Multi-uncertainty plate shell structure modeling analysis and random fatigue life prediction method

Abstract

The invention provides a multi-uncertainty plate shell structure modeling analysis and random fatigue life prediction method. The multi-uncertainty plate shell structure modeling analysis and random fatigue life prediction method comprises the following steps: performing nonlinear plate shell structure dynamic modeling by using a non-uniform rational B-spline function; improving the radial basis function neural network by using a genetic algorithm to construct an explicit mapping relationship between random input and structural response; and establishing a random fatigue life prediction method based on the explicit mapping relation. The method has the beneficial effects that the modeling, analysis and random fatigue life prediction efficiency of the multi-uncertainty nonlinear plate shell structure is remarkably improved, the influence of each parameter on the fatigue life can be independently evaluated, and the structure optimization design is reversely guided, so that the research and development period is greatly shortened.

Description

Technical Field

[0001] This invention belongs to the field of engine technology, and in particular relates to a method for modeling and analyzing plate and shell structures with multiple uncertainties and predicting random fatigue life. Background Technology

[0002] In the study of nonlinear dynamic problems involving uncertainties, perturbation methods are a relatively mature approach for solving the response of stochastic systems. First-order and second-order perturbation techniques, as important approximate analysis tools, have demonstrated significant advantages in many complex problems. First-order perturbation techniques (FOPT), through linearization expansion, can effectively handle stochastic disturbances in weakly nonlinear systems. However, first-order approximations may introduce significant errors in strongly nonlinear or highly variable stochastic problems due to neglecting higher-order terms, prompting researchers to extend their research to the field of second-order perturbations. Second-order perturbation methods significantly improve the accuracy of solving nonlinear stochastic systems by retaining the quadratic terms in the Taylor expansion. Although perturbation methods have a relatively complete theoretical foundation and extremely wide applications, their drawbacks are also quite obvious: the theoretical formulas for calculating higher-order statistics using perturbation methods are very complex and difficult to solve. Therefore, research has generally limited the stochastic analysis of structures to solving first- or second-order statistics.

[0003] Stochastic analysis methods based on digital simulation techniques such as Monte Carlo (MCS) and Quasi-Monte Carlo (QMCS) are among the mainstream research directions. Nonlinear structural dynamics stochastic response analysis based on MCS and its derivative QMCS is an important method for solving uncertainties in complex systems by combining probabilistic statistics with numerical simulation. The core of MCS lies in simulating the dynamic behavior of a system under random excitation or parameter perturbation using random sampling. Its basic process includes: generating a large number of random variable samples conforming to probability distributions, obtaining the system response through deterministic numerical solutions, and finally statistically analyzing the moments or probability density functions to quantify the uncertainty. MCS has the advantages of strong universality and no need to simplify the system model, but the computational cost increases exponentially with the number of uncertain parameters, and the convergence speed depends on the total number of samples. To address the efficiency bottleneck of MCS, researchers proposed QMCS. QMCS improves the convergence speed by replacing pure random sampling or Latin hypercube sampling with low-biased sequences (such as Sobol sequences), but it still faces difficulties in solving high-dimensional uncertainty problems.

[0004] In recent years, analytical methods that use surrogate models to replace governing equations for solving structural nonlinear stochastic responses have become a research hotspot. Traditional methods such as MCS and perturbation methods face challenges of low computational efficiency and insufficient accuracy when solving high-dimensional nonlinear problems. MCS requires a large number of samples to capture randomness, resulting in extremely high computational costs, while perturbation methods are only suitable for weakly nonlinear systems and are difficult to handle strongly nonlinear or nonstationary responses. These limitations have prompted researchers to turn to surrogate model techniques to balance computational efficiency and accuracy requirements. The stochastic finite element method expands discrete random fields using chaotic polynomials, effectively quantifying the influence of uncertainties such as material parameters and geometric defects on nonlinear dynamic responses. Similarly, geometric methods such as spectral stochastics use Chebyshev basis functions to expand the functional relationship between random inputs and response outputs, achieving efficient solutions for stochastic responses. However, both chaotic polynomials and Chebyshev basis functions in multidimensional space are constructed in the form of tensor products, which still cannot avoid the exponential growth of computational costs, making them infeasible when dealing with problems with multiple uncertainties. Summary of the Invention

[0005] In view of this, the present invention aims to propose a method for modeling and analyzing plate and shell structures with multiple uncertainties and predicting stochastic fatigue life, so as to solve the problem of stochastic vibration response analysis and fatigue life prediction of dynamic systems of plate and shell structures with multiple uncertainties.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows: A method for modeling and analyzing plate and shell structures with multiple uncertainties and predicting stochastic fatigue life includes the following steps: S1. Nonlinear plate and shell structure dynamics modeling is performed using non-uniform rational B-spline functions; S2. Use genetic algorithms to improve radial basis neural networks to construct explicit mapping relationships between random inputs and structural responses; S3. A method for predicting stochastic fatigue life based on explicit mapping relationships.

[0007] Furthermore, in step S1, nonlinear plate and shell structure dynamics modeling is performed using non-uniform rational B-spline functions, including: S11. Using Kirchhoff's plate and shell theory and higher-order shear deformation theory, establish a higher-order hypothetical displacement field; S12. Based on von Kármán's nonlinear theory and the assumption of elastic materials, the integral control equations for plate and shell structures are constructed according to d'Alembert's principle. S13. Within the framework of isogeometric analysis, a C1 continuous discrete displacement field and strain field are established using non-uniform rational B-spline basis functions to construct a matrix-form nonlinear high-order plate and shell dynamic model.

[0008] Furthermore, in step S2, the radial basis function neural network is improved using a genetic algorithm to construct an explicit mapping relationship between random inputs and structural responses, including: S21. Using the Karhunen-Loève expansion, a set of random variables is constructed with several independent random variables to quantify the multiple uncertainties in the geometry, materials, and loads of the plate and shell structure. S22. Based on the number of random variables and the boundary values ​​of the random variable set, establish a hypercubic domain as the sample space in the form of tensor product. S23. Extract a random sample set based on the sample space, establish the corresponding plate and shell model for each sample according to the modeling method in step S1, and solve the dynamic response. S24. Construct a two-layer radial basis neural network using the exact solution method to approximate the relationship between the random sample set and the dynamic response, and construct an explicit mapping relationship between random input and output. S25. Parameter optimization based on genetic algorithm.

[0009] Furthermore, in step S22, the dimension of the sample space is equivalent to the number of random variables, and the boundary of each dimension is equivalent to the boundary of the random variable value corresponding to that dimension.

[0010] Furthermore, in step S25, the parameters are optimized based on the genetic algorithm, including: S251, Generate a dimension of The matrix includes Individuals, including Each element corresponds to the expansion rate parameter of each radial basis function. Based on this initial population, iterative evolution begins. When the number of generations reaches a preset value and no individuals meeting the conditions have evolved, new samples are added to regenerate the initial population and the operation is restarted until individuals meeting the error accuracy are produced. S252. The mean squared error value is used as the fitness function to quantify the performance of each individual. Based on the fitness function value, the next generation of population is generated through selection, crossover and mutation operations on the basis of the current population. S253. When an individual that meets the requirements appears during the evolution process, the genetic algorithm is terminated. This individual is the optimal value of the radial basis function neural network diffusion speed parameter.

[0011] Furthermore, in step S251, the radial basis functions are Gaussian-type radial basis functions.

[0012] Furthermore, in step S3, a method for predicting stochastic fatigue life is established based on explicit mapping relationships, including: S31. Generate a random parameter sample set based on the probability density function of the random variable set in step S2; S32. Based on step S2, construct the mapping relationship and generate the von Mises stress response time history curves corresponding to the random parameter sample set. S33. Using the rainflow counting method, count the stress response time history curves of each von Mises stress response cycle to obtain the stress amplitude, average stress, and number of stress cycles. S34. By comparing the SN curve, the maximum stress cycle number of fatigue life is obtained. The fatigue damage per unit time of each von Mises stress response time history curve is obtained using the linear damage accumulation theory, and the expected fatigue life of the stochastic dynamic system is obtained accordingly.

[0013] Compared with existing technologies, the method for modeling and analyzing plate and shell structures with multiple uncertainties and predicting stochastic fatigue life described in this invention has the following advantages: This invention employs non-uniform rational B-spline functions to achieve accurate modeling of high-order plate and shell structures with nonlinear dynamics, and conducts nonlinear dynamic response analysis of these structures based on isogeometric methods. An uncertainty quantification method is introduced, utilizing genetic algorithms and radial basis function neural networks to efficiently establish an explicit mapping between random inputs and structural responses, accurately approximating the nonlinear implicit relationships in the plate and shell control equations. This mapping, combined with time-domain fatigue life analysis techniques, enables the prediction of stochastic fatigue life of structures under multiple uncertainties, and further quantifies the sensitivity of fatigue life to various uncertainties. This invention significantly improves the efficiency of modeling, analysis, and stochastic fatigue life prediction for nonlinear plate and shell structures with multiple uncertainties, enabling independent evaluation of the impact of each parameter on fatigue life, and providing reverse guidance for structural optimization design, thereby greatly shortening the research and development cycle. Attached Figure Description

[0014] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of the RBF parameters described in an embodiment of the present invention; Figure 2 This is a schematic diagram of the parameter optimization process based on genetic algorithm as described in an embodiment of the present invention; Figure 3 This is a schematic diagram of the stochastic fatigue life analysis process based on SIGA-RBFNN-GA as described in an embodiment of the present invention; Figure 4 This is a schematic diagram comparing the number of converged samples of the response surface in an embodiment of the present invention; Figure 5 This is a schematic diagram of the SN curve of the 6061-T6 aluminum alloy described in an embodiment of the present invention; Figure 6This is a schematic diagram illustrating the convergence of fatigue life analysis with increasing sample size according to an embodiment of the present invention. Detailed Implementation

[0015] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0016] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0017] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0018] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] Step 1: Perform nonlinear plate and shell structure dynamics modeling using non-uniform rational B-spline functions. Using Kirchhoff's plate and shell theory and higher-order shear deformation theory, the higher-order assumed displacement field is established, and its expression is as follows: (1); in, 、 and Indicates the interior of the shell 、 and Directional displacement, 、 and Indicates the displacement of the mid-surface of the plate / shell. and Indicates higher-order displacement and rotation angle. Indicates the thickness of the plate / shell. .

[0020] Based on von Kármán's nonlinear theory and the assumption of elastic materials, integral governing equations for plate and shell structures are constructed according to d'Alembert's principle. Within an isogeometric analysis framework, C is established using non-uniform rational B-spline basis functions. 1 A nonlinear high-order plate and shell dynamic model in matrix form is constructed from continuous discrete displacement and strain fields.

[0021] Step 2: Construct an explicit mapping relationship between random inputs and structural responses using a genetic algorithm to improve the radial basis function neural network. Constructing a set of random variables from several independent random variables using the Karhunen-Loève expansion This involves quantifying the multiple uncertainties in the geometry, materials, and loads of plate and shell structures. Based on... The number of random variables and their value boundaries are determined by establishing a hypercube domain as the sample space in the form of a tensor product. The dimension of the hypercube domain is equal to the number of random variables, and the boundary of each dimension is equal to the value boundary of the corresponding random variable. Random sample sets are extracted based on the sample space. The shell model corresponding to each sample is established according to the modeling method in step (1), and the dynamic response is solved.

[0022] A two-layer radial basis function neural network is constructed using the exact solution method to approximate the relationship between the random sample set and the dynamic response. An explicit mapping relationship between random input and output is constructed, as shown in the following expression: (2); in, For the first Radial basis functions For the first A column vector of undetermined weight coefficients. The number of samples used to approximate the function. This refers to the extended speed parameter.

[0023] Using Gaussian-type radial basis functions, and considering the differences in the sensitivity of the structural response to various random parameters, independent definitions are used. By controlling the scope of each radial basis function, the sample requirements for the function approximation process can be significantly reduced in problems with multiple uncertainties, such as... Figure 1 As shown.

[0024] The expressions for the radial basis functions are as follows: (3); Among them, parameters Distance from the center position The radial basis function value at that location.

[0025] Using genetic algorithms to obtain the optimal Combinations, such as Figure 2 As shown, the details are as follows: 1. Generate a dimension of A matrix containing Individuals, each containing Each element corresponds to one of the radial basis functions. Based on this initial population, iterative evolution begins. When the number of generations reaches a preset value and no individuals meeting the conditions have evolved, new samples are added to regenerate the initial population and the operation is restarted until individuals meeting the error precision are produced.

[0026] 2. The mean squared error (MSE) value is used as the fitness function to quantify the performance of each individual. Based on the fitness function value, the next generation of the population is generated through selection, crossover, and mutation operations on the basis of the current population.

[0027] 3. The genetic algorithm terminates when a suitable individual appears during the evolutionary process; this individual represents the radial basis function neural network diffusion rate parameter. The optimal value.

[0028] Step 3: Establish a stochastic fatigue life prediction method based on explicit mapping relationships. Based on the method in step 2, an explicit mapping relationship is constructed, and random fatigue life analysis is carried out. First, a random parameter sample set is generated according to the probability density function of the random variable set after uncertainty quantification in step 2. Then, the mapping relationship is constructed based on the method in step 2, and the von Mises stress response time history curves corresponding to the random parameter sample set are quickly generated. Next, each von Mises stress response time history curve is cyclically counted using the rainflow counting method to obtain the stress amplitude, mean stress, and number of stress cycles. Finally, the maximum number of stress cycles for fatigue life is obtained by comparing with the SN curve, and the fatigue damage per unit time for each von Mises stress response time history curve is obtained using the linear damage accumulation theory. And based on this, the expected fatigue life of the stochastic dynamic system can be obtained. For example... Figure 3 As shown.

[0029] Example 1: The geometric model and boundary conditions consist of a square plate with four fixed sides, each 0.25m in length and width and 0.0025m in thickness. Stochastic dynamic response analysis and fatigue life prediction are performed under cannon firing load conditions. The material used is 6061-T6 aluminum alloy, widely used in the aerospace field, with a Young's modulus of [missing value]. Pa, Poisson's ratio is The density is kg / m3.

[0030] In the dynamic analysis of a plate under the impact load of an aircraft gun, two types of uncertainties exist simultaneously: structural randomness and load randomness. The structural randomness stems from the randomness of material properties; considering only the Young's modulus and density of the metal, both are random. The load randomness arises from the randomness of the intensity of the aircraft gun impact load. Random variables are used... , and The randomness in the Young's modulus, density, and impact load strength of metals and aircraft cannons is characterized respectively, and random variables are assumed. , and Centered on the deterministic analysis reference value, the three random variables are uniformly distributed within a range of ±5%, and are independent of each other.

[0031] Based on random variables and their combinations, four operating conditions were designed to verify the advantages of this invention in the analysis of single-random-variable random vibration problems and multi-random-variable random vibration problems. The four operating conditions are three operating conditions that include only a single random variable, and one operating condition that includes all random variables. The operating condition numbers and their corresponding input spaces are shown in Table 1.

[0032] Table 1 For four working conditions, dynamic response surfaces of displacement response are constructed using the traditional radial basis function neural network-based response surface construction method (SIGA-RBFNN) and the improved method of this invention (SIGA-RBFNN-GA). The efficiency of SIGA-RBFNN-GA is verified by comparing the number of samples required for the convergence of the dynamic response surfaces.

[0033] To eliminate the interference of sample sequence type on convergence speed, SIGA-RBFNN and SIGA-RBFNN-GA are constructed using the exact same random sample set. Furthermore, the maximum Frobenius norm of the input space is used as the maximum scale of that input space. In SIGA-RBFNN, the expansion velocity parameter is adjusted... The RBF coverage is set to 0.5 to 4 times the maximum scale of the input space, and a dynamic response surface is constructed every 0.1 times the maximum scale of the input space. In SIGA-RBFNN-GA, the expansion rate parameter of each RBF is limited to 0.5 to 4 times the maximum scale of the input space. Additionally, the number of individuals per generation is set to 100, the maximum number of generations is 100, the crossover probability is 50%, the mutation probability is 50%, and 5 high-fitness individuals are retained in each generation. The convergence of the response surface is determined at that time. The comparison results of the number of samples required for response surface convergence under the four operating conditions are as follows: Figure 4 As shown in the figure, the results of SIGA-RBFNN-GA and some results of SIGA-RBFNN are presented. The numbers in the figure represent the ratio of the RBF coverage area to the maximum scale of the input space in SIGA-RBFNN.

[0034] As shown in the figure, under the three operating conditions with a single random variable, the number of samples required for the convergence of the SIGA-RBFNN-GA response surface is basically the same as the number of samples required for the optimal RBF coverage range of SIGA-RBFNN. However, under the operating condition containing three random variables simultaneously, the number of samples required for SIGA-RBFNN-GA is significantly lower than the total number of samples within the RBF coverage range of SIGA-RBFNN. Furthermore, during the construction of the dynamic response surface using SIGA-RBFNN, some samples within the 0.5 to 4 times coverage range failed to converge within a limited number of samples (100 sets). Moreover, when the coverage range is less than 0.5 times or exceeds 4 times the maximum scale of the input space, it is difficult for the dynamic response surface constructed using SIGA-RBFNN to converge.

[0035] Overall, SIGA-RBFNN and SIGA-RBFNN-GA perform similarly when constructing response surfaces in a one-dimensional input space. However, SIGA-RBFNN-GA is more efficient in multi-dimensional input spaces. This is mainly because all RBFs in SIGA-RBFNN have the same coverage, while each RBF in SIGA-RBFNN-GA has its own specific coverage. Specifically, when the response surface is in a one-dimensional input space, the objective function has only one independent variable. Considering the smoothness of the response surface, the coverage of the RBFs does not change drastically within one dimension, so the two methods require similar sample sizes for convergence. However, for response surfaces in a three-dimensional input space, the selection of the RBF coverage must consider not only the situation within each dimension but also the differences between the three dimensions. Typically, the objective function's sensitivity to the three dimensions is not consistent. In this case, using a uniform coverage for all RBFs makes it difficult to account for the differences in sensitivity of the response surface across different dimensions. Therefore, the number of convergence samples for the dynamic response surface of SIGA-RBFNN-GA is significantly less than that of SIGA-RBFNN.

[0036] Table 2 As shown in Table 2, when multiple random factors exist in the system, SIGA-RBFNN-GA requires fewer samples to construct the mapping relationship between random inputs and responses compared to SIGA-RBFNN with optimal parameters. Furthermore, the majority of the time spent constructing the response surface comes from sample computation; therefore, SIGA-RBFNN-GA is significantly more efficient than SIGA-RBFNN in constructing response surfaces with multiple random variables.

[0037] This invention integrates radial basis function neural networks and genetic algorithms to determine the optimal coverage range of basis functions for a specific stochastic system during the training process, resulting in a significant improvement in efficiency in problems with multiple uncertainties.

[0038] Example 2: Considering that the plate model is under multiaxial stress at all points, the von Mises stress at the upper surface of the plate's center point is taken as the critical stress to assess the plate's fatigue damage. The rainflow counting method and fatigue life calculation formula are used for fatigue life assessment.

[0039] The SN curve of 6061-T6 aluminum alloy can be defined by the Basquin expression as follows: ; (4); in, The fatigue cycle stress ratio, In order to achieve a stress ratio The equivalent stress value below, The values ​​represent the maximum stress values, and all stresses are expressed in imperial units (ksi). The SN curves for four loading methods are as follows: Figure 5 As shown.

[0040] After the SIGA-RBFNN-GA response surface is constructed, the stochastic fatigue life analysis based on SIGA-RBFNN-GA is as follows: First, the probability density function satisfied by the parameters with randomness in the stochastic dynamic system is determined, and a random parameter sample set is generated based on the probability density function; then, von Mises stress response time history curves corresponding to the random parameter sample sets are generated one by one based on the SIGA-RBFNN-GA response surface; then, the cyclic counting of each von Mises stress response time history curve is performed according to the rainflow counting method to obtain the stress amplitude, stress mean, and stress cycle number; finally, based on the stress amplitude and stress mean, the maximum stress cycle number of fatigue life is obtained by comparing with the SN curve, and then the fatigue damage per unit time of each von Mises stress response time history curve is solved according to the linear damage accumulation theory. Furthermore, the fatigue damage per unit time of a stochastic dynamic system with parametric randomness under a specific probability density function is obtained.

[0041] Through the above-described stochastic fatigue life analysis process based on SIGA-RBFNN-GA, fatigue damage assessments were performed for four different operating conditions. It was assumed that Young's modulus, density, and gun impact load intensity all follow a uniform distribution in the input space, and that the sample size for the random parameters selected for each of the four operating conditions was 100,000.

[0042] By gradually increasing the number of stress time history samples in the random fatigue life analysis pipeline, the convergence of fatigue life results with the increase of sample size was analyzed. The convergence results are as follows: Figure 6 As shown in the figure, the convergence rate of fatigue damage is basically consistent across the four working conditions. Specifically, the analysis results tend to converge when the sample size reaches 100, but significant oscillations still occur. When the sample size reaches 10,000, the analysis results essentially converge with minimal oscillations, at which point the fatigue damage assessment results can be considered reliable. The von Mises stress-time history data used in the convergence test were all generated based on SIGA-RBFNN-GA. It should be noted that obtaining 100,000 samples by solving the governing equations requires approximately 46,300 days. Therefore, this invention provides feasibility for fatigue damage assessment in systems with multiple uncertainties.

[0043] This invention uses a proxy model to quickly generate a large number of response samples with the same probabilistic characteristics as the original system. This has a significant advantage in terms of computational cost compared to solving equations to obtain samples, thus providing a feasible approach for fatigue life assessment of multi-parameter uncertain systems.

[0044] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for modeling and analyzing plate and shell structures with multiple uncertainties and predicting stochastic fatigue life, characterized by: Includes the following steps: S1. Nonlinear plate and shell structure dynamics modeling is performed using non-uniform rational B-spline functions; S2. Use genetic algorithms to improve radial basis neural networks to construct explicit mapping relationships between random inputs and structural responses; S3. A method for predicting stochastic fatigue life based on explicit mapping relationships; In step S1, nonlinear plate and shell structure dynamics modeling is performed using non-uniform rational B-spline functions, including: S11. Using Kirchhoff's plate and shell theory and higher-order shear deformation theory, establish a higher-order hypothetical displacement field; S12. Based on von Kármán's nonlinear theory and the assumption of elastic materials, the integral control equations for plate and shell structures are constructed according to d'Alembert's principle. S13. Within the framework of isogeometric analysis, establish C using non-uniform rational B-spline basis functions. 1 A nonlinear high-order plate and shell dynamic model in matrix form is constructed from continuous discrete displacement and strain fields.

2. The method for modeling and analyzing plate and shell structures with multiple uncertainties and predicting stochastic fatigue life according to claim 1, characterized in that: In step S2, a genetic algorithm is used to improve the radial basis function neural network to construct an explicit mapping relationship between random inputs and structural responses, including: S21. Using the Karhunen-Loève expansion, a set of random variables is constructed with several independent random variables to quantify the multiple uncertainties in the geometry, materials, and loads of the plate and shell structure. S22. Based on the number of random variables and the boundary values ​​of the random variable set, establish a hypercubic domain as the sample space in the form of tensor product. S23. Extract a random sample set based on the sample space, establish the corresponding plate and shell model for each sample according to the modeling method in step S1, and solve the dynamic response. S24. Construct a two-layer radial basis neural network using the exact solution method to approximate the relationship between the random sample set and the dynamic response, and construct an explicit mapping relationship between random input and output. S25. Parameter optimization based on genetic algorithm.

3. The method for modeling and analyzing plate and shell structures with multiple uncertainties and predicting stochastic fatigue life according to claim 2, characterized in that: In step S22, the dimension of the sample space is equivalent to the number of random variables, and the boundary of each dimension is equivalent to the boundary of the random variable value corresponding to that dimension.

4. The method for modeling and analyzing plate and shell structures with multiple uncertainties and predicting stochastic fatigue life according to claim 2, characterized in that: In step S25, the parameters are optimized based on the genetic algorithm, including: S251, Generate a dimension of The matrix includes Individuals, including Each element corresponds to the expansion rate parameter of each radial basis function. Based on this initial population, iterative evolution begins. When the number of generations reaches a preset value and no individuals meeting the conditions have evolved, new samples are added to regenerate the initial population and restart the operation until individuals meeting the error accuracy are produced. S252. The mean squared error value is used as the fitness function to quantify the performance of each individual. Based on the fitness function value, the next generation of population is generated through selection, crossover and mutation operations on the basis of the current population. S253. When an individual that meets the requirements appears during the evolution process, the genetic algorithm is terminated. This individual is the optimal value of the radial basis function neural network diffusion speed parameter.

5. The method for modeling and analyzing plate and shell structures with multiple uncertainties and predicting stochastic fatigue life according to claim 4, characterized in that: In step S251, the radial basis functions are Gaussian type radial basis functions.

6. The method for modeling and analyzing plate and shell structures with multiple uncertainties and predicting stochastic fatigue life according to claim 1, characterized in that: In step S3, a method for predicting stochastic fatigue life is established based on explicit mapping relationships, including: S31. Generate a random parameter sample set based on the probability density function of the random variable set in step S2; S32. Based on step S2, construct the mapping relationship and generate the von Mises stress response time history curves corresponding to the random parameter sample set. S33. Using the rainflow counting method, count the stress response time history curves of each von Mises stress response cycle to obtain the stress amplitude, average stress, and number of stress cycles. S34. By comparing the SN curve, the maximum stress cycle number of fatigue life is obtained. The fatigue damage per unit time of each von Mises stress response time history curve is obtained using the linear damage accumulation theory, and the expected fatigue life of the stochastic dynamic system is obtained accordingly.

Images