Variable-angle fiber self-repairing structure optimization method with uncertain load size and direction

Abstract

The invention provides a variable-angle fiber self-repairing structure optimization method with uncertain load size and direction. The method comprises the following steps: constructing a variable-angle fiber self-repairing structure optimization array; multiple sets of self-repairing structures are determined; assembling an overall stiffness matrix; constructing a probability and interval hybrid model; selecting a self-repairing structure to be optimized; solving the sensitivity of the target function and the constraint condition to the design variables under the sensitive loading condition, and updating the design variables of the self-repairing structure by adopting an MMA algorithm; whether the updated design variables of the self-repairing structure meet convergence conditions or not is judged, if yes, an optimization result is output, optimization is ended, and if not, the macroscopic base structure is updated, the orthogonal pipe network is added again to form multiple sets of self-repairing structures, and next-generation optimization is carried out. And the adaptive capacity to actual working conditions and the mechanical bearing performance are both considered.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of topology optimization and self-repairing, and particularly relates to a variable-angle fiber self-repairing structure optimization method with uncertain load size and direction. BACKGROUND

[0002] With the continuous development of composite material application technology, the service environment of composite materials is more complex and severe. Long-term service can easily cause damage to the surface and interior of the material, resulting in economic losses. The concept of self-repairing is expected to solve this problem. There is a self-repairing agent in the orthogonal pipe network (self-repairing carrier), which can quickly and efficiently repair the damaged part when the material is damaged. However, the addition of the orthogonal pipe network inevitably causes a decrease in the performance of the composite material structure. Using topology optimization to optimize the composite material structure, the orthogonal pipe network structure and the fiber arrangement can compensate for the influence of the orthogonal pipe network on the structure performance. In addition, under complex working conditions, the size and direction of the load often change with the service time. Therefore, by taking the uncertain load size and direction as the working condition, and introducing variable-angle fiber composite material as the structure material, the self-repairing structure is optimized, so that the topology structure has good mechanical properties, can overcome complex working conditions, and realizes rapid repair of damage and prolongs the service time.

[0003] Some self-repairing structure optimization often focuses on the optimization of the size and proportion of the self-repairing carrier under the condition of a certain load, and does not comprehensively consider the material structure, the orthogonal pipe network structure and the fiber arrangement, greatly reducing the optimization space of the self-repairing structure. Moreover, because of the lack of optimization of the robustness of the self-repairing structure under uncertain load conditions, the practicality and guidance of this optimization method in actual working conditions are not strong. SUMMARY

[0004] In order to solve the above technical problems, the application provides a variable-angle fiber self-repairing structure optimization method with uncertain load size and direction, which is used to solve the problems in the prior art.

[0005] In one aspect, the application provides the following technical scheme, a variable-angle fiber self-repairing structure optimization method with uncertain load size and direction, comprising: constructing a variable-angle fiber self-repairing structure optimization formula with uncertain load size and direction; embedding orthogonal pipe networks with different pipe diameters and pipe spacings in the macroscopic basic structure to form multiple self-repairing structures; solving the unit stiffness matrix under different fiber angles, and assembling the overall stiffness matrix according to different self-repairing structure distributions; constructing a probability and interval mixed model with uncertain load size and direction; Solving the flexibility values of different self-repairing structures under sensitive loading conditions to select the self-repairing structure to be optimized; Based on the total stiffness matrix, the probability and interval hybrid model and the variable angle fiber self-repairing structure optimization formula, the sensitivity of the objective function and the constraint condition to the design variable under the sensitive loading condition is solved, and the design variable of the self-repairing structure is updated by using the MMA algorithm; It is judged whether the design variable of the updated self-repairing structure meets the convergence condition, and if yes, the optimization result is output, and the optimization is ended, otherwise the macroscopic basic structure is updated and the orthogonal pipe network is re-added to form a plurality of self-repairing structures for next generation optimization.

[0006] Compared with the prior art, the beneficial effects of the present application are that the present application describes the uncertain changes of the load size and direction by using the probability and interval hybrid model, and simultaneously optimizes the composite material configuration, the orthogonal pipe network structure and the fiber arrangement by using the topology optimization method, aiming at optimizing the mechanical properties of the self-repairing structure and enhancing the robustness thereof under complex working conditions.

[0007] Preferably, the step of constructing the variable angle fiber self-repairing structure optimization formula under the uncertain load size and direction comprises: The finite element model of the variable angle fiber self-repairing structure under the uncertain load size and direction is constructed, the element density, the element fiber angle, the pipe spacing and the pipe radius of the pipe network are taken as the design variables, the flexibility under the sensitive loading condition is taken as the objective function, and the structure volume percentage is taken as the constraint condition, so as to construct the optimization formula of the variable angle fiber self-repairing structure under the uncertain load size and direction, wherein the optimization formula of the variable angle fiber self-repairing structure is: ; In the formula, are the optimal pipe diameter and pipe spacing respectively, is the number of pipe diameters, is the number of pipe spacing, , , , is each pipe diameter, , , , is each pipe spacing, n is the total number of design domain elements, is the element density vector, , , , is each element density, is the element fiber angle vector, , , , fiber angle of each element, sensitive load direction, flexibility value of self-repairing structure under sensitive loading condition, sensitive load vector, total displacement vector, is e element density, penalty factor, is e node displacement vector of element, is e element stiffness matrix of element, random bounded parameter, total perturbation matrix under perturbation angle is nominal load vector with size, total stiffness matrix, volume of structure, volume of design domain, volume constraint percentage, fiber angle of element, e is minimum value of element density.

[0008] Preferably, the step of embedding different pipe diameters and pipe spacing in the macroscopic base structure respectively to form multiple sets of self-repairing structures comprises: embedding pipe-like diameters and pipe-like spacing together into the macroscopic base structure to form pipe-like orthogonal pipe networks, and performing local correction on the orthogonal pipe networks to obtain multiple sets of self-repairing structures.

[0009] Preferably, the step of solving element stiffness matrix under different fiber angles, and assembling total stiffness matrix according to different self-repairing structure distribution comprises: setting shear modulus, elastic modulus, and Poisson's ratio of the composite material; extracting fiber laying angles of all elements in the design domain, and calculating element stiffness matrix of each element under respective fiber laying angle based on the shear modulus, elastic modulus, and Poisson's ratio of the composite material: ; ; ; ; wherein, is e ​​​unit stiffness matrix corresponding to fiber angle, is strain-displacement matrix, is elastic matrix in global coordinate system, is unit thickness, is elastic matrix in fiber principal direction coordinate system, is longitudinal modulus of single layer material, is transverse modulus of single layer material, is longitudinal Poisson's ratio of single layer material, is transverse Poisson's ratio of single layer material, is shear modulus of material, is unit e conversion matrix corresponding to fiber angle, is unit e fiber angle; According to different self-repairing structure distribution, the degree of freedom number of each unit stiffness matrix is determined, and is inserted into the corresponding position of the overall stiffness matrix, and the insertion process satisfies the corresponding relationship between the size of the overall stiffness matrix and the size of the unit stiffness matrix, and the relationship between the overall degree of freedom number and the unit degree of freedom number, to obtain the overall stiffness matrix.

[0010] Preferably, the step of constructing the probability and interval hybrid model of uncertain load size and direction comprises: A random bounded probability parameter is used to weight and assign the size of the uncertain load: ; In the formula, is a random bounded probability parameter, is the nominal load vector of the direction, is the nominal load vector of the size; An interval variable is determined, and a single position, a single quantity, and a second-order perturbation rotation matrix are defined: ; In the formula, is the perturbation angle; Based on the interval variable and the second-order perturbation rotation matrix The sensitive load vector is regarded as the overall perturbation rotation matrix multiplied by the nominal load vector of the direction to obtain the equilibrium equation: ; ; In the formula, is the overall displacement vector, is the total stiffness matrix, is the unit matrix; determine the probability and interval mixed model of the load size and direction uncertainty based on the balance equation: .

[0011] Preferably, the step of selecting the self-repairing structure to be optimized by solving the flexibility values of different self-repairing structures under the sensitive loading condition comprises: obtaining the nominal load vector of the direction with a random bounded probability parameter and solving the sensitive load direction according to the interval variable, wherein the sensitive load direction comprises first, second and third sensitive load directions, the first and second sensitive load directions are respectively and , is the nominal load direction, and are the perturbations with the maximum positive and negative stiffnesses in the nominal load direction respectively; and ; determine the mathematical equation for solving the extreme point: ; , is the third sensitive load direction, is the difference between the third sensitive load direction and the nominal load direction, is the flexibility value under the third sensitive load direction, is the flexibility value under the nominal load direction, is the unit density vector; solve the mathematical equation to obtain the value of the sensitive load direction: ; use the second Taylor expansion and calculate the flexibility values of the same self-repairing structure under the three sensitive load directions, select the structure with the minimum selection index in each self-repairing structure as the self-repairing structure to be optimized.

[0012] Preferably, the step of solving the sensitivity of the design variable under the sensitive loading condition based on the total stiffness matrix, the probability and interval mixed model and the optimization formula of the variable angle fiber self-repairing structure, and updating the design variable of the self-repairing structure by using the MMA algorithm comprises: determine the mathematical expression of the sensitivity of the objective function to the unit density: ; is the flexibility value of the self-repairing structure under the sensitive loading condition,​​​ is the flexibility value under the nominal load direction, is the cell density vector, is the sensitive load direction, is the difference between the sensitive load direction and the nominal load direction; According to the minimization optimization principle of the objective function, the sensitivity value is negative, and the absolute maximum sensitivity value under the three types of sensitive loading conditions is selected to update the density design variable; Update the fiber angle using the sensitivity of the compliance to the fiber angle in the nominal load direction: The mathematical expression of the sensitivity of flexibility to fiber angle in the nominal load direction is: ; ; Where, is the strain displacement matrix, is the elastic matrix in the fiber principal direction coordinate system, is the unit thickness, For unit e The fiber angle, is the overall displacement vector, is the overall stiffness matrix, is the penalty factor, For the structure e The nodal displacement vector of the element, For the structure e The element stiffness matrix of the element, For unit e The transformation matrix corresponding to the fiber angle is, is the horizontal coordinate in the local coordinate system of the unit, is the ordinate in the local coordinate system of the element; The mathematical expression for solving the volume constraint sensitivity to element density and element fiber angle is: ; ; Where, is the volume filled with material units, is the volume of the structure, for e cell density, n is the total number of design domain elements; The sensitivity of flexibility to element density under sensitive loading conditions, the sensitivity of flexibility to fiber angle under nominal load direction, and the sensitivity of volume constraint to element density and fiber angle are substituted into the MMA algorithm to update the design variables.

[0013] Preferably, the step of judging whether the design variable of the self-repairing structure after updating satisfies a convergence condition, yes, outputting an optimization result, ending optimization, or no, updating the macroscopic basic structure and rejoining the orthogonal pipe network to form a plurality of self-repairing structures for next generation optimization comprises: judging whether the maximum difference between the design variables of the self-repairing structure after updating of two adjacent iterations is less than a threshold value, yes, outputting an optimization result, ending optimization, or no, re-forming a plurality of self-repairing structures, calculating a stiffness matrix and a size and direction uncertain load vector, finding a sensitive loading condition, selecting a self-repairing structure to be optimized, calculating an objective function and a sensitivity, until a convergence condition is satisfied to end optimization. BRIEF DESCRIPTION OF DRAWINGS

[0014] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort based on these drawings.

[0015] Figure 1 A flow chart of the variable angle fiber self-repairing structure optimization method with uncertain load size and direction provided by the embodiment of the present application; Figure 2 A structure design domain diagram in the embodiment of the present application; Figure 3 A structure and fiber angle diagram for final optimization of the macroscopic basic structure in the embodiment of the present application; Figure 4 A macroscopic basic structure, fiber angle and orthogonal pipe network diagram for final optimization of the self-repairing structure in the embodiment of the present application.

[0016] The embodiments of the present application will be further described below with reference to the drawings. DETAILED DESCRIPTION

[0017] The embodiments of the present application will be described in detail below, and examples of the embodiments are shown in the drawings, wherein the same or similar notations represent the same or similar elements or elements with the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are intended to explain the embodiments of the present application, and cannot be understood as a limitation of the present application.

[0018] Embodiment one In the embodiments of the present application, as shown in Figure 1 a variable angle fiber self-repairing structure optimization method with uncertain load size and direction, comprising: S1, constructing a variable angle fiber self-repairing structure optimization formula with uncertain load size and direction; Wherein, the step S1 includes: A finite element model of a variable-angle fiber self-repairing structure with uncertain load magnitude and direction was constructed. The unit density, unit fiber angle, pipe spacing, and pipe radius of the pipe network were used as design variables. The flexibility under sensitive loading conditions was used as the objective function, and the structural volume percentage was used as the constraint condition. The optimization formula of the variable-angle fiber self-repairing structure with uncertain load magnitude and direction was constructed. The optimization formula of the variable-angle fiber self-repairing structure is: ; Where, are the optimal pipe diameter and pipe spacing, respectively. is the number of pipe diameter types, is the number of pipe spacing types, , , , For each pipe diameter type, , , , For each pipe spacing type, n is the total number of design domain elements, is the cell density vector, , , , is the density of each unit, is the unit fiber angle vector, , , , is the fiber angle of each unit, is the sensitive load direction, is the flexibility value of the self-repairing structure under sensitive loading conditions, is the sensitive load vector, is the overall displacement vector, for e cell density, is the penalty factor, For the structure e The nodal displacement vector of the element, For the structure e The element stiffness matrix of the element, is a random bounded parameter, is the disturbance angle The overall perturbation matrix under , is the nominal load vector of magnitude, is the overall stiffness matrix, is the volume of the structure, is the design domain volume, is the volume constraint percentage, is the unit e fiber angle, is the minimum unit density.

[0019] It can be understood that the finite element model of the variable-angle fiber self-repairing structure under uncertain load conditions is constructed, in the embodiment, the initial laying angle of the fiber of the variable-angle fiber self-repairing composite material is 0°, that is the positive direction of the axis, the nominal load direction under the uncertain load condition is 270°, that is the negative direction of the axis. There is only one direction angle of the fiber in the single unit grid of the fiber-reinforced composite material, which is parallel to the plane of the structure, as shown in Figure 2 , Figure 2 a cantilever beam example, which specifically represents the structure design domain, the finite element grid is divided, the number of grids in the axis direction is 90 and 30 respectively, the unit is set to a four-node rectangular element, all nodes on the left side of the design domain are fully constrained, a unit load vertically downward is loaded at the lower right corner of the design domain, the initial value of the unit density in the design domain is 0.4, and the upper limit of the volume percentage of the solid area and the design domain is 0.65. Based on the finite element model and the variable density method framework, a mathematical model of the variable-angle fiber self-repairing structure under uncertain load conditions is constructed, the unit density, the unit fiber angle, the pipe spacing and the radius of the micro-pipe network are taken as design variables, the percentage of the structure volume is taken as a constraint condition, and the minimum flexibility under the sensitive loading condition is taken as the target, that is, the optimization formula in the above formula can be obtained. The above optimization formula can be regarded as the general outline of the technical scheme of the present application, which includes the optimization target, the objective function, the constraint condition and the like. In order to avoid the singularity of the stiffness matrix, the .

[0020] S2, embedding different pipe diameters and pipe spacings in the macroscopic basic structure to form a plurality of self-repairing structures; The step S2 comprises: embedding the pipe diameter and the pipe spacing into the macroscopic basic structure to form the orthogonal pipe network, and locally correcting the orthogonal pipe network to obtain a plurality of self-repairing structures; Specifically, the self-repairing structure is composed of the macroscopic basic structure and the embedded orthogonal pipe network. The macroscopic basic structure specifically refers to the solid structure before the pipe network is embedded, and the self-repairing structure is the solid structure after the orthogonal pipe network is removed from the macroscopic basic structure.

[0021] S3, solve the element stiffness matrix under different fiber angles, and assemble the overall stiffness matrix according to different self-repairing structure distributions; The step S3 comprises: S31, set the shear modulus, elastic modulus and Poisson's ratio of the composite material.

[0022] S32, extract the fiber laying angle of all elements in the design domain, and calculate the element stiffness matrix of each element under the respective fiber laying angle based on the shear modulus, elastic modulus and Poisson's ratio of the composite material: ; ; ; ; In the formula, is e the element stiffness matrix under the corresponding fiber angle of the element, is the strain displacement matrix, is the elastic matrix under the global coordinate system, is the thickness of the element, is the elastic matrix under the fiber main direction coordinate system, is the longitudinal modulus of the single-layer material, is the transverse modulus of the single-layer material, is the longitudinal Poisson's ratio of the single-layer material, is the transverse Poisson's ratio of the single-layer material, is the shear modulus of the material, is the conversion matrix of the element e under the corresponding fiber angle, is the fiber angle of the element e ; In this embodiment, the shear modulus , the elastic modulus , , the Poisson's ratio , of the composite material are set.

[0023] S33, according to different self-repairing structure distributions, determine the degree of freedom number of each element stiffness matrix, and insert it into the corresponding position of the overall stiffness matrix, and the insertion process satisfies the corresponding relationship between the size of the overall stiffness matrix and the size of the element stiffness matrix, and the relationship between the overall degree of freedom number and the element degree of freedom number, to obtain the overall stiffness matrix.

[0024] S4, construct a probability and interval mixed model with uncertain load size and direction; The step S4 comprises: S41. Use random bounded probability parameters to assign weighted values ​​to the size of the uncertain load: ; Where, is a random bounded probability parameter, is the nominal load vector in the direction, is the nominal load vector of magnitude; Among them, the random bounded probability parameter obeys a normal distribution with mean 1.

[0025] S42. Determine the interval variable and define a single position, single number second-order perturbation rotation matrix : ; Where, is the disturbance angle; Specifically, through interval variables, that is, arrays represents a bounded perturbation in the load direction, where is the nominal load direction, and There are maximum forward and reverse and The disturbance of clockwise is negative and the disturbance of counterclockwise is positive, that is, and Respectively represent the upper and lower load directions of the load range, among which the nominal load direction is The negative direction of the axis is 270°, the maximum forward and reverse direction is ,therefore and 265° and 275° represent the upper and lower load directions of the load range respectively.

[0026] S43, based on the interval variable and the second-order perturbation rotation matrix The sensitive load vector Considered as the overall perturbation rotation matrix Multiply the nominal load vector by the direction , to obtain the equilibrium equation: ; ; Where, is the overall displacement vector, is the overall stiffness matrix, is the identity matrix; Specifically, the position and number of the second-order perturbation matrix in the above formula correspond one-to-one to the position and number of the applied load.

[0027] S44, determine the probability and interval mixed model of the load size and direction uncertainty based on the balance equation: Specifically, since the value of each time is different, in the subsequent optimization process, when the optimization result reaches a steady state, the self-repairing structure with the maximum flexibility, i.e., the worst case, is selected as the final optimization result output to meet the influence of the load size change on the self-repairing structure.

[0028] S5, select the self-repairing structure to be optimized by solving the flexibility values of different self-repairing structures under sensitive loading conditions; The step S5 includes: S51, obtain the nominal load vector in the direction with a random bounded probability parameter and solve the sensitive load direction according to the interval variable, wherein the sensitive load direction includes the first, second and third sensitive load directions, and the first and second sensitive load directions are and , is the nominal load direction, and are the disturbances with the maximum direct and inverse and in the nominal load direction; Specifically, the nominal load vector in the direction is obtained with a random bounded probability parameter, and on this basis, the sensitive load direction is solved according to the interval variable.

[0029] S52, determine the mathematical equation for solving the extreme point: In the formula, , is the third sensitive load direction, is the difference between the third sensitive load direction and the nominal load direction, is the flexibility value in the third sensitive load direction, is the flexibility value in the nominal load direction, is the unit density vector.

[0030] S53, solve the mathematical equation to obtain the value of the sensitive load direction:

[0031] S54, use the second Taylor expansion and calculate the flexibility values of the same self-repairing structure in the three sensitive load directions, select the structure with the minimum selection index in each self-repairing structure as the self-repairing structure to be optimized.

[0032] ​​​S6, based on the total stiffness matrix, the probability and interval hybrid model and the variable angle fiber self-healing structure optimization formula, the sensitivity of the objective function, the constraint condition to the design variable under the sensitive loading condition is solved, and the design variable of the self-healing structure is updated by using the MMA algorithm; Wherein, the step S6 comprises: S61, the mathematical expression of the sensitivity of the objective function to the unit density is determined: ; In the formula, is the flexibility value of the self-healing structure under the sensitive loading condition, is the flexibility value in the nominal load direction, is the unit density vector, is the sensitive load direction, is the difference between the sensitive load direction and the nominal load direction.

[0033] S62, according to the minimum optimization principle of the objective function, the sensitivity value is negative, and the absolute value of the maximum sensitivity value under three kinds of sensitive loading conditions is selected to update the density design variable; S63, the sensitivity of the flexibility in the nominal load direction to the fiber angle is used to update the fiber angle: Wherein, the mathematical expression of the sensitivity of the flexibility in the nominal load direction to the fiber angle is: ; ; In the formula, is the strain displacement matrix, is the elastic matrix in the fiber main direction coordinate system, is the unit thickness, is the fiber angle of the unit e , is the total displacement vector, is the total stiffness matrix, is the penalty factor, is the node displacement vector of the unit in the structure e , is the unit stiffness matrix of the unit in the structure e , is the conversion matrix of the unit e corresponding to the fiber angle, is the horizontal coordinate in the unit local coordinate system, is the vertical coordinate in the unit local coordinate system; The mathematical expression of the sensitivity of the volume constraint to the unit density and the unit fiber angle is: ; ; V is the volume of the material filled unit, V is the volume of the structure, V is the volume of the structure, V is the volume of the structure, e unit density, n V is the volume of the structure, S64, the sensitivity of the flexibility under the sensitive loading condition to the unit density, the sensitivity of the flexibility under the nominal load direction to the fiber angle, and the sensitivity of the volume constraint to the unit density and the fiber angle are substituted into the MMA algorithm to update the design variables.

[0034] S7, judge whether the updated design variables of the self-repairing structure meet the convergence condition, if yes, output the optimization result and end the optimization, otherwise update the macroscopic base structure and re-add the orthogonal pipe network to form multiple sets of self-repairing structures for next generation optimization.

[0035] The step S7 comprises: judging whether the maximum difference between the updated design variables of the self-repairing structure of adjacent two iterations is less than a threshold value, if yes, outputting the optimization result and ending the optimization, if no, re-composing multiple sets of self-repairing structures, calculating the stiffness matrix and the size and direction uncertain load vector, finding the sensitive loading condition, selecting the self-repairing structure to be optimized, calculating the objective function and sensitivity, until the convergence condition is met to end the optimization. It can be understood that the absolute value of the maximum difference between the design variables of two iterations is judged, if yes, the optimization result is outputted and the optimization is ended, if no, multiple sets of self-repairing structures are re-composed, the stiffness matrix and the size and direction uncertain load vector are calculated, the sensitive loading condition is found, the self-repairing structure to be optimized is selected, the objective function and sensitivity are calculated, until the convergence condition is met to end the optimization. As shown in Figure 3 The final obtained macroscopic base structure and unit fiber distribution are shown in FIG. 6, it can be seen that the arrangement angle of the fiber completely conforms to the force transmission structure of the topological configuration, and is evenly distributed in all units of the design domain. As shown in Figure 4 The final obtained macroscopic base structure, fiber distribution and arrangement of the orthogonal pipe network are shown in FIG. 7.

[0036] The variable-angle fiber self-repairing structure optimization method provided by the embodiment of the present application is used for describing uncertain changes in the load size and direction through a probability and interval hybrid model, and simultaneously used for optimizing the composite material configuration, the orthogonal pipe network structure and the fiber arrangement by using a topology optimization method, aiming at optimizing the mechanical properties of the self-repairing structure and enhancing the robustness of the self-repairing structure under complex working conditions, simulating the actual working conditions by using uncertain load size and direction, and combining the variable-angle fiber composite material, so that the mechanical properties of the self-repairing structure are enhanced, and the self-repairing structure has good self-repairing performance, and meanwhile, the self-repairing structure has the adaptability to the actual working conditions and the mechanical load bearing performance of light weight.

[0037] The technical features of the above-described embodiments can be combined in any manner, and to make the description concise, all possible combinations of the technical features in the above-described embodiments are not described, however, as long as the combinations of the technical features do not exist contradictions, they should be considered as the scope of the present disclosure.

[0038] The above-described embodiments only express several implementation manners of the present application, the description is more specific and detailed, but it should not be understood as the limitation of the patent scope of the present application. It should be pointed out that, for the ordinary skilled in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A method for optimizing a variable-angle fiber self-repair structure with uncertain load magnitude and direction, characterized in that: include: Construct an optimized formula for a variable-angle fiber self-repairing structure with uncertain load magnitude and direction; Orthogonal pipe networks with different pipe diameters and pipe spacings are embedded in the macro-infrastructure to form multiple sets of self-repairing structures; Solve the unit stiffness matrix under different fiber angles and assemble the overall stiffness matrix according to different self-repairing structure distributions; Construct probabilistic and interval mixed models with uncertain load magnitude and direction; By solving the flexibility values ​​of different self-repairing structures under sensitive loading conditions, the self-repairing structure to be optimized is selected; Solve the sensitivity of the objective function and the constraints to the design variables under sensitive loading conditions based on the overall stiffness matrix, the probability and interval hybrid model, and the variable-angle fiber self-repairing structure optimization formula, and use the MMA algorithm to update the design variables of the self-repairing structure; It is determined whether the updated design variables of the self-repairing structure meet the convergence conditions. If so, the optimization results are output and the optimization is terminated. Otherwise, the macro-infrastructure is updated and the orthogonal pipe network is re-added to form multiple sets of self-repairing structures for the next generation of optimization.

2. The method for optimizing a variable-angle fiber self-repair structure with uncertain load magnitude and direction according to claim 1, characterized in that: The steps of constructing an optimized formula for a variable-angle fiber self-repairing structure with uncertain load magnitude and direction include: A finite element model of a variable-angle fiber self-repairing structure with uncertain load magnitude and direction was constructed. The unit density, unit fiber angle, pipe spacing, and pipe radius of the pipe network were used as design variables. The flexibility under sensitive loading conditions was used as the objective function, and the structural volume percentage was used as the constraint condition. The optimization formula of the variable-angle fiber self-repairing structure with uncertain load magnitude and direction was constructed. The optimization formula of the variable-angle fiber self-repairing structure is: ； Where, are the optimal pipe diameter and pipe spacing, respectively. is the number of pipe diameter types, is the number of pipe spacing types, , , , For each pipe diameter type, , , , For each pipe spacing type, n is the total number of design domain elements, is the cell density vector, , , , is the density of each unit, is the unit fiber angle vector, , , , is the fiber angle of each unit, is the sensitive load direction, is the flexibility value of the self-repairing structure under sensitive loading conditions, is the sensitive load vector, is the overall displacement vector, for e cell density, is the penalty factor, For the structure e The nodal displacement vector of the element, For the structure e The element stiffness matrix of the element, is a random bounded parameter, is the disturbance angle The overall perturbation matrix under is the nominal load vector of magnitude, is the overall stiffness matrix, is the volume of the structure, is the design domain volume, is the volume constraint percentage, For unit e The fiber angle, is the minimum cell density.

3. The method for optimizing a variable-angle fiber self-repair structure with uncertain load magnitude and direction according to claim 1, characterized in that: The steps of embedding orthogonal pipe networks of different pipe diameters and pipe spacings in the macroscopic infrastructure to form multiple sets of self-repairing structures include: Will Type of pipe diameter and The spacing between similar pipes is composed of The quasi-orthogonal pipe network is embedded in the macro-infrastructure and the orthogonal pipe network is locally modified to obtain multiple sets of self-repairing structures.

4. The method for optimizing a variable-angle fiber self-repair structure with uncertain load magnitude and direction according to claim 1, characterized in that: The steps of solving the unit stiffness matrix at different fiber angles and assembling the overall stiffness matrix according to different self-repairing structure distributions include: Set the shear modulus, elastic modulus, and Poisson's ratio of the composite material; The fiber placement angles of all elements in the design domain are extracted, and the element stiffness matrix of each element at its respective fiber placement angle is calculated based on the shear modulus, elastic modulus, and Poisson's ratio of the composite material: ； ； ； ； Where, for e The element stiffness matrix of the element corresponding to the fiber angle, is the strain displacement matrix, is the elastic matrix in the global coordinate system, is the unit thickness, is the elastic matrix in the fiber principal direction coordinate system, is the longitudinal modulus of the single layer material, is the transverse modulus of the single layer material, is the longitudinal Poisson's ratio of the single-layer material, is the transverse Poisson's ratio of the single-layer material, is the shear modulus of the material, For unit e The transformation matrix corresponding to the fiber angle is, For unit e Fiber angle; According to the different self-repairing structure distributions, the degree of freedom number of each unit stiffness matrix is ​​determined and inserted into the corresponding position of the overall stiffness matrix. The insertion process satisfies the correspondence between the size of the overall stiffness matrix and the size of the unit stiffness matrix, as well as the relationship between the overall degree of freedom number and the unit degree of freedom number, so as to obtain the overall stiffness matrix.

5. The method for optimizing a variable-angle fiber self-repair structure with uncertain load magnitude and direction according to claim 1, characterized in that: The steps of constructing a probability and interval mixed model with uncertain load magnitude and direction include: The size of the uncertain load is weighted using random bounded probability parameters: ； Where, is a random bounded probability parameter, is the nominal load vector in the direction, is the nominal load vector of magnitude; Determine the interval variables and define a single-position, single-number second-order perturbation rotation matrix : ； Where, is the disturbance angle; Based on the interval variable and the second-order perturbation rotation matrix The sensitive load vector Considered as the overall perturbation rotation matrix Multiply the nominal load vector by the direction , to obtain the equilibrium equation: ； ； Where, is the overall displacement vector, is the overall stiffness matrix, is the identity matrix; Determine the probability and interval hybrid model of the load magnitude and direction uncertainty based on the equilibrium equation: 。 6. The method for optimizing a variable-angle fiber self-repair structure with uncertain load magnitude and direction according to claim 1, characterized in that: The step of selecting a self-repairing structure to be optimized by solving the compliance values ​​of different self-repairing structures under sensitive loading conditions includes: The nominal load vector of the direction is obtained by using random bounded probability parameters and the sensitive load direction is solved according to the interval variable, wherein the sensitive load direction includes the first, second and third types of sensitive load directions, and the first and second types of sensitive load directions are respectively and , is the nominal load direction, and There are maximum forward and reverse and disturbance; Determine the solution Mathematical equation of extreme point: ； Where, , It is the third type of sensitive load direction. is the difference between the third type of sensitive load direction and the nominal load direction, is the flexibility value under the third sensitive load direction, is the flexibility value under the nominal load direction, is the cell density vector; Solve the mathematical equation to obtain the value of the sensitive load direction: ； The quadratic Taylor expansion is used to calculate the flexibility of the same self-repairing structure under three types of sensitive load directions. The maximum flexibility value is used as the selection index, and the structure with the smallest selection index among the repair structures is selected as the self-repairing structure to be optimized.

7. The method for optimizing a variable-angle fiber self-repair structure with uncertain load magnitude and direction according to claim 1, characterized in that: The steps of solving the objective function and the sensitivity of the constraint conditions to the design variables under sensitive loading conditions based on the overall stiffness matrix, the probability and interval hybrid model and the variable angle fiber self-repairing structure optimization formula, and updating the design variables of the self-repairing structure using the MMA algorithm include: Mathematical expression that determines the sensitivity of the objective function to cell density: ； Where, is the flexibility value of the self-repairing structure under sensitive loading conditions, is the flexibility value under the nominal load direction, is the cell density vector, is the sensitive load direction, is the difference between the sensitive load direction and the nominal load direction; According to the minimization optimization principle of the objective function, the sensitivity value is negative, and the absolute maximum sensitivity value under the three types of sensitive loading conditions is selected to update the density design variable; Update the fiber angle using the sensitivity of the compliance to the fiber angle in the nominal load direction: The mathematical expression of the sensitivity of flexibility to fiber angle in the nominal load direction is: ； ； Where, is the strain displacement matrix, is the elastic matrix in the fiber principal direction coordinate system, is the unit thickness, For unit e The fiber angle, is the overall displacement vector, is the overall stiffness matrix, is the penalty factor, For the structure e The nodal displacement vector of the element, For the structure e The element stiffness matrix of the element, For unit e The transformation matrix corresponding to the fiber angle is, is the horizontal coordinate in the local coordinate system of the unit, is the ordinate in the local coordinate system of the element; The mathematical expression for solving the volume constraint sensitivity to element density and element fiber angle is: ； ； Where, is the volume filled with material units, is the volume of the structure, for e cell density, n is the total number of design domain elements; The sensitivity of flexibility to element density under sensitive loading conditions, the sensitivity of flexibility to fiber angle under nominal load direction, and the sensitivity of volume constraint to element density and fiber angle are substituted into the MMA algorithm to update the design variables.

8. The method for optimizing a variable-angle fiber self-repair structure with uncertain load magnitude and direction according to claim 1, characterized in that: The step of determining whether the updated design variables of the self-repairing structure meet the convergence conditions, outputting the optimization results and ending the optimization if they meet the convergence conditions, and otherwise updating the macro-infrastructure and re-adding the orthogonal pipe network to form multiple sets of self-repairing structures for the next generation of optimization includes: Determine whether the maximum difference between the updated design variables of the self-repairing structure of two adjacent iterations is less than a threshold value. If so, output the optimization result and end the optimization. If not, reassemble multiple sets of self-repairing structures, calculate the stiffness matrix and the magnitude and direction uncertain load vector, find sensitive loading conditions, select the self-repairing structure to be optimized, calculate the objective function and sensitivity, and end the optimization until the convergence conditions are met.

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