Method and system for predicting maximum stress intensity of composite material based on wave function

Abstract

The invention discloses a method and system for predicting the maximum stress intensity of a composite material based on a wave function, and the method comprises the steps: taking the composite material as a microscopic unit continuum, and introducing the wave function to describe the microscopic interaction and stress transfer mechanism of the composite material. Utilizing finite element analysis and numerical simulation methods to construct a wave function model of an internal stress field of the composite material; carrying out stress decomposition on the isotropic material through a Helmholtz formula, carrying out expansion on the isotropic material layer by adopting a new vector form wave function, and introducing a scale factor for optimization calculation; solving the wave function to obtain stress distribution of the composite material; and according to the stress distribution, searching a stress peak region by using a mathematical optimization algorithm, and predicting the maximum stress intensity value of the composite material. The method is characterized in that behaviors of the composite material in a complex stress state can be accurately simulated through the wave function model, so that the maximum stress intensity is accurately predicted, and the research result can meet the requirements of industries and fields such as aerospace, automobile manufacturing and construction.

Description

Technical Field

[0001] The present invention belongs to the field of composite material strength prediction, and in particular relates to a method and system for predicting the maximum stress strength of composite materials based on wave functions. Background Art

[0002] In the field of materials science and engineering, stress analysis of composite materials (such as composite laminates) is an important engineering and technical issue. Composite materials are usually composed of multiple layers of materials laid in different directions, and their mechanical behavior is affected by many factors such as fiber direction, interlayer interface, and loading conditions. The prediction program and system for the maximum stress strength of composite materials mainly consists of three core modules: data input and processing module, model building and simulation module, and result analysis and output module. Each module has a specific function and works together to achieve the prediction of the maximum stress strength of composite materials. Among them, the wave function method can be considered in the simulation analysis to solve the stress distribution of composite materials under loading conditions. Due to the anisotropy and interlayer interaction of composite materials, it is also necessary to make necessary corrections and optimizations to the established wave function model. The wave function method provides a clear mathematical deconstruction, which helps to accurately explain and analyze the stress distribution of composite materials, thereby making the problem-solving process clearer and more systematic. This clear mathematical expression is not only conducive to in-depth understanding and analysis, but also lays a solid foundation for subsequent numerical calculations and predictions.

[0003] In summary, the stress distribution of composite materials under different working conditions is complex, and traditional methods are difficult to accurately predict their maximum stress intensity, which affects the safe use and design optimization of materials. Studying the wave function method to predict the maximum stress intensity of elastic waves under complex material conditions is an urgent problem to be solved, which has broad application prospects and important research value. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method and system for predicting the maximum stress intensity of composite materials based on wave function WBM. By introducing the wave function theory, solving the wave equation and analyzing the characteristics of the wave function, the behavior of composite materials under complex stress states can be accurately simulated, thereby more accurately predicting the stress distribution and changes of materials during the stress process, and providing a scientific basis for the structural design of composite materials in engineering fields such as aerospace, automobiles, and construction.

[0005] Technical solution: A method for predicting the maximum stress intensity of a composite material based on a wave function of the present invention comprises the following steps:

[0006] Step 1: Based on the wave function theory in quantum mechanics, the composite material is regarded as a continuum composed of multiple microscopic units. By introducing appropriate wave functions to describe the interaction and stress transfer mechanism between microscopic units, a wave function model of the internal stress field of the composite material is constructed;

[0007] Step 2: Decompose the stress of isotropic materials by using the Helmholtz formula, and expand the anisotropic material layer using a new vector form wave function;

[0008] Step 3, solving the wave function according to the numerical calculation method to obtain the stress distribution of the composite material under specific load conditions;

[0009] Step 4: Based on the stress distribution, use a mathematical optimization algorithm to search for the stress peak area and predict the maximum stress intensity of the composite material.

[0010] Furthermore, in step 1, a wave function model of the internal stress field of the composite material is constructed using finite element analysis and numerical simulation methods.

[0011] Furthermore, in step 1, the wave function model for constructing the internal stress field of the composite material is specifically as follows: the calculation domain is divided into non-overlapping convex sub-computational domains, and in order to ensure that two adjacent sub-domains Ω (α) and Ω (β) The border The compatibility of displacement and stress is achieved, the convergence of the constructed wave function is achieved, and the boundary continuity condition is imposed:

[0012]

[0013] Among them, u n (x)=u1n1+u2n2,u τ (x)=u1τ1+u2τ2, n=(n1,n2) T and τ=(τ1,τ2) T =(n2,-n1) T They represent the normal vector and tangent vector of the boundary respectively, u1 and u2 are the displacements in the x1 and x2 directions respectively; t n (x) = t1n1 + t2n2, t τ (x) = t1τ1 + t2τ2, t1 = σ 11 n1+σ 12 n2, t2 = σ 21 n1+σ 22 n2,σ ij (i,j=1,2) are stress field components.

[0014] Furthermore, step 2 specifically includes the following steps:

[0015] Step 2.1. Processing of stress decomposition of isotropic materials: Shear wave: Δψ t +k t ψ t =0, we get

[0016]

[0017] Longitudinal waves: Δψ l +k l ψ l =0, we get

[0018]

[0019] Finally, we can get:

[0020] in, is the wave function, is the wave function contribution factor, n a , n b , n c , n d is the number of wave functions, and Represents the convex domain Ω (α) The minimum rectangular box size, Represents an imaginary unit.

[0021] Step 2.2: Process of dealing with stress decomposition of anisotropic materials:

[0022] The wave function in the new vector form is expanded, which is specifically expressed as

[0023]

[0024] here, is the algebraic co-formula of D. At this time, the anisotropic elastic equation to be processed is adjusted to:

[0025] Du=0

[0026] here

[0027] Among them, C m,n (m,n=1,2,6) represents the anisotropic material parameters, ρ is the density, ω=2πf is the angular frequency, f is the frequency, So, we can get:

[0028]

[0029] in, δ2=2C 11 C 26 -2C 12 C 16 , δ4=2C 22 C 16 -2C 12 C 26 , δ6=(C 11 +C 66 )ρω 2 ,δ7=2(C 16 +C 26 )ρω 2 ,δ8=(C 22 +C 66 )ρω 2 and δ9=ρ 2 ω 4 .

[0030] Finally, all the wave field values ​​at each grid point in the calculation area are decomposed to obtain the following basis functions and approximate solutions:

[0031]

[0032] in,

[0033]

[0034]

[0035] and is the unknown wave number component to be determined, and is the unknown coefficient, and is the upper bound for the unknown coefficient subscript.

[0036] Furthermore, in step 2, when the wave function of the anisotropic material layer is expanded using a new vector form, the computational properties of the wave function of the anisotropic material layer are improved by introducing a scaling factor.

[0037] Furthermore, step 3 is as follows: To avoid discretization of the computational domain, some large values ​​hinder the WBM from generating numerical solutions, so the wave function scaling is introduced and the proportional factor is defined.

[0038]

[0039] i=1,2,3,4,m=0,1,2,…

[0040]

[0041]

[0042] in, and are the maximum and minimum values ​​in the x1 direction, and are the maximum and minimum values ​​in the x2 direction, represents the imaginary part of .

[0043] Furthermore, in step 4, according to the stress distribution, the influence of multiple factors of the material on the prediction results is considered and corresponding corrections are made.

[0044] Furthermore, in step 4, the use of a mathematical optimization algorithm to search for the stress peak region specifically includes: using a hybrid simulated annealing algorithm to search for the stress peak region to predict the maximum stress intensity of the composite material.

[0045] The present invention also discloses a prediction system for the maximum stress intensity of composite materials based on wave functions, comprising:

[0046] Data input module: This module is used to input basic information of microstructure parameters, material properties and external loading conditions of composite materials;

[0047] Model building and loading module: automatically build the microstructure model and wave function model of the composite material based on the input data; simulate the external loading conditions in the model and set the parameters of the loading direction and loading rate;

[0048] Numerical calculation module: Use efficient numerical calculation methods to solve the wave function model and calculate the stress distribution of composite materials; monitor the calculation process in real time to ensure the accuracy and stability of the calculation results;

[0049] Result Analysis Module: Performs in-depth analysis of the calculated stress distribution to identify high stress areas and potential failure points in the composite material.

[0050] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0051] (1) The present invention searches for the stress peak area based on the stress distribution obtained by the wave function method with the help of a mathematical optimization algorithm, thereby predicting the maximum stress intensity of the composite material. Considering the uncertainty of factors such as material parameters and loading conditions, an uncertainty quantification method is used to evaluate the uncertainty range of the prediction results. This helps to better understand the reliability of the prediction results and provide a more valuable reference for engineering decision-making.

[0052] (2) The present invention introduces the wave function theory. By solving the wave equation and analyzing the characteristics of the wave function, the behavior of composite materials under complex stress states can be accurately simulated, thereby more accurately predicting the stress distribution and changes of materials during the stress process, providing a scientific basis for the structural design of composite materials in engineering fields such as aerospace, automobiles, and construction. It helps to improve the maximum stress strength of composite materials and meet various engineering needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a schematic diagram of a method and system flow chart for predicting the maximum stress strength of a composite material according to the present invention;

[0054] Figure 2 Problem description for composite materials;

[0055] Figure 3 The displacement at 15kHz calculated by WBM (left) and finite element method (FEM) (right);

[0056] Figure 4 The stress at 15kHz calculated by WBM (left) and FEM (right);

[0057] Figure 5 Convergence curves of displacements calculated by WBM and FEM at 2, 13, and 24 kHz;

[0058] Figure 6 Convergence curves of stress calculated by WBM and FEM at 2, 13 and 24 kHz. DETAILED DESCRIPTION

[0059] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0060] The present invention provides a method and system for predicting the maximum stress intensity of a composite material based on a wave function, such as Figure 1 As shown, the following steps are included:

[0061] Step 101: Based on the wave function theory in quantum mechanics, the composite material is regarded as a continuum composed of multiple microscopic units, and the interaction and stress transfer mechanism between the microscopic units are described by introducing appropriate wave functions, and a wave function model of the internal stress field of the composite material is constructed;

[0062] Specifically, the computational domain is divided into non-overlapping convex sub-computational domains. To ensure that two adjacent sub-domains Ω (α) and Ω (β) The border The compatibility of displacement and stress is achieved to achieve the convergence of the constructed wave function and impose the continuity condition on the boundary:

[0063]

[0064] Among them, u n (x)=u1n1+u2n2,u τ (x)=u1τ1+u2τ2, n=(n1,n2) T and τ=(τ1,τ2) T =(n2,-n1) T They represent the normal vector and tangent vector of the boundary respectively, u1 and u2 are the displacements in the x1 and x2 directions respectively; tn (x) = t1n1 + t2n2, t τ (x) = t1τ1 + t2τ2, t1 = σ 11 n1+σ 12 n2, t2 = σ 21 n1+σ 22 n2,σ ij (i,j=1,2) are stress field components.

[0065] In each subregion, the regional variables are approximately represented by the following four sets of basis functions, which are represented by superscripts a, b, c and d:

[0066]

[0067] in, and is the wave function that satisfies the governing equation, and is the wave function contribution factor, and is the number of wave functions.

[0068] Step 102: Decompose the stress of the isotropic material by using the Helmholtz formula, and expand the anisotropic material layer by using a new vector form wave function;

[0069] Specifically, the Helmholtz formula is used to decompose isotropic materials into two forms: longitudinal elastic waves and transverse shear waves:

[0070] Shear wave: by Δψ t +k t ψ t =0, we get

[0071]

[0072] Longitudinal wave: by Δψ l +k l ψ l =0, we get

[0073]

[0074] Finally, we can get:

[0075] in, is the wave function, and Represents the convex domain Ω (α) The minimum rectangular box size, Represents an imaginary unit.

[0076] However, the elastic dynamics equations of anisotropic materials are difficult to decouple, so the wave function is expanded in a new vector form, which is expressed as

[0077]

[0078] here, is the algebraic co-formula of D. At this time, the anisotropic elastic equation to be processed is adjusted to

[0079] Du=0

[0080] here

[0081] Among them, C m,n (m,n=1,2,6) represents the anisotropic material parameters, ρ is the density, ω=2πf is the angular frequency, f is the frequency,

[0082] So, we can get:

[0083]

[0084] in, δ2=2C 11 C 26 -2C 12 C 16 , δ4=2C 22 C 16 -2C 12 C 26 , δ6=(C 11 +C 66 )ρω 2 ,δ7=2(C 16 +C 26 )ρω 2 ,δ8=(C 22 +C 66 )ρω 2 and δ9=ρ 2 ω 4 .

[0085] Finally, all the wave field values ​​at each grid point in the calculation area are decomposed to obtain the following basis functions and approximate solutions:

[0086]

[0087] in,

[0088]

[0089] and is the unknown wave number component to be determined, and is the unknown coefficient, and is the upper bound for the unknown coefficient subscript.

[0090] Step 103: solving the wave function according to a numerical calculation method to obtain the stress distribution of the composite material under specific load conditions;

[0091] Specifically, for anisotropic materials, the expression characteristics of the wave function include truncation of the infinite basis functions. The truncation is based on the following:

[0092]

[0093] in, and They are and is an integer cutoff value, T (1≤T≤6) is a predefined cutoff factor, and k represents the maximum wave number.

[0094] In order to avoid discretization of the computational domain, some large values ​​hinder the WBM from generating numerical solutions, so the wave function scaling is introduced and the proportional factor is defined.

[0095]

[0096] i=1,2,3,4,m=0,1,2,…

[0097]

[0098] in, and are the maximum and minimum values ​​in the x1 direction, and are the maximum and minimum values ​​in the x2 direction, represents the imaginary part of .

[0099] The stress distribution obtained by the wave function method and the classical finite element method is given by Figure 4 shown.

[0100] Step 104: Based on the stress distribution, a hybrid simulated annealing algorithm is used to search for the stress peak region and predict the maximum stress intensity value of the composite material.

[0101] The hybrid simulated annealing algorithm refers to the combination of the genetic algorithm and the simulated annealing algorithm. It uses the global search capability of the genetic algorithm to quickly locate the potential optimal solution area in the solution space, and uses the local search capability of the simulated annealing algorithm to perform a detailed search in the potential optimal solution area, thereby improving the accuracy of the solution and the convergence speed of the algorithm.

[0102] The specific steps are as follows:

[0103] Step 1: According to the stress distribution area, the maximum number of generations M, the number of individuals P and the initial temperature T are given, and the population is randomly initialized;

[0104] Step 2: Determine whether the current population meets the convergence condition. If so, output the individual as the optimal solution and end the algorithm; otherwise, proceed to the next step.

[0105] Step 3: Perform crossover and mutation operations on the solution set to select new individuals;

[0106] Step 4: Generate a new population;

[0107] Step 5: Determine whether the maximum number of generations M has been reached. If so, output the optimal solution and the calculation ends; otherwise, increase the number of generations by one, modify the annealing temperature, and return to step 2 to continue the calculation.

[0108] During the optimization process, different annealing speeds are selected according to the number of generations. Before the 30th generation, the classic annealing method is used, which is slower:

[0109]

[0110] After 30 generations, use a faster annealing method:

[0111]

[0112] Among them, gen represents the generation number of the current calculation.

[0113] The present invention is further described in detail below with reference to an embodiment of the process of predicting the maximum stress of a composite material.

[0114] by Figure 2 For example, the composite material region Ω (1) and Ω (3) The top and bottom parts of are anisotropic materials. The material properties are given as follows:

[0115] E1=161.3GPa, E2=8.82GPa, G 12 =5.331GPa,ρ=1580kg / m 3 , v 12 =0.33

[0116] Region Ω (2) It is an isotropic material with a material property of E=70×10 9 N / m 2 ,ρ=2790kg / m 3 , v = 0.3. On the top boundary, apply t τ =0N / m 2 and In the rest, the boundary conditions are u n =0m,t τ =0N / m 2 .

[0117] Figure 3 and Figure 4 The displacement u2 and stress σ obtained by WBM and FEM at 15kHz are shown respectively 22 In WBM, the cutoff factor T is set to 3, that is, Ω (1) ,Ω (2) and Ω (3) The regions have 440, 280, and 440 wave functions, respectively. It can be seen from the figure that the displacement and stress are continuous at the interface of adjacent regions.

[0118] Displacement u1 and stress σ calculated by WBM and FEM 11 The convergence curves at 2, 13 and 24kHz are as follows: Figure 5 and 6 shown.

[0119] According to the stress distribution obtained by the wave function method, the stress peak area is searched with the help of mathematical optimization algorithm to predict the maximum stress intensity of the composite material. Considering the uncertainty of factors such as material parameters and loading conditions, the uncertainty quantification method is used to evaluate the uncertainty range of the prediction results. It helps to better understand the reliability of the prediction results and provide more valuable reference for engineering decision-making.

[0120] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention.

Claims

1. A method for predicting the maximum stress intensity of composite materials based on wave function, characterized in that: The following steps are involved: Step 1: Based on the wave function theory in quantum mechanics, the composite material is regarded as a continuum composed of multiple microscopic units. By introducing appropriate wave functions to describe the interaction and stress transfer mechanism between microscopic units, a wave function model of the internal stress field of the composite material is constructed; Step 2: Decompose the stress of isotropic materials by using the Helmholtz formula, and expand the anisotropic material layer using a new vector form wave function; Step 3, solving the wave function according to the numerical calculation method to obtain the stress distribution of the composite material under specific load conditions; Step 4: Based on the stress distribution, use a mathematical optimization algorithm to search for the stress peak area and predict the maximum stress intensity of the composite material.

2. The method for predicting the maximum stress intensity of composite materials based on wave function according to claim 1, characterized in that: In step 1, a wave function model of the internal stress field of the composite material is constructed using finite element analysis and numerical simulation methods.

3. The method for predicting the maximum stress intensity of composite materials based on wave function according to claim 1, characterized in that: In step 1, the wave function model for constructing the internal stress field of the composite material is specifically: The computational domain is divided into non-overlapping convex sub-domains to ensure that two adjacent sub-domains Ω (α) and Ω (β) The border The compatibility of displacement and stress is achieved, the convergence of the constructed wave function is achieved, and the boundary continuity condition is imposed: Among them, u n (x)=u1n1+u2n2,u τ (x)=u1τ1+u2τ2, n=(n1,n2) T and τ=(τ1,τ2) T =(n2,-n1) T They represent the normal vector and tangent vector of the boundary respectively, u1 and u2 are the displacements in the x1 and x2 directions respectively; t n (x) = t1n1 + t2n2, t τ (x) = t1τ1 + t2τ2, t1 = σ 11 n1+σ 12 n2, t2 = σ 21 n1+σ 22 n2,σ ij (i,j=1,2) are stress field components.

4. The method for predicting the maximum stress intensity of composite materials based on wave function according to claim 1, characterized in that: Step 2 specifically includes the following steps: Step 2.1: Processing of stress decomposition of isotropic materials: Shear wave: by Δψ t +k t ψ t =0, we get Longitudinal waves: Δψ l +k l ψ l =0, we get Finally, we can get: in, is the wave function, is the wave function contribution factor, n a , n b , n c , n d is the number of wave functions, and Represents the convex domain Ω (α) The minimum rectangular box size, represents an imaginary unit; Step 2.2: Process of dealing with stress decomposition of anisotropic materials: The wave function in the new vector form is expanded, which is specifically expressed as here, is the algebraic co-formula of D. At this time, the anisotropic elastic equation to be processed is adjusted to: Du=0 Among them, C m,n (m,n=1,2,6) represents the anisotropic material parameters, ρ is the density, ω=2πf is the angular frequency, f is the frequency, So, we can get: Among them, δ2=2C 11 C 26 -2C 12 C 16 , δ4=2C 22 C 16 -2C 12 C 26 , δ6=(C 11 +C 66 I am 2 ,δ7=2(C 16 +C 26 I am 2 ,δ8=(C 22 +C 66 I am 2 and δ9=ρ 2 oh 4 ; Finally, all the wave field values ​​at each grid point in the calculation area are decomposed to obtain the following basis functions and approximate solutions: in, and is the unknown wave number component to be determined, and is the unknown coefficient, and is the upper bound for the subscript of the unknown coefficient.

5. The method for predicting the maximum stress intensity of composite materials based on wave function according to claim 1, characterized in that: In step 2, when the wave function of the anisotropic material layer is expanded using a new vector form, the computational properties of the wave function of the anisotropic material layer are improved by introducing a scaling factor.

6. The method for predicting the maximum stress intensity of composite materials based on wave function according to claim 1, characterized in that: Step 3 is as follows: To avoid discretization of the computational domain, some large values ​​hinder the WBM from generating numerical solutions, so the wave function scale is introduced and the proportional factor is defined. i=1,2,3,4,m=0,1,2,… in, and are the maximum and minimum values ​​in the x1 direction, and are the maximum and minimum values ​​in the x2 direction, represents the imaginary part of .

7. The method for predicting the maximum stress intensity of composite materials based on wave function according to claim 1, characterized in that: In step 4, according to the stress distribution, the influence of multiple factors of the material on the prediction results is considered and corresponding corrections are made.

8. The method for predicting the maximum stress intensity of composite materials based on wave function according to claim 1, characterized in that: In step 4, the use of a mathematical optimization algorithm to search for the stress peak region specifically includes: using a hybrid simulated annealing algorithm to search for the stress peak region to predict the maximum stress intensity of the composite material.

9. A prediction system for maximum stress intensity of composite materials based on wave function, used to implement the method of claim 1, characterized in that: include: Data input module: This module is used to input basic information of microstructure parameters, material properties and external loading conditions of composite materials; Model building and loading module: automatically build the microstructure model and wave function model of the composite material based on the input data; simulate the external loading conditions in the model and set the parameters of the loading direction and loading rate; Numerical calculation module: Use efficient numerical calculation methods to solve the wave function model and calculate the stress distribution of composite materials; Monitor the calculation process in real time to ensure the accuracy and stability of the calculation results; Result Analysis Module: Performs in-depth analysis of the calculated stress distribution to identify high stress areas and potential failure points in the composite material.

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