Multi-scale optimization design method for variable stiffness reliability of fiber reinforced composite material

Abstract

The invention discloses a fiber reinforced composite material variable stiffness reliability multi-scale optimization design method, and belongs to the technical field of composite material structure reliability optimization design. The method comprises the following steps: constructing a composite material multi-scale reliability topological optimization model considering material and load uncertainty; an improved single-cycle single-vector chaos control (SLSV-MCC) method is provided, and probability constraints are efficiently and accurately processed by adopting a current design point gradient and a stable factor; and in combination with a normal distribution fiber optimization (NDFO) model, parameterizing a discrete fiber angle to realize synchronous optimization of a macroscopic topology and a microcosmic fiber path. According to the method, the problems of low calculation efficiency and unstable convergence when the existing method is faced with multi-scale and strong-nonlinearity problems are effectively solved, and a lightweight composite material design scheme with high reliability in an uncertain environment can be obtained.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of composite structure reliability optimization design, and particularly relates to a variable stiffness reliability multiscale optimization design method for fiber-reinforced composite materials. BACKGROUND

[0002] Fiber-reinforced composite materials have become an ideal material for realizing structural lightweighting in the fields of aerospace, new energy vehicles and the like due to their excellent specific strength, specific stiffness and designability. The load-bearing efficiency of the structure can be significantly improved by optimizing the fiber path distribution (i.e. variable stiffness design).

[0003] At present, composite structure optimization design mainly focuses on the deterministic optimization framework, i.e. simultaneously optimizing the macroscopic structure topology and the microscopic fiber laying angle. However, various uncertainties inevitably exist in engineering practice, such as the dispersion of material properties, manufacturing process fluctuations and load environment variations. If these uncertainties are ignored in optimization, the "optimal" design may face a high risk of failure under actual service conditions.

[0004] Although reliability-based design optimization (RBDO) methods are introduced to ensure structural safety, they face significant challenges when applied to composite laminates: 1) design variable dimension disaster: both the macroscopic topology and the microscopic fiber angle are design variables, resulting in a large number of variables. 2) convergence difficulty: when the fiber angle is used as a design variable, the objective function is non-convex and highly nonlinear, leading to unstable and inaccurate convergence in the reliability analysis process.

[0005] Existing efficient RBDO methods such as single-loop single vector (SLSV) are prone to large errors or even divergence when dealing with such highly nonlinear problems due to insufficient approximation accuracy. Therefore, there is an urgent need for an efficient, stable and accurate reliability optimization design method to realize lightweighting and robust design of composite structures in an uncertain environment. SUMMARY

[0006] To solve the problems of design variable dimension disaster and convergence difficulty in the prior art, the present application provides a variable stiffness reliability multiscale optimization design method for fiber-reinforced composite materials, which can efficiently and stably handle material property and load uncertainty, simultaneously optimize the macroscopic topology layout and the microscopic fiber laying path of the composite material under the premise of meeting the given reliability index, and realize the ultimate lightweighting and high reliability of the structure.

[0007] To achieve the above-mentioned application purposes, the technical scheme adopted by the present application is as follows: a variable stiffness reliability multiscale optimization design method for fiber-reinforced composite materials, comprising the following steps:

[0008] S1: define the optimization problem and set parameters, specify the design domain, boundary conditions, material properties and external load conditions of the structure to be optimized, quantify the uncertainty parameters of material performance and load conditions and set the target reliability index;

[0009] S2: perform structure geometric modeling and finite element meshing, distinguish the design domain and non-design domain, and assign initial values of macro-topology design variables and micro-fiber angle design variables to each element in the design domain;

[0010] S3: assemble the overall stiffness matrix of the structure, including solving the overall displacement vector, force vector and overall stiffness matrix of the structure;

[0011] S4: taking the total volume of the structure as the objective function, taking the flexibility of the structure as the constraint function, and based on the improved single-cycle single-vector chaos control method, evaluating the flexibility value at the approximate MPP;

[0012] S5: solving the sensitivity information of the objective function and the constraint function to the macro-topology design variable and the micro-fiber angle design variable;

[0013] S6: input the design variables, objective function value, constraint function value and sensitivity information into the optimization solver to obtain new design variables;

[0014] S7: determine whether the new design variables meet the preset convergence criteria or whether the maximum number of iterations is reached, if not, return to step S3, if yes, terminate the iteration and output the final optimization design.

[0015] Further, in the S4, based on the improved single-cycle single-vector chaos control method, when evaluating the flexibility value at the approximate MPP, the gradient of the performance function to the random parameter vector is calculated, including the following steps:

[0016] A1: all material parameters and load parameters that need to be considered uncertainty are constructed into a random variable vector, and the point in the standard normal space is mapped back to the original random space through transformation;

[0017] The transformation formula is:

[0018]

[0019] Wherein, is the value of the random variable vector in the original space, is the mean vector of the random variable vector, is the standard deviation vector of the random variable vector, is the point in the standard normal space, is the current iteration number;

[0020] A2: At the current random variable vector, call the finite element analysis function to calculate the baseline performance function value. ;

[0021] in, The limit state function is constructed based on compliance. The value of , , The default compliance constraint value. For a vector of random variables The overall structural compliance value calculated by finite element analysis under the defined specific material properties and load conditions;

[0022] A3: Perform the following operations on each component of the random variable vector in sequence:

[0023] Apply a small perturbation to the components of the current random variable to create a perturbation vector. and order ;

[0024] in, Temporary disturbance vector The first in One portion, For the first random variable in the vector... The mean of each component, For the first random variable in the vector... The standard deviation of each component For the first In the next iteration, the midpoint of the standard normal space The One portion, The preset small tolerance is set to 0.001;

[0025] Perform a new finite element analysis on the perturbed vector and calculate the performance function value. ;

[0026] Using the central difference formula, we can calculate approximate values ​​of the partial derivatives of the performance function with respect to the current random variable components:

[0027]

[0028] in, For the current random variable components;

[0029] A4: After traversing all random variable components, the gradient of the random parameter vector is obtained by assembling them.

[0030] Furthermore, the MPP update formula for the improved single-loop single-vector chaotic control method is as follows:

[0031]

[0032]

[0033] wherein, is the MPP in the standard normal space in the i-th optimization iteration, is the mean vector of the random parameters, is the target reliability index, is the target failure probability, , is the target failure probability, is the inverse function of the standard normal distribution, is the standard deviation vector of the random parameters, with superscript is the transpose symbol, is the new direction vector obtained after introducing chaos control in the MPP update, is the MPP in the i-th optimization iteration, is the MPP in the i-th optimization iteration, is the MPP in the i-th optimization iteration, is the stability factor, is the convolution matrix, is the vector function defined.

[0034] Further, the sensitivity information of the objective function to the macro-topology design variable and the micro-fiber angle design variable is:

[0035] The objective function is the normalized volume , the sensitivity of which to the macro-topology design variable is 1, and the sensitivity of which to the micro-fiber angle design variable is 0, and the formula is:

[0036]

[0037]

[0038] wherein, is the current volume of the structure, is the initial total volume of the design domain, is the area of a single element in the finite element model, is the thickness of a single layer in the composite laminate, is the total number of layers of the composite laminate, is the total number of elements in the finite element model, is the i-th layer of the composite laminate, is the i-th layer of the composite laminate, is the i-th element in the finite element model.

[0039] ​​Further, the sensitivity information of the constraint function to the macro-topology design variable is:

[0040] The constraint function is

[0041] where, is the compliance, is the global displacement vector of the structure solved by finite element analysis, is the global stiffness matrix of the structure assembled by the stiffness matrix of all elements, the superscript is the transpose symbol;

[0042] The constraint function is obtained by the adjoint method The sensitivity of the constraint function to the macro-topology design variable is:

[0043]

[0044]

[0045]

[0046] where, is the stiffness matrix of the element in the layer, is the domain where the element is located, is the geometry matrix, is the macroscopic equivalent constitutive matrix of the layer, is the integral of the element domain in the finite element analysis, is the penalty factor of the macro-topology variable, is the element constitutive matrix determined by the micro-fiber angle; Considering the chain rule correction of density filtering and Heaviside threshold projection, the sensitivity of the constraint function to the filtered variable is calculated by the chain rule:

[0047]

[0048]

[0049]

[0050]

[0051] where, is the physical projection variable, ​​​​​0.001 for non-zero minima, a parameter to control the projection sharpness, a projection threshold value;

[0052] filtered variables all original design variables within its filtering radius a weighted average, then the constraint function the final sensitivity of a certain original design variable is:

[0053]

[0054]

[0055] where, is the set of cells containing the original design variable in all filtered neighborhoods, is the cell where the original design variable is located, is the filtered variable located in cell , is the weight function, is the i-th original design variable located within the filtered neighborhood, is the loop index for summing over all variables in the filtered neighborhood, representing the i-th original design variable, is the loop index used in the summation calculation, is the filtered neighborhood of cell , consisting of all cells with a distance less than the filtering radius to cell . Further, the sensitivity information of the constraint function to the micro-fiber angle design variable is: the constraint function

[0056] sensitivity of the constraint function to the micro-fiber angle design variable is:

[0057]

[0058]

[0059]

[0060] According to the NDFO model, let the basis function , then the normalized weight coefficient and its derivative are expressed as:

[0061]

[0062] ​​​

[0063]

[0064]

[0065] where, is the index of the candidate fiber orientation, is the penalty parameter of the NDFO model, is the total number of candidate fiber orientations, is the loop index used in summation calculation, representing the th candidate fiber orientation, is the loop index used in summation calculation, is the unit constitutive matrix corresponding to the micro fiber angle design variable exactly equal to the candidate fiber orientation ;

[0066] To improve the continuity of fiber paths in the optimization result and satisfy the manufacturing constraints, the micro fiber angle design variable is filtered by a nonlinear continuous filtering strategy, which is implemented by a filtering domain centered at the target unit :

[0067] Define the filtering domain , the weight function of the center unit :

[0068]

[0069] where, is the discrete fiber continuous filtering radius, and are the coordinates of the center unit and the neighboring units within the filtering domain, respectively, is the distance between two units, is the power of the weight function;

[0070] The micro design variable of the filtered center unit is calculated by the weighted average of all original variables within its filtering domain:

[0071]

[0072] Based on the chain rule, the sensitivity of the constraint function to the micro fiber angle design variable is:

[0073]

[0074] .

[0075] The beneficial effects of the present application are:

[0076] (1) High efficiency: the SLSV-MCC method adopted is in a single loop format, without the need for nested time-consuming reliability analysis loops, and the calculation efficiency is comparable to that of traditional deterministic optimization.

[0077] (2) High precision and stability: by using the current design point gradient and the MCC stability strategy, the precision of the MPP search is significantly improved, and the convergence instability problem caused by strong nonlinearity is solved.

[0078] (3) Strong engineering practicability: multiple uncertainties are effectively handled, and the obtained optimized design has higher reliability and robustness under actual service environment. At the same time, through the NDFO model and filtering strategy, clear, continuous and easy-to-manufacture fiber paths and topological structures can be obtained.

[0079] (4) Universality: the framework is not only applicable to the compliance constraint, but also can be extended to reliability optimization problems of various performance constraints such as strength and frequency. BRIEF DESCRIPTION OF DRAWINGS

[0080] Figure 1 It is a flow chart of a fiber-reinforced composite variable stiffness reliability multiscale optimization design method.

[0081] Figure 2 It is a comparison diagram of MPP approximation principles of traditional SLSV and SLSV-MCC method of the present application.

[0082] Figure 3 It is a schematic diagram of optimization design domain, boundary conditions and load of a two-dimensional composite laminate.

[0083] Figure 4 It is a comparison diagram of final optimization results of deterministic multiscale optimization (DMDO) and reliability multiscale optimization (RBMDO) of the present application. DETAILED DESCRIPTION

[0084] The present application will be further described below in conjunction with the drawings and specific embodiments.

[0085] As shown in Figure 1 , a fiber-reinforced composite variable stiffness reliability multiscale optimization design method comprises the following steps:

[0086] S1: define the optimization problem and set the parameters, clearly define the design domain, boundary conditions, material properties and external load conditions of the structure to be optimized, quantify the uncertainty parameters of material performance and load conditions and set the target reliability index;

[0087] S2: Perform structural geometric modeling and finite element mesh generation, distinguish between the design domain and the non-design domain, and assign initial values ​​to macroscopic topological design variables and microscopic fiber angle design variables for each element in the design domain;

[0088] S3: Assemble the overall stiffness matrix of the structure, including solving the overall displacement vector, force vector and overall stiffness matrix of the structure;

[0089] S4: Using the total structural volume as the objective function and structural compliance as the constraint function, and based on the improved single-loop single-vector chaotic control method, the compliance value is evaluated at approximately MPP.

[0090] This invention explicitly considers the randomness of material properties (such as elastic modulus) and load conditions (magnitude and direction). With the goal of minimizing structural volume and the requirement that structural compliance meets a specific failure probability as a reliability constraint, an RBMDO mathematical model for composite laminates is established.

[0091] The improved single-loop single-vector chaotic control (SLSV-MCC) method, when evaluating the compliance value at approximately MPP, calculates the gradient of the performance function with respect to the random parameter vector, including the following sub-steps:

[0092] When performing MPP approximation within the SLSV-MCC framework, one of the core steps is to compute the performance function ( For random parameter vectors gradient , and To represent the material properties and load conditions, the first The and the first A random parameter. This gradient is used to determine the steepest descent direction in the standard normal space ( ). (Vector). In the specific implementation of this invention, the central difference method is used for numerical calculation. Although this method introduces certain computational costs, it is adopted because of its excellent adaptability to complex finite element models and its ease of implementation.

[0093] This step is the core of this invention. In each round of optimization iteration, the SLSV-MCC method is embedded to handle probabilistic constraints:

[0094] Current point gradient application: Based on the design variable values ​​of the current iteration step (k), calculate the sensitivity of the performance function (such as compliance) to random parameters. This can more accurately reflect the current state than using information from the previous iteration step (k-1).

[0095] Chaotic Controlled Stable MPP Search: Utilizing an improved chaotic control (MCC) strategy, a stability factor (typically...) is introduced. =0.7), the updating direction of the most probable point (MPP) is smoothed. This operation can effectively suppress the iteration oscillation caused by the high nonlinearity of the performance function, and significantly improve the stability of the convergence process.

[0096] Efficient probabilistic constraint evaluation: Through the above SLSV-MCC process, complex probabilistic constraints (such as ) are efficiently converted into equivalent deterministic constraints (e.g. ) within a single loop without nested time-consuming reliability analysis loops, where is a probabilistic operator, representing the probability of the event inside the brackets, is the limit state function. Its input is a random variable, which represents the safety state of the structure when , and represents the failure state of the structure when . In this invention, , that is, the difference between the structural compliance and the allowable constraint value, is a random variable vector containing all parameters considering uncertainty (such as material properties, load size and direction), is the target failure probability, which is the maximum failure probability limit allowed by the designer in advance, and is the performance index of reliability design, is the most probable point found in the original random space in the th optimization iteration. This point is the point with the maximum probability density on the failure surface ( ), and makes the greatest contribution to the failure probability.

[0097] The specific calculation is carried out in the MPP search iteration loop, and the process is as follows:

[0098] A1: All material parameters and load parameters considering uncertainty are constructed into a random variable vector , which contains material properties ( ), load size ( ) and direction ( ) and the like. In each iteration, the point in the standard normal space is mapped back to the original random space through transformation;

[0099] The transformation formula is:

[0100]

[0101] wherein, is the value of the random variable vector in the original space, is the mean vector of the random variable vector, is the standard deviation vector of the random variable vector, is the point in the standard normal space, is the current iteration number;

[0102] A2: In the current random variable vector At this point, the finite element analysis function is invoked to calculate the baseline performance function value. ;

[0103] in, Limit state function constructed based on compliance The value of , , The default compliance constraint value is used, therefore, What is actually being calculated is ,Right now In reliability analysis, this function is used to determine the structural state when... It is considered invalid at this time; For a vector of random variables The overall structural compliance value calculated by finite element analysis under the defined specific material properties and load conditions;

[0104] A3: Perform the following operations on each component of the random variable vector in sequence:

[0105] Apply a small perturbation to the components of the current random variable to create a perturbation vector. and order ;

[0106] in, Temporary disturbance vector The first in One portion, For the first random variable in the vector... The mean of each component, For the first random variable in the vector... The standard deviation of each component For the first In the next iteration, the midpoint of the standard normal space The One portion, The preset small tolerance is set to 0.001;

[0107] Perform a new finite element analysis on the perturbed vector and calculate the performance function value. ;

[0108] Using the central difference formula, we can calculate approximate values ​​of the partial derivatives of the performance function with respect to the current random variable components:

[0109]

[0110] in, For the current random variable components;

[0111] A4: After traversing all random variable components, the gradient of the random parameter vector is obtained by assembling them.

[0112] The gradient vector obtained in this way Used to calculate unit vectors This vector indicates the update direction of MPP. Furthermore, a collinear average vector (CMV) strategy is introduced. Smoothing is performed; when the direction vector fluctuates drastically after three consecutive iterations, it is averaged to suppress oscillations, thereby significantly improving the stability and convergence of the MPP search process.

[0113] This invention addresses the issue of poor approximation accuracy in highly nonlinear problems using the traditional SLSV method by making the following key improvements: First, it uses the gradient of the current design point. In the MPP approximation, the gradient of the design point at the current optimization iteration step (k) is used instead of the gradient of the previous iteration step (k-1), thus more accurately capturing changes in the performance function. Simultaneously, it introduces improved chaos control (MCC) by incorporating a stability factor. This smooths out the update direction of MPP, effectively suppresses oscillations during the iteration process, and significantly improves convergence stability.

[0114] like Figure 2 As shown, the improvement of the SLSV-MCC method of this invention compared to the traditional SLSV is intuitively demonstrated. Traditional SLSV ( Figure 2 a) Using the gradient of the previous iteration point leads to an MPP approximation bias; while SLSV-MCC ( Figure 2 b) By utilizing the gradient of the current design point and chaotic control, the MPP estimation is made more accurate and the convergence is more stable.

[0115] The MPP update formula for the improved single-loop single-vector chaotic control method is as follows:

[0116]

[0117]

[0118] in, In the first In the next optimization iteration, the approximate MPP in the standard normal space is obtained. Let be the mean vector of random parameters. For the target reliability index, , The probability of target failure. It is the inverse function of the standard normal distribution. Let be the standard deviation vector of random parameters, with superscripts... It is the transpose symbol. a new direction vector obtained after introducing chaos control in the MPP update, the MPP in the first optimization iteration, the MPP in the first optimization iteration, a stability factor, a convolution matrix, which is taken as an identity matrix in the specific implementation of the present application, a vector function defined by the formula for calculating the update direction of the MPP, the optimization design variable in the first optimization iteration.

[0119] S5: solve the sensitivity information of the objective function and the constraint function to the macroscopic topological design variable and the microscopic fiber angle design variable;

[0120] The sensitivity information of the objective function to the macroscopic topological design variable and the microscopic fiber angle design variable is:

[0121] The objective function is the normalized volume , the sensitivity of which to the macroscopic topological design variable is 1, and the sensitivity of which to the microscopic fiber angle design variable is 0, and the formula is:

[0122]

[0123]

[0124] wherein, is the current volume of the structure, is the initial total volume of the design domain, is the area of a single element in the finite element model, is the thickness of a single layer in the composite laminate, is the total number of layers of the composite laminate, is the total number of elements in the finite element model, is the first layer of the composite laminate, is the first element in the finite element model.

[0125] The sensitivity information of the constraint function to the macroscopic topological design variable is:

[0126] The constraint function is the compliance

[0127] wherein, is the compliance, The global displacement vector of the structure is obtained by finite element analysis, The global stiffness matrix of the structure is assembled by the stiffness matrix of all elements, and the superscript is the transpose symbol;

[0128] The constraint function is obtained by the adjoint method The sensitivity of the macro-topology design variable is:

[0129]

[0130]

[0131] In the summation calculation, since the variable only affects the corresponding element , the contribution of the remaining elements is zero.

[0132]

[0133] where, is the stiffness matrix of the th element in the th layer, is the domain where the th element in the th layer is located, is the geometry matrix, is the macroscopic equivalent constitutive matrix of the th in the th layer, is the integral of the element domain in finite element analysis, is the penalty factor of the macro-topology variable, usually , used to drive the intermediate density value to the two ends of 0 / 1, is the element constitutive matrix determined by the micro-fiber angle;

[0134] This sensitivity also needs to consider the chain rule correction of density filtering and Heaviside projection. By the adjoint method, the sensitivity of the function (such as compliance ) to the physical projection variable is directly obtained . This is the starting point of all subsequent corrections.

[0135] The physical projection variable is mapped from the filtered variable by the Heaviside threshold projection function. The corrected Heaviside function is represented as:

[0136]

[0137] Constraint function Filtered variable The sensitivity of the filtered variable is calculated by the chain rule:

[0138]

[0139] where, is the derivative of the projection function, which can be analytically solved:

[0140]

[0141] where, is the physical projection variable, is a small positive number, set to 0.001, to prevent the overall stiffness matrix from being singular, is a parameter to control the sharpness of the projection, which is gradually increased in the optimization, is a projection threshold, usually set to 0.5;

[0142] Filtered variable is obtained by the weighted average of all the original design variables within its filtering radius , taking the linear density filtering as an example:

[0143]

[0144] where, is the filtering neighborhood of element ; is the weight function, is the pre-set filtering radius, is the distance between the element centers.

[0145] Since one original variable may be located in the filtering neighborhood of multiple different elements (denoted as element ), the final sensitivity of the constraint function to a certain original design variable needs to aggregate the sensitivity contributions from all the elements that are affected by :

[0146]

[0147]

[0148] where, is the set of elements that contain the original design variable in their filtering neighborhood, is the element where the original design variable is located, is the element that is located in the element The filtered variables, For the weight function, For the first one located in the filtering neighborhood One original design variable, This is the loop index when summing all variables within the filtered neighborhood, representing the... One original design variable, For the circular index used in the summation calculation, For unit The filtered neighborhood is composed of all elements related to the unit. Distance less than filter radius The unit composition.

[0149] The sensitivity information of the constraint function to the microfiber angle design variable is as follows:

[0150] constraint functions Design variables for microfiber angles The sensitivity is:

[0151]

[0152]

[0153] The core lies in solving the macroscopic equivalent constitutive matrix. For micro variables partial derivatives .

[0154] According to the NDFO model, let the basis functions Then the normalized weight coefficients Its derivative is expressed as:

[0155]

[0156]

[0157]

[0158]

[0159] in, Number the candidate fiber pavement angles. The penalty parameter for the NDFO model decreases continuously during optimization to drive fiber angle sharpening. The total number of candidate corners, The circular index used in the summation calculation represents the first... The basis functions corresponding to each candidate fiber layup angle. For the circular index used in the summation calculation, Design variables for microfiber angles Precisely equal to the candidate fiber lay angle When the corresponding unit constitutive matrix;

[0160] To improve the continuity of the fiber path in the optimization result and meet the manufacturing constraints, the micro-fiber angle design variable A nonlinear continuous filtering strategy is adopted, which realizes the following through a filtering domain centered on the target unit

[0161] Define the filtering domain Inner unit The weight function of the center unit :

[0162]

[0163] Where, is the discrete fiber continuous filtering radius, and are the coordinates of the center unit and the adjacent unit in the filtering domain respectively, is the distance between the two units, is the power of the weight function;

[0164] The micro design variable of the filtered center unit is calculated by the weighted average of all original variables in its filtering domain:

[0165]

[0166] This filtering formula simultaneously considers the micro-fiber angle variable and the macro-topological variable , ensuring that the fiber angle is smoothed only in the solid material region ( ).

[0167] Based on the chain rule, the sensitivity of the constraint function to the micro-fiber angle design variable is:

[0168]

[0169]

[0170] ​​The present application is based on the first order shear deformation theory, adopts the SIMP (Solid Isotropic Material with Penalization) method with Heaviside threshold projection for topology optimization at the macro scale, and suppresses the chessboard phenomenon through density filtering, adopts the Normal Distribution Fiber Optimization (NDFO) interpolation format for parameterization of the fiber laying angle at the micro scale, and through a continuous micro design variable, the material constitutive matrix of each candidate angle is weighted and interpolated by using the normal distribution function, and the design variable is driven to clear to a specific candidate angle through the continuous descending strategy. In addition, the continuous filtering is applied to the micro design variable, the multi-scale variable stiffness optimization design of the fiber reinforced composite material is realized, and the reliable optimization design result with continuous fibers is obtained.

[0171] At this point, the accurate calculation of the complete sensitivity of the micro design variable is completed, and the key direction information is provided for the optimization solver.

[0172] S6: input the design variable, the objective function value, the constraint function value and the sensitivity information into the optimization solver, and obtain a new design variable;

[0173] S7: judge whether the new design variable meets the preset convergence standard or whether the maximum iteration number is reached, if not, return to step S3, if yes, terminate the iteration and output the final optimization design.

[0174] In an embodiment of the present application, the optimization design domain, boundary conditions and load of the two-dimensional composite material laminated plate are as shown in Figure 3 Figure 3 In the method, the material principal coordinate system of the composite orthotropic laminated plate is defined as:

[0175] 1 direction: along the main direction of the fiber;

[0176] 2 direction: perpendicular to the fiber direction;

[0177] 3 direction: along the thickness direction of the plate.

[0178] The corresponding material elastic parameters are:

[0179] E 11 : the elastic modulus of the material along the main direction of the fiber (1 direction);

[0180] E 22 : the elastic modulus of the material perpendicular to the fiber direction (2 direction);

[0181] G​12 : The ability of a material to resist shear deformation in the 1-2 plane (shear modulus).

[0182] The final optimization results of deterministic multi-scale optimization (DMDO) and reliability-based multi-scale optimization (RBMDO) of the present application are shown in Table 1 Figure 4 By comparing the results of DMDO and RBMDO, it is proved that the method of the present application can generate more robust topology and fiber path after considering uncertainty, effectively reducing the risk of failure.

[0183] The present application proposes a variable stiffness reliability topology optimization design method for fiber-reinforced composites by fusing the improved single-loop single-vector chaotic control (SLSV-MCC) method and the normal distribution fiber optimization (NDFO) model. The method significantly improves the accuracy and convergence stability of MPP approximation by introducing the current design point gradient and the chaotic control strategy; at the same time, the NDFO model is used to effectively parameterize the discrete fiber angle, and the macroscopic topology and microscopic fiber path are optimized cooperatively, which essentially solves the two technical problems existing in the prior art. Through numerical examples, it is verified that the method effectively improves the reliability and robustness of the design while ensuring the calculation efficiency, and based on rigorous theoretical derivation, it has high engineering popularization value and application adaptability.

[0184] Those skilled in the art will realize that the embodiments described herein are for the purpose of helping the reader understand the principles of the present application and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations according to the technical inspiration disclosed in the present application without departing from the essence of the present application, and these modifications and combinations are still within the scope of protection of the present application.

Claims

1. A method for multi-scale reliability optimization design of fiber-reinforced composites with variable stiffness, characterized in that, The method comprises the following steps: S1: defining an optimization problem and setting parameters, specifying the design domain, boundary conditions, material properties and external load conditions of the structure to be optimized, quantifying the uncertainty parameters of material performance and load conditions and setting target reliability indicators; S2: performing structure geometric modeling and finite element meshing, distinguishing the design domain and non-design domain, and assigning initial values of macroscopic topological design variables and microscopic fiber angle design variables to each unit in the design domain; S3: assembling the overall stiffness matrix of the structure, including solving the overall displacement vector, force vector and overall stiffness matrix of the structure; S4: taking the total volume of the structure as the objective function, taking the structural compliance as the constraint function, and evaluating the compliance value at the approximate MPP based on the improved single-cycle single-vector chaos control method; S5: solving the sensitivity information of the objective function and the constraint function to the macroscopic topological design variable and the microscopic fiber angle design variable; S6: inputting the design variables, objective function value, constraint function value and sensitivity information into the optimization solver to obtain new design variables; S7: determining whether the new design variables meet the preset convergence criteria or whether the maximum number of iterations is reached, if not, returning to step S3, if yes, terminating the iteration and outputting the final optimization design.

2. The fiber-reinforced composite variable-stiffness reliability multiscale optimization design method according to claim 1, characterized in that, In the S4, when evaluating the compliance value at the approximate MPP based on the improved single-cycle single-vector chaos control method, the gradient of the performance function to the random parameter vector is calculated, comprising the following steps: A1: all material parameters and load parameters that need to be considered uncertain are constructed into a random variable vector, and points in the standard normal space are mapped back to the original random space through transformation; The transformation formula is: ； wherein is the value of the random variable vector in the original space, is the mean vector of the random variable vector, is the standard deviation vector of the random variable vector, is a point in the standard normal space, is the current iteration number; A2: At the current random variable vector, call the finite element analysis function to compute the performance function value for the baseline ; wherein is an ultimate state function constructed based on the compliance is a value of , is a preset compliance constraint value is a compliance value of the structure calculated by finite element analysis under the specific material properties and load conditions defined by the random variable vector ​ A3: each component of the random variable vector is sequentially operated as follows: performing a small perturbation on the current random variable component to create a perturbation vector and let ; wherein, is a temporary disturbance vector is the th component in the is the mean of the th component in the random variable vector is the standard deviation of the th component in the random variable vector is the th component of the point in the standard normal space at the th iteration is a preset tiny tolerance, taken as 0.001; A new finite element analysis is performed on the disturbed vector to calculate the performance function value ; Using the central difference formula, the partial derivative approximation value of the performance function value to the current random variable component is calculated: ； wherein is the current random variable component; A4: after traversing all random variable components, the gradient of the random parameter vector is obtained by assembling.

3. The fiber-reinforced composite variable-stiffness reliability multiscale optimization design method according to claim 2, characterized in that, The MPP update formula of the improved single-cycle single-vector chaos control method is: ； ； where is the MPP in the standard normal space in the th optimization iteration, is the mean vector of the random parameters, is the target reliability index, , is the target failure probability, is the inverse function of the standard normal distribution, is the standard deviation vector of the random parameters, with superscript is the transpose symbol, is the new direction vector obtained after introducing chaos control in the MPP update, is the MPP in the th optimization iteration, is the MPP in the th optimization iteration, is the stabilization factor, is the convolution matrix, is the vector function defined.

4. The fiber-reinforced composite stiffness-variable reliability multiscale optimization design method according to claim 3, characterized in that, The sensitivity information of the objective function to the macroscopic topological design variable and the microscopic fiber angle design variable is: The objective function is normalized volume with sensitivity 1 to macro-topology design variables and sensitivity 0 to micro-fiber angle design variables , which is given by ； ； wherein, is the current volume of the structure, is the initial total volume of the design domain, is the area of a single element in the finite element model, is the thickness of a single ply in the composite laminate, is the total number of plies in the composite laminate, is the total number of elements in the finite element model, is the ply of the composite laminate, is the element in the finite element model.

5. The fiber-reinforced composite stiffness-variable reliability multiscale optimization design method according to claim 4, characterized in that, The sensitivity information of the constraint function to the macroscopic topological design variable is: The constraint function is wherein, is the compliance, is the global displacement vector of the structure obtained by finite element analysis, is the global stiffness matrix of the structure assembled from the stiffness matrices of all elements, the superscript is the transposition symbol; By the adjoint method, the constraint function The sensitivity of the macro-topology design variable is: ； ； ； in, For the first Layer The stiffness matrix of element number 1. For the first Layer The domain where the numbered unit is located. For geometric matrices, For the first Layer The macroscopic equivalent constitutive matrix of the symbol. In finite element analysis, this represents the integration over the element domain. The penalty factor for macroscopic topological variables. The constitutive matrix of the unit cell is determined by the microfiber angle; Considering the chain rule modification of the density filter and the Heaviside threshold projection, the constraint function is calculated by the chain rule as the sensitivity of the filtered variable ； ； ； wherein, is a physical projection variable, is a non-zero minimum value, taken as 0.001, is a parameter to control the projection sharpness, is a projection threshold value; Post-filtered variables from all original design variables within its filtering radius The weighted average gives the constraint function The final sensitivity of a certain original design variable is ； ； in, Include the original design variables in all filtered neighborhoods. The set of units, Original design variables Located in the unit, For the unit The filtered variables, For the weight function, For the first one located in the filtering neighborhood One original design variable, This is the loop index when summing all variables within the filtered neighborhood, representing the... One original design variable, For the circular index used in the summation calculation, For unit The filtered neighborhood is composed of all elements related to the unit. Distance less than filter radius The unit composition.

6. The fiber-reinforced composite stiffness-variable reliability multiscale optimization design method according to claim 5, characterized in that, The sensitivity information of the constraint function to the microscopic fiber angle design variable is: Constraint function Sensitivity of the micro-fiber angle design variable is: ； ； According to the NDFO model, let the basis function The normalized weight coefficient and its derivative are expressed as: ； ； ； ； wherein, is the number of candidate fiber lay angles, is the penalty parameter for the NDFO model, is the total number of candidate lay angles, is the loop index used in the summation calculation, representing the th candidate fiber lay angle, is the loop index used in the summation calculation, is the unit constitutive matrix corresponding to when the micro fiber angle design variable is exactly equal to the candidate fiber lay angle . To improve the continuity of fiber paths in the optimization result and to satisfy manufacturing constraints, the micro-fiber angle design variables A nonlinear continuous filtering strategy is employed, which realizes the following by a filtering domain centered on a target element : Defining filter domains Inner cell To the center cell Weight function : ； wherein, is the continuous filtration radius of the discrete fiber, and are the coordinates of the central cell and the neighboring cell within the filtration domain, respectively, is the distance between the two cells, is the power of the weight function; then the microdesign variables of the filtered center cell are calculated from the weighted average of all original variables within its filter domain ； Based on the chain rule, the constraint function The sensitivity of the micro-fiber angle design variable is: ； 。

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