Integrated optimization design method for thin-wall reinforced structure

Abstract

The invention discloses an integrated optimization design method for a thin-wall reinforced structure, and relates to the related field of ultra-lightweight structure design methods, and the method comprises the steps: building a topological optimization finite element model with the structural flexibility as a target and the volume fraction as a constraint; obtaining the relationship between the radius and the thin-wall thickness in isotropic filtering of a variable field for thin-wall morphology design; obtaining an isotropic filtering matrix used in a thin-wall morphology design variable field; through two-step anisotropic-isotropic filtering and Sigmoid projection operation, an intermediate field and a thin-wall field are extracted; performing anisotropic filtering and Sigmoid projection on the reinforcement variable field to obtain a rib field; combining the intermediate field, the thin-wall field and the rib field to construct a material interpolation model; calculating the flexibility of the structure; based on structural flexibility, density and sensitivity; and updating the thin-wall thickness field, the thin-wall morphology field and the reinforcement variable field according to the sensitivity. The lightweight design effect and efficiency of the thin-wall reinforced structure are improved, and the method has important engineering application value in multiple high-tech fields.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ultra-lightweight structure design methods, and in particular to a thin-walled ribbed structure integrated optimization design method for thin-walled morphology-thickness and rib layout-topology. BACKGROUND

[0002] The thin-walled ribbed structure is a structure form with lightweight and high-strength characteristics. By introducing an optimized distribution of rib topology configuration in the thin-walled base, the stiffness, stability and carrying efficiency of the structure are significantly improved. Combined with integrated forming process, the collaborative manufacturing of complex curved surface morphology and rib layout can be realized, and it is widely used in aerospace, new energy vehicles, ships and other fields.

[0003] Due to the mass of the power system, the total mass of the electric vehicle is generally increased by 200-400 kg compared with the same size fuel vehicle. Studies have shown that for every 10 kg reduction in vehicle weight, the range can be increased by about 2.5 km. In order to ensure the driving range of the vehicle, the electrification of the automobile faces more stringent lightweight requirements. In the vehicle structure, key large components such as shock towers, front wall plates, longitudinal beams and battery pack shells widely adopt thin-walled ribbed design, which has great potential for weight reduction. The research on the optimization design method of thin-walled ribbed structure can significantly reduce the vehicle weight and improve the range.

[0004] The design and optimization of thin-walled ribbed structure involves multi-parameter coupling problems, including thin-walled morphology, thickness distribution, and rib topology configuration and spatial layout. However, incomplete parameter optimization, suboptimal solution produced by serial optimization strategy, and difficulty in geometric modeling representation, etc. limit the lightweight capability of thin-walled ribbed structure. SUMMARY

[0005] To solve the above difficulties, the present application proposes a thin-walled ribbed structure integrated optimization design for thin-walled morphology-thickness and rib layout-topology. The method uses two-step filtering and projection technology to extract thin-walled morphology and thickness distribution characteristics, establishes parameterized representation of rib layout and topology configuration based on anisotropic filtering and variable threshold projection technology, and constructs a material interpolation model to realize unified description of the two types of characteristics, thereby realizing collaborative optimization design of thin-walled morphology-thickness and rib layout-topology.

[0006] The present application discloses a thin-walled ribbed structure integrated optimization design method, which comprises the following steps:

[0007] Step 1: Establish a topology optimization finite element model with structural flexibility as the target and volume fraction as the constraint, and set the minimum thin-walled thickness and the maximum thin-walled thickness;

[0008] Step 2: Perform isotropic PDE filtering on the thin-walled thickness field to obtain the relationship between the radius and the thin-walled thickness for isotropic filtering in the thin-walled topography design variable field;

[0009] Step 3: Obtain the isotropic filtering matrix for the thin-walled topography design variable field according to the relationship expression between the radius and the thin-walled thickness;

[0010] Step 4: Extract the intermediate field and the thin-walled field through two-step anisotropic-isotropic filtering and Sigmoid projection operation;

[0011] Step 5: Obtain the rib field by performing anisotropic filtering and Sigmoid projection on the stiffening variable field;

[0012] Step 6: Combine the intermediate field, the thin-walled field and the rib field to construct a material interpolation model;

[0013] Step 7: Perform finite element analysis combined with the material interpolation model to calculate the flexibility of the structure;

[0014] Step 8: Solve to obtain the flexibility and density of the structure, and the sensitivity of both with respect to the design variables;

[0015] Step 9: According to the derived sensitivity, update the thin-walled thickness field, the thin-walled topography field and the stiffening variable field using the moving asymptote method;

[0016] Step 10: When the convergence condition is met, stop the optimization iteration and output the optimization result, otherwise repeat steps 2 to 9.

[0017] Further, in step 1, the thin-walled thickness field , the thin-walled topography field and the stiffening variable field are initialized to establish a topology optimization model with the structure flexibility as the target and the volume fraction as the constraint;

[0018] The physical parameters and optimization parameters of the optimization model are initialized, and the minimum thin-walled thickness and the maximum thin-walled thickness are set;

[0019] Among them, the topology optimization model with the structure flexibility as the target and the volume fraction as the constraint is:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] where, denotes the minimization of the structural compliance, denotes the constraint condition, denotes the transpose of a matrix; denotes the total stiffness matrix of the structure, and denotes the global displacement and load vectors; is the element number, denotes the number of elements in the design domain; denotes the element node displacement vector, denotes the element stiffness matrix, is the element elastic modulus; is the thin-walled thickness design variable field, is the thin-walled topography design variable field, is the stiffened design variable field; denotes the volume fraction constraint; is the volume fraction, is the element density, is the element volume; denotes the predetermined threshold value.

[0027] Further, in step 2, first, the chessboard phenomenon and mesh dependence of the thin-walled thickness field are avoided by means of isotropic PDE filtering, and a filtered field is established and the interpolation function of the thin-walled thickness , and the solution format of the PDE filtering is as follows:

[0028]

[0029] where, is the gradient operator, is the density field before filtering, is the density field after filtering, and the coefficient matrix is defined as:

[0030] ; ; ;

[0031] where, is the three base vectors of the element filtering direction coordinate system, is the matrix composed of the three base vectors, is the filtering radius corresponding to the three base vector directions, is the diagonal matrix corresponding to the three-direction filtering radius;

[0032] the thin-walled thickness field is isotropically PDE filtered with a first filter radius satisfying , the filtered field is represented by an interpolation function of the thin-walled thickness :

[0033]

[0034] where and are the minimum and maximum values of the thin-walled thickness, respectively;

[0035] Secondly, a relationship expression between the third filter radius of the isotropic filter in the thin-walled topography design variable field and the thin-walled thickness is constructed;

[0036] The unit thin-walled thickness determines the unit third filter radius of the isotropic filter in the thin-walled topography design variable field, i.e.:

[0037]

[0038]

[0039] represents a diagonal matrix of the filter radius of the second-step isotropic PDE filter, represents a diagonal matrix creation function.

[0040] Further, in step 3, according to the relationship expression between the third filter radius and the thin-walled thickness , the isotropic filter matrix in the thin-walled topography design variable field is obtained by combining the numerical discretization method:

[0041]

[0042] where is the filter matrix related to the unit thin-walled thickness , used in the isotropic filtering process of the thin-walled topography design variable field ; is a gradient operator, is a coefficient matrix, is a filtered field, is a unit shape function, is an integral region of the unit , and The first term and the second term are in a numerical discrete form.

[0043] Further, in step 4, the following steps are further included:

[0044] Step 41: Design variables are discretized with a second filter radius Anisotropic PDE filtering is performed for the filter radius to obtain a cell density , in the direction of the rib The second filter radius is set in the direction of the rib tends to infinity;

[0045] Step 42: Based on the filtering, a clear 0-1 distribution topology can be obtained by combining a Sigmoid projection function, the first Cell density after cell filtering Cell density obtained after projection is:

[0046]

[0047] In the formula, is the sharpness of the projection, is the projection threshold of the cell , the first represents the first Cell density after cell filtering Cell density obtained after projection

[0048] Step 43: The anisotropic filtered field is projected with the first sharpness , the first threshold as parameters to obtain , set ; wherein the first threshold is a vector composed of the normalized height of the cell along the rib direction;

[0049] An isotropic filter matrix is combined to perform isotropic filtering on to obtain a cell density ; according to the spatial gradient norm field definition, the spatial gradient norm field of the cell density is calculated to obtain the final thick-thin wall morphology field .

[0050] Further, in step 43, the spatial gradient norm of the cell e is:

[0051]

[0052] wherein, is the base direction of the three-dimensional spatial gradient, is the direction gradient calculation matrix, is the unit density corresponding node density, the value of which is derived from the calculation of implementing isotropic filtering obtains:

[0053]

[0054] is the corresponding unit density field node density field vector, indicates the node density field after the third step of isotropic filtering;

[0055] the spatial gradient norm field is normalized:

[0056]

[0057]

[0058] wherein, is the normalization factor, for the unit its normalization factor satisfies , is the unit thin-walled thickness;

[0059] then the is projected with the second sharpness , the second threshold as the parameters to obtain the final thickening thin-walled topography field .

[0060] Further, in step 5, by performing anisotropic filtering on the stiffening variable field with a fourth filtering radius and Sigmoid projection with the third sharpness , the third threshold as the parameters, the rib field is obtained to describe the unidirectional distribution of rib characteristics; wherein the third threshold is the vector composed of the normalized height of the unit along the stiffening direction.

[0061] Further, in step 6, the elastic modulus and the density in the design domain are designed as:

[0062]

[0063] where, to avoid the numerical singularity of the minimum elastic modulus, is the elastic modulus of the solid element, , is the penalty factor, , denotes the final thickening thin-walled topography field, denotes the rib field.

[0064] Further, in step 8, the structural flexibility and the mass sensitivity with respect to the design variables can be obtained by the following formula:

[0065]

[0066]

[0067] where, is the structural flexibility, denotes the volume fraction constraint, denotes the element volume, denotes the density of the element , the subscripts and both denote the element number, denotes the design variable of the element h, denotes the element node displacement vector, denotes the element elastic modulus, denotes the element stiffness matrix;

[0068] can be expanded by the chain rule:

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] to avoid the numerical singularity of the minimum elastic modulus, , is the penalty factor, denotes the final thickening thin-walled topography field of the element e, denotes the stiffener field, is the density of element e, denotes the thin-walled thickness design variable field in the element variable, denotes the thin-walled topography design variable field in the element variable, denotes the stiffened design variable field in the element variable, denotes the stiffener field in the element variable;

[0076] Next, the derivation of and is as follows:

[0077] where, can be expanded using the chain rule:

[0078]

[0079] Substituting into yields:

[0080]

[0081] In the formula, is the normalized spatial gradient norm field of element e, is the second sharpness, is the base direction of the three-dimensional spatial gradient, is the directional gradient calculation matrix, is the element density corresponding to the node density, which satisfies:

[0082]

[0083] Take the partial derivative of both sides of the above formula:

[0084]

[0085] According to the calculation formula of the isotropic filtering matrix

[0086] , the derivation of is as follows: Substituting yields:

[0087]

[0088] And by the above-mentioned way And The derivation process.

[0089] The present application has the following advantages:

[0090] The design method provided by the present application improves the design freedom of thin-walled stiffened structures to a new dimension, improves the lightweight design level and design efficiency of thin-walled stiffened structures, and provides a new technical path for high-performance lightweight design of vehicle structures, which has important engineering application value in the fields of aerospace, new energy vehicles and the like.

[0091] The present application adopts two-step anisotropic-isotropic PDE filtering and Sigmoid projection method to extract the thin-walled topography distribution in space, and introduces the thin-walled thickness design variable into the isotropic filtering, which realizes the generation of non-uniform thickness thin-walled and the controllable range of thin-walled thickness while ensuring the continuity of material distribution.

[0092] The present application combines the characteristics of isotropic filtering and anisotropic filtering, adopts multi-step filtering and projection operation, and effectively describes the variable-thickness thin-walled feature and rib geometric constraint. This method is based on the continuum density method topology optimization framework and is easy to integrate into existing simulation optimization software.

[0093] The present application develops an integrated concurrent topology optimization model of thin-walled stiffened structure. In the optimization iteration, the thin-walled topography variable, the thin-walled thickness variable and the stiffened design variable are updated at the same time, which overcomes the problem of low optimization efficiency and falling into local optimum by using the current serial optimization strategy.

[0094] The present application uses PDE filtering to replace the density filtering used in the existing method, which not only improves the definition efficiency of the filtering matrix, but also can be extended to parallel computing, which is helpful for processing large-scale optimization tasks. BRIEF DESCRIPTION OF DRAWINGS

[0095] Figure 1 A flowchart of thin-walled stiffened structure integrated optimization design of thin-walled topography-thickness and rib layout-topology constructed by the present application;

[0096] Figure 2 A schematic diagram for describing the variable-thickness thin-walled topography distribution and rib feature by multi-step PDE filtering and Sigmoid projection operation of the present application;

[0097] Figure 3 A schematic diagram of an installation example of a motor suspension bracket in a new energy vehicle front cabin of the present application;

[0098] Figure 4 A design domain and design working condition of a motor suspension bracket of the present application; Figure 3 ​

[0099] Figure 5 For the present invention Figure 4 The example demonstrates topology optimization results with compliance minimization as the objective.

[0100] Figure 6 For the present invention Figure 5 A schematic diagram of the thickened thin-walled morphology resulting from topology optimization. Detailed Implementation

[0101] The present invention will be further described below with reference to specific embodiments, and the advantages and features of the present invention will become clearer as a result. However, these embodiments are merely exemplary and do not constitute any limitation on the scope of the present invention. Those skilled in the art should understand that modifications or substitutions can be made to the details and form of the technical solutions of the present invention without departing from the spirit and scope of the present invention, but all such modifications and substitutions fall within the protection scope of the present invention.

[0102] like Figure 1 As shown, this example provides an integrated optimization method for thin-walled stiffened structures, encompassing thin-walled morphology, thickness, rib layout, and topology. The method specifically includes the following steps:

[0103] Step 1: Establish a finite element model according to the design requirements, determine the design domain, and initialize the thin-wall thickness field. Thin-walled morphology field and reinforced variable field A topology optimization model with structural flexibility as the objective and volume fraction as the constraint is established. The physical parameters and optimization parameters of the optimization model are initialized, and the minimum thin-wall thickness is set. and maximum thin wall thickness .

[0104] In this embodiment, the topology optimization model with structural flexibility as the objective and volume fraction as the constraint is as follows:

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111] In the formula, Indicates constraints. Represents the transpose of a matrix; Represents the overall stiffness matrix of the structure. and denote global displacement and load vectors; is the element number, denotes the number of design domain elements; denotes the element node displacement vector, denotes the element stiffness matrix, is the element elastic modulus; is the thin-walled thickness design variable field, is the thin-walled topography design variable field, is the stiffened design variable field; denotes the volume fraction constraint; is the volume fraction, is the element density, is the element volume; denotes the predetermined threshold value.

[0112] Step 2: Perform isotropic PDE filtering on the thin-walled thickness field to establish the filtered field and the interpolation function of the thin-walled thickness and obtain the isotropic filtered field for the thin-walled topography design variable field and the relationship expression between the third filtering radius and the thin-walled thickness .

[0113] First, isotropic PDE filtering is used to avoid the checkerboard phenomenon and grid dependence in the thin-walled thickness field. The solution format of PDE filtering is as follows:

[0114]

[0115] In the formula, is the gradient operator, is the density field before filtering, is the density field after filtering, and the coefficient matrix is defined as:

[0116] ; ; ;

[0117] In the formula, are the three basis vectors of the element filtering direction coordinate system, is the matrix composed of the three basis vectors, are the filtering radii corresponding to the three basis vector directions, is the diagonal matrix corresponding to the three-direction filtering radii. If are equal to each other, it is an isotropic filter, otherwise it is an anisotropic filter.

[0118] Performing isotropic PDE filtering with first filtering radius in three base vector directions of the unit cell satisfying , the filtered field is represented as an interpolation function of the unit cell thickness :

[0119]

[0120] where and are the minimum and maximum values of the unit cell thickness, respectively.

[0121] Unit cell thickness determines the unit cell third filtering radius of the isotropic filter in the thin-wall extraction strategy , i.e.:

[0122]

[0123]

[0124] Step 3: According to the relationship expression between the third filtering radius and the unit cell thickness established in step 2, combined with the numerical discretization method, the isotropic filtering matrix used in the thin-wall topography design variable field is obtained:

[0125]

[0126] where, is the filtering matrix related to the unit cell thickness , used in the isotropic filtering process of the thin-wall topography design variable field ; is the gradient operator, is the coefficient matrix, is the filtered field, is the unit cell shape function, is the integral region of the unit cell , and are the first and second items in the numerical discretization form.

[0127] Step 4: According to the isotropic filtering matrix obtained in step 3, through two-step anisotropic-isotropic filtering and Sigmoid projection operation, the intermediate field and the variable-thickness thin-wall topography field are extracted.

[0128] Step 41: The thin-wall topography design variable field is filtered by the isotropic filter With the second filter radius Anisotropic PDE filtering is performed on the filter radius to obtain the cell density. In the direction of rib raising Set the second filter radius. It tends towards infinity.

[0129] Step 42: Based on filtering, combining the Sigmoid projection function can yield a clear 0-1 distribution topology. Cell density after cell filtering The element density obtained after projection for:

[0130]

[0131] In the formula, For the sharpness of the projection, For unit The projection threshold, Indicates the first Cell density after cell filtering The element density is obtained after projection.

[0132] Step 43: Apply the anisotropic filtering to the filter. The field with the first sharpness First threshold Projecting the parameters yields ,set up Among them, the first threshold It is a vector consisting of the normalized height of the element along the stiffening direction.

[0133] Combined with the isotropic filtering matrix defined in step 3 ,right Isotropic filtering is performed to obtain the cell density. ;Calculate the element density according to the definition of the spatial gradient norm field. The spatial gradient norm of unit e :

[0134]

[0135] In the formula, These are the basis directions of the gradient in three-dimensional space. for directional gradient calculation matrix unit density The corresponding node density, its value is derived from the... Obtained by performing isotropic filtering:

[0136]

[0137] express The node density field after the third isotropic filtering step; the spatial gradient norm field. Normalization is performed:

[0138]

[0139]

[0140] In the formula, As a normalization factor, for the unit Its normalization factor satisfies .

[0141] Then on With second sharpness Second threshold Projecting the parameters yields the final variable-thickness thin-wall morphology field. Each unit uses the same threshold, i.e. .

[0142] Step 5: By analyzing the reinforced variable field Perform with the fourth filter radius Anisotropic filtering and with third sharpness Third threshold The rib field is obtained by projecting the sigmoid parameter onto the rib field. To describe the characteristics of unidirectionally distributed ribs. Among them, the threshold... It is a vector consisting of the normalized height of the element along the stiffening direction.

[0143] Step 6: Combine the intermediate fields obtained in steps 4 and 5 thin-walled field and tendon field A material interpolation model is constructed to obtain the elastic modulus within the design domain. and density :

[0144]

[0145] In the formula, To avoid numerically singular minimum elastic moduli, The elastic modulus of the solid element. , This is a penalty factor.

[0146] Step 7: Perform finite element analysis using the material interpolation model to calculate the structural flexibility.

[0147] Step 8: Solve the structure flexibility according to the derived sensitivity formula and density Sensitivity of the design variable with respect to the design variable

[0148]

[0149]

[0150] where denotes the design variable, the subscript and both denote the element number, which can be expanded by the chain rule:

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] Next, the derivations of and are as follows:

[0158] where can be expanded by the chain rule:

[0159]

[0160] Substituting into yields:

[0161]

[0162] where is the base direction of the three-dimensional space gradient, is the directional gradient calculation matrix, is the element density corresponding to the node density, which satisfies:

[0163]

[0164] Taking the partial derivative of the above formula on both sides yields ​

[0165]

[0166]

[0167] According to the calculation formula of the second step of the isotropic filter matrix in step 3 , the derivation , and the input , the derivation

[0168]

[0169] So far, the derivation is complete, and the derivation process of and is similar to the above, and will not be repeated.

[0170] Step 9: According to the derived sensitivity, the thin-walled thickness field , the thin-walled topography field and the stiffening variable field are updated by using the method of moving asymptotes (MMA).

[0171] Step 10: If the projection sharpness reaches the maximum sharpness and the maximum change of the design variable is less than 0.01 at the first iteration step, it is considered that the convergence condition is met, the optimization iteration is stopped and the optimization result is output; otherwise, steps 2 to 9 are repeated.

[0172] The technical implementation method disclosed by the application is as follows:

[0173] This example is a three-dimensional motor suspension support, which is installed at the mounting position of the front compartment of a new energy electric vehicle as shown in Figure 3 , the loading and constraint conditions are as shown in Figure 4 , and the filter boundary condition adopts the Dirichlet boundary condition.

[0174] Step 1: Determine the design domain of the 3D motor suspension support, and divide the finite element grid according to the unit size of 2 mm; under the braking working condition, the suspension support bears a horizontal force of 8000N; initialize the thin-walled thickness field , the thin-walled topography field and the stiffening variable field range in [0, 1]; set the elastic modulus of the material , the Poisson's ratio ; set the z direction as the stiffening direction, the minimum thin-walled thickness and the maximum thin-walled thickness ; the upper limit of the structure volume fraction 0.6, and a mathematical model of the optimization problem is established with the flexibility as the objective function.

[0175] Step 2-3: Filtering the thin-walled thickness field Performing filtering radius Isotropic PDE filtering, establishing the filtering field And the interpolation function of the thin-walled thickness , constructing the relationship expression of the isotropic filtering radius And the thin-walled thickness According to the established relationship expression of the filtering radius And the thin-walled thickness , combined with the numerical discrete method, the second-step isotropic filtering matrix is obtained.

[0176] Step 4: As shown in Figure 2 , the intermediate field and the variable-thickness thin-walled morphology field are obtained through two-step anisotropic-isotropic PDE filtering and Sigmoid projection. Let represent the Y direction as the rib direction, then the filtering radius of the anisotropic filter is taken as . The isotropic filter is defined in step 2-3. The projection sharpness and are initially set to 4, multiplied by 2 every 50 steps, and the upper limit is 64; the projection threshold is the relative height of the unit in the rib direction, and the projection threshold is set to 0.5.

[0177] Step 5: Through anisotropic filtering of the ribbed variable field and Sigmoid projection with sharpness and threshold as parameters, the rib field is obtained to describe the characteristics of the unidirectional distributed ribs. Wherein, let represent the z direction as the rib direction, then the filtering radius of the anisotropic filter is taken as ; and the sharpness updating strategy is the same as the projection sharpness and in step 4, and the threshold is a vector composed of the normalized height of the unit along the rib direction.

[0178] Step 6: Combined with the intermediate field , the thin-walled field and the rib field obtained in steps 4 and 5, the material interpolation model is constructed, and the penalty factors , Thus, the elastic modulus in the design domain is obtained and density .

[0179] Step 7-8: finite element analysis is carried out by combining the material interpolation model, the flexibility of the structure is calculated, and the flexibility of the structure and mass about the design variable is calculated according to the derived sensitivity formula.

[0180] Step 9-10: the sensitivity analysis results are submitted to the MMA solver to update the design variables. If the first iteration step, the projection sharpness , reaches the maximum sharpness and the maximum change of the design variable is less than 0.01, it is considered that the convergence condition is met, the optimization iteration is stopped and the optimization result is output; otherwise, steps 2 to 9 are repeated. The final optimization result is shown in Figure 5 and Figure 6 ; wherein, Figure 5 shows the overall optimization of the thin-walled stiffened suspension support, Figure 6 indicates the thin-walled topography and thin-walled thickness distribution.

[0181] The present application is not limited to the above specific embodiments, and those skilled in the art can implement the present application in other various specific embodiments according to the content disclosed in the examples and drawings, therefore, any design using the design structure and idea of the present application, with some simple transformation or change, falls within the protection scope of the present application.

Claims

1. A method for integrated optimization design of thin-walled reinforced structures, characterized in that, The integrated optimization design method for thin-walled reinforced structures includes the following steps: Step 1: Establish a topology optimization finite element model with structural flexibility as the objective and volume fraction as the constraint, and set the minimum and maximum thin-wall thickness; Step 2: Perform isotropic PDE filtering on the thin-wall thickness field to obtain the relationship between radius and thin-wall thickness in the isotropic filtering of the variable field used for thin-wall topography design; Step 3: Based on the relationship between radius and thin wall thickness, obtain the isotropic filtering matrix in the variable field used for thin wall topography design; Step 4: Extract the intermediate field and thin-wall field through two-step anisotropic-isotropic filtering and sigmoid projection operations; Step 5: Obtain the stiffener field by performing anisotropic filtering and Sigmoid projection on the stiffened variable field; Step 6: Combine the intermediate field, thin-wall field, and stiffener field to construct a material interpolation model; Step 7: Perform finite element analysis using the material interpolation model to calculate the structural flexibility; Step 8: Solve to obtain the structural flexibility and density, and their sensitivity to design variables; Step 9: Based on the derived sensitivity, update the thin-wall thickness field, thin-wall morphology field, and stiffening variable field using the moving asymptote method; Step 10: When the convergence condition is met, the optimization iteration stops and the optimization result is output; otherwise, repeat steps 2 to 9.

2. The integrated optimization design method for thin-walled reinforced structures according to claim 1, characterized in that, In step 1, the thin-wall thickness field is initialized. Thin-walled morphology field and reinforced variable field A topology optimization model is established with structural flexibility as the objective and volume fraction as the constraint. The physical and optimization parameters of the optimization model are initialized, and the minimum thin-wall thickness is set. and maximum thin wall thickness ; The topology optimization model with structural flexibility as the objective and volume fraction as the constraint is as follows: ； ； ； ； ； ； In the formula, This represents minimizing structural flexibility. Indicates constraints. Represents the transpose of a matrix; Represents the overall stiffness matrix of the structure. and Represents the global displacement and load vectors; For unit numbering, Indicates the number of design domain elements; Represents the element node displacement vector. Represents the element stiffness matrix. The unit elastic modulus; Design variable fields for thin-wall thickness. Design variable fields for thin-walled morphology. Variable fields for reinforcement design; Indicates volume fraction constraint; It is the volume fraction. For unit density, Unit volume; This indicates the predetermined threshold.

3. The integrated optimization design method for thin-walled reinforced structures according to claim 1, characterized in that, In step 2, isotropic PDE filtering is first used to avoid checkerboard patterns and grid dependence in the thin-walled thickness field, and a filter field is established. With thin wall thickness The interpolation function, PDE filtering, has the following solution format: ； In the formula, For gradient operators, This is the density field before filtering. The filtered density field, coefficient matrix Defined as: ； ； ； In the formula, These are the three basis vectors of the unit filter direction coordinate system. The matrix formed by these three basis vectors. Let be the filtering radius corresponding to the directions of the three basis vectors. This is the diagonal matrix corresponding to the three-directional filtering radii; For thin-walled thickness field For isotropic PDE filtering, the first filtering radius in the directions of its three basis vectors is... satisfy After filtering Field and thin wall thickness The interpolation function is expressed as: ； In the formula, and These are the minimum and maximum allowable values ​​for thin-wall thickness, respectively; Secondly, the third filtering radius for isotropic filtering in the thin-walled morphology design variable field is constructed. and thin wall thickness Relational expressions; Unit thin wall thickness The third filter radius of the element in the isotropic filter in the field that determines the design variables of the thin-walled topography , Right now: ; ； This represents the diagonal matrix of the filtering radius for the second-step isotropic PDE filtering. This represents the function for creating a diagonal matrix.

4. The integrated optimization design method for thin-walled reinforced structures according to claim 1, characterized in that, In step 3, based on the third filter radius and thin wall thickness Based on the relational expression and combined with numerical discretization methods, the isotropic filtering matrix in the thin-walled topography design variable field is obtained: ； In the formula, To match the unit thin wall thickness The relevant filtering matrix is ​​used for the design variable field of thin-walled morphology. Isotropic filtering process; For gradient operators, The coefficient matrix, For the filtered field, For unit shape functions, For unit The integration region, and For the first and second terms in the numerical discrete form.

5. The integrated optimization design method for thin-walled reinforced structures according to claim 1, characterized in that, Step 4 also includes the following steps: Step 41: Design variables With the second filter radius Anisotropic PDE filtering is performed on the filter radius to obtain the cell density. In the direction of rib raising Set the second filter radius. It tends towards infinity; Step 42: Based on filtering, combining the Sigmoid projection function can yield a clear 0-1 distribution topology. Cell density after cell filtering The element density obtained after projection for: ； In the formula, For the sharpness of the projection, For unit The projection threshold, Indicates the first Cell density after cell filtering The element density obtained after projection; Step 43: Apply the anisotropic filtering to the filter. The field with the first sharpness First threshold Projecting the parameters yields ,set up Among them, the first threshold It is a vector consisting of the normalized height of the element along the stiffening direction; Combined with isotropic filter matrix ,right Isotropic filtering is performed to obtain the cell density. ;Calculate the element density according to the definition of the spatial gradient norm field. Spatial gradient norm field The final morphological field of the thickened thin-walled structure was calculated. .

6. The integrated optimization design method for thin-walled reinforced structures according to claim 5, characterized in that, In step 43, for the spatial gradient norm of unit e for: ； In the formula, These are the basis directions of the gradient in three-dimensional space. for directional gradient calculation matrix unit density The corresponding node density, its value is derived from the... Obtained by performing isotropic filtering: ； For the corresponding unit density field The node density field vector, express The node density field after the third step of isotropic filtering; For spatial gradient norm fields Normalization is performed: ； ； In the formula, As a normalization factor, for the unit Its normalization factor satisfies , The unit thin-wall thickness; Then on With second sharpness Second threshold Projecting the parameters yields the final variable-thickness thin-wall morphology field. .

7. The integrated optimization design method for thin-walled reinforced structures according to claim 1, characterized in that, In step 5, by adjusting the reinforced variable field Perform with the fourth filter radius Anisotropic filtering and with third sharpness Third threshold The rib field is obtained by projecting the sigmoid parameter onto the rib field. To describe the rib features of a unidirectional distribution; where the third threshold It is a vector consisting of the normalized height of the element along the stiffening direction.

8. The integrated optimization design method for thin-walled reinforced structures according to claim 1, characterized in that, In step 6, the elastic modulus within the design domain and density for: ； ； In the formula, To avoid numerically singular minimum elastic moduli, The elastic modulus of the solid element. , As a penalty factor, , This represents the final thickened thin-wall morphology field. It indicates the tendon field.

9. The integrated optimization design method for thin-walled reinforced structures according to claim 1, characterized in that, In step 8, the structural compliance is obtained by solving. and quality The sensitivity relative to the design variables can be obtained from the following formula: ； ； In the formula, For structural flexibility, Indicates volume fraction constraint, Represents the unit volume. Representation unit density, subscript and Both represent unit numbers. This represents the design variables of unit h. Represents the element node displacement vector. Represents the elastic modulus of a single element. Represents the element stiffness matrix; This can be expanded using the chain rule: ； ； ； ； ； ； To avoid numerically singular minimum elastic moduli, , As a penalty factor, This represents the final thickened thin-walled topography field of element e. Indicates the ribbed field. Let e ​​be the density of element e. Represents the design variable field of thin-wall thickness The Middle Unit variable, Represents the design variable field of thin-walled morphology The Middle Unit variable, Represents the design variable field of reinforcement The Middle Unit variable, Indicates the ribbed field The Middle Unit variables; Next, respectively and Derivation: in, This can be expanded using the chain rule: ； Will Substitution have to: ； In the formula, The spatial gradient norm field of the normalized unit e, The second sharpness, These are the basis directions of the gradient in three-dimensional space. for directional gradient calculation matrix unit density The corresponding node density satisfies: ； For the left and right sides of the above equation Find the partial derivative: ； ； Based on the isotropic filtering matrix The calculation formula, derivation , bring in ,get: ； Obtain through the above methods and The derivation process.

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