step extension behavior in the crack propagation process, and stress field variation under each step of extension is determined, wherein a local stress field and a displacement field of the crack tip are calculated in real time in the crack propagation process, and the stress intensity factor and the path of the crack propagation are dynamically adjusted;

[0107] S34: the extension path and the form of the crack, the stress field variation, the stress intensity factor, and the variation data of the stress intensity factor are taken as a numerical simulation result.

[0108] It should be noted that the extended finite element method (XFEM) model: XFEM is an enhanced finite element method for simulating discontinuities such as cracks. The XFEM model can describe the crack propagation process through special shape functions without re-meshing, accurately capturing the stress field and displacement field changes near the crack tip. Numerical iteration update is a numerical calculation method that iteratively calculates the solution of the problem step by step. In crack propagation simulation, numerical iteration is used to update the stress field, displacement field and propagation path of the crack tip, so that the simulation can dynamically reflect the step-by-step propagation behavior of the crack. 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. Real-time calculation of local stress field and displacement field is a key step in XFEM simulation, ensuring accurate simulation of crack propagation.

[0109] Specifically, according to the geometric model, an XFEM model suitable for crack propagation analysis is established. The XFEM model uses enhanced shape functions to capture discontinuities in crack location and propagation process, avoiding mesh redivision in traditional finite element method during crack propagation process. 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 stress intensity factor at the crack tip and its variation data during crack propagation process calculated previously are input into the XFEM model. These data are used to guide the crack propagation direction, speed and morphology change. The XFEM model uses the input stress intensity factor data to dynamically adjust the crack propagation path and morphology, simulating the complex behavior in the actual crack propagation process.

[0110] Further, according to the change of stress intensity factor at the crack tip, the XFEM model performs numerical iteration update to gradually simulate the step-by-step propagation behavior during crack propagation process. In each iteration step, the XFEM model recalculates the local stress field and displacement field at the crack tip, adjusts the crack propagation path and morphology according to the real-time calculation results, and ensures that the simulation process can dynamically reflect the true behavior of crack propagation. Repeat the above process until the crack reaches the predetermined propagation length or failure criterion, complete the numerical simulation of the entire crack propagation. The crack propagation path and morphology, stress field change, stress intensity factor and stress intensity factor change data are output as the final results of numerical simulation. These simulation results are used for subsequent fatigue reliability analysis and life prediction, providing scientific basis for engineering structure design and safety evaluation.

[0111] The stress field and displacement field near the crack tip can be accurately captured by the numerical iterative update of the XFEM model, and the gradual expansion behavior of the crack can be dynamically reflected. Compared with the traditional finite element method, the XFEM model does not need to be regridded, which greatly improves the simulation accuracy and computational efficiency. By inputting the stress intensity factor and its change data, the XFEM model can adjust the crack propagation path and morphology in real time, accurately reflect the complex behavior in the actual crack propagation process, and improve the dynamic response capability of crack propagation prediction. The XFEM model is suitable for crack propagation analysis of complex three-dimensional structures, and can directly process complex geometry and stress field without simplifying the structure, which enhances the applicability and practicability of the model. The numerical simulation results contain detailed information of the crack propagation path, stress field change and stress intensity factor, which provides reliable input for subsequent fatigue reliability analysis and improves the accuracy and reliability of fatigue life prediction. In summary, through the numerical iterative update process of the XFEM model, this step can accurately simulate the gradual behavior of the crack propagation process, and provides an efficient and accurate tool and method for fatigue evaluation and safety analysis of engineering structures.

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

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

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

[0115] S43: apply the results of numerical simulation to the limit state equation, and solve the limit state equation by using the HLRF-BFGS optimization algorithm to obtain the reliability index of fatigue crack propagation.

[0116] It should be noted that the numerical simulation results are based on the Extended Finite Element Method (XFEM) simulation of the crack propagation process, obtaining data such as crack propagation path, stress field changes, stress intensity factor and its changes. These results reflect the crack propagation behavior of the structure under actual loading conditions and are an important foundation for reliability analysis. The reliability optimization model is a mathematical model used to evaluate the reliability of a structure during crack propagation. This model uses numerical simulation results and the probability distribution of random variables to define the failure probability and reliability index of the structure, aiming to obtain the solution closest to the failure boundary through optimization calculations. In the reliability optimization model, the objective function describes the failure condition or state of the structure during crack propagation. Typically, the objective function is expressed through the limit state equation, which takes random variables (such as crack length, stress intensity factor, etc.) as input and reflects 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 a standard normal distribution form. This transformation eliminates the correlation between variables and simplifies the calculation process in reliability analysis. Limit state equations are mathematical expressions used to describe a structure under critical conditions, reflecting the boundary at which the structure reaches its failure condition. Limit state equations typically take the form of an objective function, using random variables in a standard normal distribution space as parameters to represent the reliability boundary of the structure. The HLRF-BFGS optimization algorithm is an optimization algorithm used for reliability analysis. It combines the iterative optimization algorithm of the BFGS (Broyden-Fletcher-Goldfarb-Shanno) quasi-Newton method to solve for the minimum reliability index point in the limit state equations. It can quickly and efficiently approximate the minimum probability of structural failure.

[0117] Specifically, based on the results of numerical simulations, a reliability optimization model is constructed, taking into account crack propagation path, stress field changes, stress intensity factor, and its variation data. An objective function is defined to describe the state or condition of structural failure. The objective function typically takes the form of limit state equations, using random variables during crack propagation (such as stress intensity factor, crack length, fatigue load, etc.) as inputs, with the goal of solving for the failure probability of the structure. All random variables during crack propagation (such as stress intensity factor, crack length, etc.) are standardized and transformed to map them to a standard normal distribution space. Rosenblatt transformation or Nataf transformation is usually used for this transformation to eliminate correlations between variables. The transformed standard normal random variables are then used as inputs for solving the subsequent limit state equations.

[0118] Further, according to the converted random variables and the defined objective function, the limit state equation is determined. The 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 numerical simulation (such as crack propagation path, stress intensity factor change, etc.) are substituted into the limit state equation as boundary conditions and initial parameters for solving. The HLRF-BFGS optimization algorithm is used to solve the limit state equation. The algorithm iteratively approaches the minimum reliability index point through gradient optimization and quasi-Newton method. According to the optimization results of the HLRF-BFGS algorithm, the reliability index (such as failure probability or reliability index) of fatigue crack propagation is calculated. The calculated reliability index is output, providing 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 changes and stress intensity factor changes during the actual crack propagation process are utilized, which can accurately describe the real failure state of the structure under fatigue load, and enhance the accuracy and reliability of the reliability analysis. By converting random variables to standard normal distribution space, the correlation between variables is eliminated, simplifying the calculation process in reliability analysis. The HLRF-BFGS optimization algorithm is used to solve the limit state equation, which can quickly approach the minimum reliability index point. Compared with traditional Monte Carlo method and other methods, the solving efficiency is greatly improved. By defining the objective function and the limit state equation, the reliability optimization model can identify the failure risk of the structure during crack propagation, providing scientific basis for engineering design, structure improvement and safety assessment. The calculated fatigue crack propagation reliability index provides reliable data support for structure fatigue life prediction, which helps to develop effective maintenance and maintenance strategies, and improves the service life and safety of the structure. In summary, through the application of the reliability optimization model based on numerical simulation results and the HLRF-BFGS optimization algorithm, this step can efficiently and accurately determine the reliability of the structure during crack propagation, providing strong technical support for fatigue assessment and safety decision of engineering structures.

[0120] The embodiment is based on the random extended finite element method, simulates crack propagation of a three-dimensional plate shell structure, establishes a geometric model of a crack propagation path, calculates a stress intensity factor at a crack tip by using an interaction integral method based on the geometric model, and determines change data of the stress intensity factor in a crack propagation process; the crack propagation process is numerically simulated by using the extended finite element method based on the stress intensity factor at the crack tip and the change data of the stress intensity factor in the crack propagation process; and the fatigue crack propagation reliability is determined by using an HLRF-BFGS optimization algorithm based on a result of the numerical simulation. The embodiment establishes the geometric model of the crack propagation path of the three-dimensional plate shell structure by using the random extended finite element method, dynamically calculates the stress intensity factor at the crack tip and the change data of the stress intensity factor by using the interaction integral method, efficiently simulates the crack propagation process by using the extended finite element method, does not need to redivide a mesh, and significantly improves simulation accuracy and efficiency; and the reliability optimization calculation is performed by using the HLRF-BFGS optimization algorithm based on the result of the numerical simulation, the limit state equation can be quickly solved compared with a traditional method, and the accuracy and efficiency of the fatigue reliability evaluation are improved.

[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 described: four improvements are made on the basis of the existing calculation strategy, one is that the stress intensity factor of the displacement method is replaced by the interaction integral calculation, the calculation accuracy of the stress intensity factor is improved; two is that the mesh coincidence method of the finite element calculation is replaced by the extended finite element method, the difficulty of mesh division in the crack propagation process is avoided; three is that the two-dimensional element is replaced by the three-dimensional shell element, and the calculation ability for the three-dimensional plate shell structure is realized; and four is that the original gradient optimization algorithm is replaced by the HLRF-BFGS algorithm, and the calculation efficiency of the reliability is improved. Through the above improvements, the fatigue time-varying reliability SXFEM calculation method suitable for the three-dimensional plate shell structure and capable of simultaneously considering the randomness of the crack propagation direction and the crack propagation speed is proposed on the basis of the original two-dimensional calculation method.

[0122] The application embodiment also provides a fatigue time-varying reliability calculation device, please refer to Figure 4 , Figure 4 The application embodiment further provides a fatigue time-varying reliability calculation device, please refer to

[0123] The geometric model construction module 401 is configured to simulate crack propagation of a three-dimensional plate shell structure based on the random extended finite element method, and establish a geometric model of a 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 using the interaction integral method, and to determine the change data of the stress intensity factor during crack propagation.

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

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

[0127] The fatigue time-varying reliability calculation device provided in this application, employing the fatigue time-varying reliability calculation method described in the above embodiments, can solve the technical problem of how to improve the evaluation effect of structural fatigue reliability. Compared with the prior art, the beneficial effects of the fatigue time-varying reliability calculation device provided in this application are the same as those of the fatigue time-varying reliability calculation method provided in the above embodiments, and other technical features in the fatigue time-varying reliability calculation device are the same as those disclosed in the methods of the above embodiments, and will not be repeated here.

[0128] This application provides a fatigue time-varying reliability calculation device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the fatigue time-varying reliability calculation method in the above embodiments.

[0129] The following is for reference. Figure 5 The diagram illustrates a structural schematic suitable for implementing the fatigue time-varying reliability calculation device in the embodiments of this application. The fatigue time-varying reliability calculation device in the embodiments of this application may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), PMPs (Portable Media Players), in-vehicle terminals (e.g., in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 5 The fatigue time-varying reliability calculation device shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0130] like Figure 5As shown, the fatigue time-varying reliability calculation device can include a processing device 1001 (for example, a central processor, a graphics processor, etc.) that can perform various appropriate actions and processes according to programs stored in a read-only memory (ROM) 1002 or programs loaded from a storage device 1003 into a random access memory (RAM) 1004. In the RAM 1004, various programs and data required for the fatigue time-varying reliability calculation device to operate are also stored. The processing device 1001, the ROM 1002, and the RAM 1004 are connected to each other through a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Generally, the following systems can be connected to the I / O interface 1006: an input device 1007 including, for example, a touch screen, a touch pad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, a gyroscope, etc.; an output device 1008 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; the storage device 1003 including, for example, a magnetic tape, a hard disk, etc.; and a communication device 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 fatigue time-varying reliability calculation device with various systems is shown in the figure, it should be understood that all the systems shown are not required to be implemented or possessed. More or fewer systems can be alternatively implemented or possessed.

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

[0132] The fatigue time-varying reliability calculation device provided by the present application adopts the fatigue time-varying reliability calculation method in the above-mentioned embodiments, 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 fatigue time-varying reliability calculation device provided by the present application has the same beneficial effects as the fatigue time-varying reliability calculation method provided by the above-mentioned embodiments, and other technical features in the fatigue time-varying reliability calculation device are the same as the features disclosed in the previous embodiment method, which will not be repeated here.

[0133] It should be understood that the various parts disclosed in this application can be implemented using 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 suitable manner in one or more embodiments or examples.

[0134] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0135] This application provides a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon, the computer-readable program instructions being used to execute the fatigue time-varying reliability calculation method in the above embodiments.

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

[0137] The aforementioned computer-readable storage medium may be included in the fatigue time-varying reliability calculation device; or it may exist independently and not assembled into the fatigue time-varying reliability calculation device.

[0138] The computer readable storage medium described above carries one or more programs, when the one or more programs are executed by the fatigue time-varying reliability calculation device, cause the fatigue time-varying reliability calculation device to: based on a random extended finite element method, perform crack propagation simulation on a three-dimensional plate shell structure, and establish a geometric model of a crack propagation path; based on the geometric model, calculate a stress intensity factor of a crack tip by using an interaction integral method, and determine variation data of the stress intensity factor in a crack propagation process; based on the stress intensity factor of the crack tip and the variation data of the stress intensity factor in the crack propagation process, perform numerical simulation on the crack propagation process by using an extended finite element method; and based on a result of the numerical simulation, perform optimization on the crack propagation process by using an HLRF-BFGS optimization algorithm, and determine a reliability of fatigue crack propagation. Computer program code for carrying out operations of the present application can be written in one or more programming languages or combinations of languages including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages such as C or similar programming languages. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can 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 the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0139] The computer readable storage medium described above carries one or more programs, when the one or more programs are executed by the fatigue time-varying reliability calculation device, cause the fatigue time-varying reliability calculation device to: based on a random extended finite element method, perform crack propagation simulation on a three-dimensional plate shell structure, and establish a geometric model of a crack propagation path; based on the geometric model, calculate a stress intensity factor of a crack tip by using an interaction integral method, and determine variation data of the stress intensity factor in a crack propagation process; based on the stress intensity factor of the crack tip and the variation data of the stress intensity factor in the crack propagation process, perform numerical simulation on the crack propagation process by using an extended finite element method; and based on a result of the numerical simulation, perform optimization on the crack propagation process by using an HLRF-BFGS optimization algorithm, and determine a reliability of fatigue crack propagation. Computer program code for carrying out operations of the present application can be written in one or more programming languages or combinations of languages including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages such as C or similar programming languages. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can 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 the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0140] The modules described in the embodiments of the present application can be implemented in the form of software or in the form of hardware. In some cases, the names of the modules do not constitute a limitation on the modules themselves.

[0141] The computer readable storage medium provided in the present application is a computer readable storage medium, which stores computer readable program instructions (i.e., a computer program) for executing the fatigue time-varying reliability calculation method described above, 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 computer readable storage medium provided in the present application has the same beneficial effects as the fatigue time-varying reliability calculation method provided in the above embodiments, and will not be described here.

[0142] The computer program product provided in the present 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 computer program product provided in the present application has the same beneficial effects as the fatigue time-varying reliability calculation method provided in the above embodiments, and will not be described here.

[0143] The computer program product provided in the present 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 computer program product provided in the present application has the same beneficial effects as the fatigue time-varying reliability calculation method provided in the above embodiments, and will not be described here.

[0144] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application, and any equivalent structure or equivalent process transformation using the content of the present application specification and drawings, or direct or indirect application in other related technical fields, are also included in the patent processing scope of the present application.

Claims

1. A method of computing fatigue time-varying reliability, characterized by, The method comprises: obtaining structure initial crack parameters, including crack formation time, crack position, and crack initial length; based on the structure initial crack parameters, defining random variables in the crack propagation process, including crack propagation speed, crack propagation direction, and stress intensity factor; statistical distribution analysis is performed on the crack formation time, the crack position, and the crack initial length 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; in the crack propagation process, the crack length, crack angle, and stress intensity factor dependent on the random variables are dynamically generated; based on the crack length, the crack angle, and the stress intensity factor, the random change of non-initial variables in each crack propagation process is determined; based on the random expansion finite element method, the crack propagation of a three-dimensional plate shell structure is simulated to establish a geometric model of the crack propagation path; based on the geometric model, the stress and displacement data of the crack tip are extracted by using the finite element method; the crack tip coverage path is obtained, and based on the coverage path and the stress and displacement data, the J integral value is determined by using the interaction integral method, and the J integral value is applied to different crack propagation modes; according to the J integral value and the elastic modulus and Poisson's ratio of the material, the stress intensity factor is determined, wherein different crack propagation modes correspond to different stress intensity factors; numerical difference analysis is performed on the stress intensity factor to determine the change data of the stress intensity factor; based on the stress intensity factor of the crack tip and the change data of the stress intensity factor in the crack propagation process, the crack propagation process is numerically simulated by using the extended finite element method; based on the results of numerical simulation, the HLRF-BFGS optimization algorithm is used to optimize the crack propagation process to determine the reliability of fatigue crack propagation.

2. The method of claim 1, wherein, The step of numerically simulating the crack propagation process by using the extended finite element method based on the stress intensity factor of the crack tip and the change data of the stress intensity factor in the crack propagation process comprises: based on the geometric model, an XFEM model is established; the stress intensity factor of the crack tip and the change data of the stress intensity factor in the crack propagation process are input into the XFEM model to determine the propagation path and morphology of the crack; according to the change of the stress intensity factor of the crack tip, numerical iteration is updated to simulate the step-by-step expansion behavior in the crack propagation process and determine the stress field change under each step of expansion, wherein the local stress field and displacement field of the crack tip are calculated in real time during the crack propagation process, and the stress intensity factor and path of the crack propagation are dynamically adjusted; the propagation path and morphology of the crack, the stress field change, the stress intensity factor, and the change data of the stress intensity factor are taken as the numerical simulation results.

3. The method of claim 1, wherein, The step of optimizing the crack propagation process by using the HLRF-BFGS optimization algorithm based on the results of numerical simulation to determine the reliability of fatigue crack propagation comprises: based on the results of numerical simulation, a reliability optimization model is constructed, and a target function is defined; The random variable in the crack propagation process is converted into a standard normal distribution space, and a limit state equation is determined according to the target function; The result of the numerical simulation is applied to the limit state equation, and the limit state equation is solved by using the HLRF-BFGS optimization algorithm to obtain a reliability index of fatigue crack propagation.

4. A fatigue time-varying reliability calculation device characterized by comprising: The device comprises: The geometric model construction module is configured to acquire initial crack parameters of a structure, including crack formation time, crack position, and crack initial length; define random variables in a crack propagation process based on the initial crack parameters of the structure, including crack propagation speed, crack propagation direction, and stress intensity factor; perform statistical distribution analysis on the crack formation time, the crack position, and the crack initial length to obtain an input vector; describe changes of fatigue load as a random variable by a probability distribution function based on the input vector; dynamically generate crack length, crack angle, and stress intensity factor dependent on the random variables in the crack propagation process; determine random changes of non-initial variables in each crack propagation process based on the crack length, the crack angle, and the stress intensity factor; and perform crack propagation simulation on a three-dimensional plate shell structure based on a random propagation finite element method to establish a geometric model of a crack propagation path; The strength factor determination module is configured to extract stress and displacement data of a crack tip by using a finite element method based on the geometric model; acquire a coverage path of the crack tip; determine a J integral value by using an interaction integral method based on the coverage path and the stress and displacement data, and apply the J integral value to different crack propagation modes; and determine a stress intensity factor according to the J integral value and an elastic modulus and a Poisson's ratio of a material, wherein different crack propagation modes correspond to different stress intensity factors; and perform numerical difference analysis on the stress intensity factor to determine change data of the stress intensity factor. The numerical simulation module is configured to perform numerical simulation on the crack propagation process by using an extended finite element method based on the stress intensity factor of the crack tip and the change data of the stress intensity factor in the crack propagation process. The target module is configured to optimize the crack propagation process by using an HLRF-BFGS optimization algorithm based on a result of the numerical simulation to determine a reliability of fatigue crack propagation.

5. A computer device, comprising: The device comprises a memory, a processor, and a fatigue time-varying reliability calculation program stored on 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 according to any one of claims 1 to 3.

6. A storage medium, characterized by The storage medium stores a fatigue time-varying reliability calculation program, and the fatigue time-varying reliability calculation program implements the steps of the fatigue time-varying reliability calculation method according to any one of claims 1 to 3 when executed by a processor.

7. A computer program product, characterised in that, The computer program product comprises a computer program, and the computer program implements the steps of the fatigue time-varying reliability calculation method according to any one of claims 1 to 3 when executed by a processor.

Images