A thin-walled stiffened structure integrated optimization design method

Abstract

The application discloses a kind of thin-walled stiffened structure integrated optimization design method, it is related to the field of super-lightweight structure design method, including establishing the topology optimization finite element model with structural flexibility as target, volume fraction as constraint;The relationship of radius and thin-walled thickness used in isotropic filtering in thin-walled topography design variable field is obtained;The isotropic filtering matrix used in thin-walled topography design variable field is obtained;Through two-step anisotropic-isotropic filtering and Sigmoid projection operation, intermediate field and thin-walled field are extracted;Anisotropic filtering and Sigmoid projection are carried out to stiffening variable field to obtain rib field;Material interpolation model is constructed in combination with intermediate field, thin-walled field and rib field;The flexibility of structure is calculated;Based on structural flexibility, density and sensitivity;According to sensitivity, thin-walled thickness field, thin-walled topography field and stiffening variable field are updated.The application improves the lightweight design effect and efficiency of thin-walled stiffened structure, and has important engineering application value in multiple high-tech fields.

Description

Technical Field

[0001] This invention relates to the field of ultra-lightweight structural design methods, and in particular to an integrated optimization design method for thin-walled stiffened structures based on thin-wall morphology, thickness, rib layout, and topology. Background Technology

[0002] Thin-walled stiffened structures are a type of structure that combines lightweight and high strength. By introducing an optimized distribution of stiffeners into a thin-walled matrix, the stiffness, stability, and load-bearing efficiency of the structure are significantly improved. Combined with integrated molding technology, complex curved surfaces and stiffener layouts can be manufactured in a coordinated manner, making them widely used in aerospace, new energy vehicles, shipbuilding, and other fields.

[0003] Due to the weight limitations of their powertrain systems, electric vehicles generally weigh 200-400 kg more than their gasoline-powered counterparts of the same size. Studies show that for every 10 kg reduction in vehicle weight, the driving range can increase by approximately 2.5 km. To ensure sufficient driving range, vehicle electrification faces increasingly stringent lightweighting requirements. In the overall vehicle structure, key components such as shock absorber towers, front bulkheads, longitudinal beams, and battery pack housings widely employ thin-walled reinforced designs, offering significant weight reduction potential. Research into optimized design methods for thin-walled reinforced structures can significantly reduce overall vehicle weight and improve driving range.

[0004] The design and optimization of thin-walled stiffened structures involves a multi-parameter coupling problem, including key parameters such as thin-wall morphology, thickness distribution, and stiffener topology and spatial layout. However, problems such as incomplete parameter optimization considerations, suboptimal solutions generated by sequential optimization strategies, and difficulties in geometric modeling and characterization limit the lightweighting capabilities of thin-walled stiffened structures. Summary of the Invention

[0005] To address the aforementioned challenges, this invention proposes an integrated optimization design for thin-walled stiffened structures, encompassing thin-walled morphology, thickness, rib layout, and topology. This method employs two-step filtering and projection techniques to extract the thin-walled morphology and thickness distribution features. Based on anisotropic filtering and variable threshold projection techniques, it establishes a parametric characterization of the rib layout and topological configuration. A material interpolation model is then constructed to achieve a unified description of these two types of features, thereby realizing the collaborative optimization design of thin-walled morphology, thickness, rib layout, and topology.

[0006] This invention discloses an integrated optimization design method for thin-walled reinforced structures, which includes the following steps:

[0007] 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;

[0008] 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;

[0009] 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;

[0010] Step 4: Extract the intermediate field and thin-wall field through two-step anisotropic-isotropic filtering and sigmoid projection operations;

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

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

[0013] Step 7: Perform finite element analysis using the material interpolation model to calculate the structural flexibility;

[0014] Step 8: Solve to obtain the structural flexibility and density, and their sensitivity to design variables;

[0015] 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;

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

[0017] Furthermore, 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.

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

[0019] The topology optimization model with structural flexibility as the objective and volume fraction as the constraint is as follows:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] 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.

[0027] Furthermore, 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:

[0028]

[0029] In the formula, For gradient operators, This is the density field before filtering. The filtered density field, coefficient matrix Defined as:

[0030]

[0031]

[0032] 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;

[0033] 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:

[0034]

[0035] In the formula, and These are the minimum and maximum allowable values ​​for thin-wall thickness, respectively;

[0036] Secondly, the third filtering radius for isotropic filtering in the thin-walled morphology design variable field is constructed. and thin wall thickness Relational expressions;

[0037] 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:

[0038]

[0039]

[0040] 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.

[0041] Furthermore, 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:

[0042]

[0043] 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.

[0044] Furthermore, step 4 also includes the following steps:

[0045] 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;

[0046] 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:

[0047]

[0048] 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;

[0049] 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 heights of the elements along the stiffening direction;

[0050] Combined with isotropic filter matrix ,right Isotropic filtering is performed to obtain the cell density. ;Calculate the element density according to the definition of spatial gradient norm field. Spatial gradient norm field The final morphological field of the thickened thin-walled structure was calculated. .

[0051] Furthermore, in step 43, for the spatial gradient norm of unit e for:

[0052]

[0053] In the formula, Let be 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:

[0054]

[0055] For the corresponding unit density field The node density field vector, express The node density field after the third step of isotropic filtering;

[0056] For spatial gradient norm fields Normalization is performed:

[0057]

[0058]

[0059] In the formula, As a normalization factor, for the unit Its normalization factor satisfies , The unit thin-wall thickness;

[0060] Then on With second sharpness Second threshold Projecting the parameters yields the final variable-thickness thin-wall morphology field. .

[0061] Furthermore, 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.

[0062] Furthermore, in step 6, the elastic modulus within the design domain is... and density for:

[0063]

[0064] 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.

[0065] Furthermore, 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:

[0066]

[0067]

[0068] 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;

[0069] This can be expanded using the chain rule:

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] 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 area. For 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;

[0077] Next, respectively and Derivation:

[0078] in, This can be expanded using the chain rule:

[0079]

[0080] Will Substitution have to:

[0081]

[0082] In the formula, The spatial gradient norm field of the normalized unit e, The second sharpness, Let be the basis directions of the gradient in three-dimensional space. for directional gradient calculation matrix unit density The corresponding node density satisfies:

[0083]

[0084] For the left and right sides of the above equation Find the partial derivative:

[0085]

[0086]

[0087] Based on the isotropic filtering matrix The calculation formula is derived. , bring in ,get:

[0088]

[0089] Obtain through the above methods and The derivation process.

[0090] The beneficial effects achieved by this invention are:

[0091] The design method provided by this invention elevates the design freedom of thin-walled stiffened structures to a new dimension, improves the lightweight design level and efficiency of thin-walled stiffened structures, and provides a brand-new technical path for high-performance lightweight design of vehicle structures. It has important engineering application value in aerospace, new energy vehicles and other fields.

[0092] This invention employs a two-step anisotropic-isotropic PDE filtering and Sigmoid projection method to extract the spatial distribution of thin-wall morphology. The thin-wall thickness design variable is introduced into the isotropic filtering, which, while ensuring the continuity of material distribution, achieves the generation of non-uniform thickness thin walls and controllable thin-wall thickness range.

[0093] This invention combines the characteristics of isotropic and anisotropic filtering, and employs multi-step filtering and projection operations to effectively describe the characteristics of thin-walled structures with varying thicknesses and the geometric constraints of ribs. This method is based on the continuum density method topology optimization framework and is easy to integrate into existing simulation optimization software.

[0094] This invention develops an integrated concurrent topology optimization model for thin-walled stiffened structures. In the optimization iteration, the thin-walled morphology variables, thin-walled thickness variables, and stiffening design variables are updated simultaneously, overcoming the problems of getting trapped in local optima and low optimization efficiency in the current serial optimization strategy.

[0095] This invention replaces the density filtering used in existing methods with PDE filtering, which not only improves the efficiency of defining the filtering matrix, but also extends to parallel computing, which helps to handle large-scale optimization tasks. Attached Figure Description

[0096] Figure 1 A flowchart illustrating the integrated optimization design of a thin-walled stiffened structure based on thin-walled morphology, thickness, rib layout, and topology, as described in this invention.

[0097] Figure 2 This is a schematic diagram illustrating the morphological distribution and rib features of a variable-thickness thin-walled structure described by the present invention through multi-step PDE filtering and Sigmoid projection operations.

[0098] Figure 3 This is a schematic diagram illustrating an example of the installation of a motor mounting bracket in the front compartment of a new energy vehicle according to the present invention.

[0099] Figure 4 For the present invention Figure 3 Design domain and operating conditions of motor suspension brackets;

[0100] Figure 5 For the present invention Figure 4 The example demonstrates topology optimization results with compliance minimization as the objective.

[0101] Figure 6 For the present invention Figure 5 A schematic diagram of the thickened thin-walled morphology resulting from topology optimization. Detailed Implementation

[0102] 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.

[0103] 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:

[0104] 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 .

[0105] In this embodiment, the topology optimization model with structural flexibility as the objective and volume fraction as the constraint is as follows:

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] In the formula, 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.

[0113] Step 2: Analyze the thickness field of the thin-walled structure. Perform isotropic PDE filtering and establish the filter field. With thin wall thickness The interpolation function is used to obtain the variable field for thin-walled morphology design. The third filter radius in isotropic filtering and thin wall thickness Relational expressions.

[0114] First, isotropic PDE filtering is used to avoid checkerboard patterns and grid dependence in the thickness field of thin walls. The solution format for PDE filtering is as follows:

[0115]

[0116] In the formula, For gradient operators, This is the density field before filtering. The filtered density field, coefficient matrix Defined as:

[0117]

[0118]

[0119] 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. If If the values ​​are equal, it is an isotropic filter; otherwise, it is an anisotropic filter.

[0120] 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:

[0121]

[0122] In the formula and These represent the minimum and maximum allowable values ​​for thin-wall thickness, respectively.

[0123] Unit thin wall thickness The third filter radius of the unit cell in the isotropic filter of the thin-wall extraction strategy determines the thin-wall extraction strategy. ,Right now:

[0124]

[0125]

[0126] Step 3: Based on the third filter radius established in Step 2 and thin wall thickness The relational expression, combined with numerical discretization methods, yields the isotropic filtering matrix in the variable field used for thin-walled topography design:

[0127]

[0128] 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.

[0129] Step 4: Based on the isotropic filtering matrix obtained in Step 3, extract the intermediate field through two-step anisotropic-isotropic filtering and sigmoid projection operations. and the morphology field of thin-walled structures with varying thickness .

[0130] Step 41: Design variable fields for thin-walled morphology 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.

[0131] 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:

[0132]

[0133] 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.

[0134] 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.

[0135] 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 spatial gradient norm field. The spatial gradient norm of unit e :

[0136]

[0137] In the formula, Let be 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:

[0138]

[0139] express The node density field after the third isotropic filtering step; the spatial gradient norm field. Normalization is performed:

[0140]

[0141]

[0142] In the formula, As a normalization factor, for the unit Its normalization factor satisfies .

[0143] 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. .

[0144] 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.

[0145] 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 :

[0146]

[0147] In the formula, To avoid numerically singular minimum elastic moduli, The elastic modulus of the solid element. , This is a penalty factor.

[0148] Step 7: Perform finite element analysis using the material interpolation model to calculate the structural flexibility.

[0149] Step 8: Solve for the structural compliance using the derived sensitivity formula. and density Relative to design variables The sensitivity can be obtained from the following formula:

[0150]

[0151]

[0152] In the formula, Indicates design variables, subscript and Both represent unit numbers. This can be expanded using the chain rule:

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159] Next, respectively and Derivation:

[0160] in, This can be expanded using the chain rule:

[0161]

[0162] Will Substitution have to:

[0163]

[0164] In the formula, Let be the basis directions of the gradient in three-dimensional space. for directional gradient calculation matrix unit density The corresponding node density satisfies:

[0165]

[0166] For the left and right sides of the above equation Taking the partial derivative, we can obtain

[0167]

[0168]

[0169] Based on the isotropic filtering matrix in step 3, step 2 The calculation formula is derived. , bring in ,get

[0170]

[0171] At this point, The derivation is complete, and and The derivation process is similar to that described above, so it will not be repeated here.

[0172] Step 9: Based on the derived sensitivity, update the thin-wall thickness field using the Method of Moving Asymptotes (MMA). Thin-walled morphology field and reinforced variable field .

[0173] Step 10: If the first During the iteration step, the projection sharpness Achieve maximum sharpness If the maximum change of the design variable is less than 0.01, then the convergence condition is considered met, the optimization iteration stops and the optimization result is output; otherwise, repeat steps 2 to 9.

[0174] The technical implementation method disclosed in this invention is as follows:

[0175] This embodiment is a three-dimensional motor suspension bracket, and its installation position in the front compartment of a new energy electric vehicle is as follows: Figure 3 As shown, the loading and constraint conditions are as follows: Figure 4 As shown, the filtering boundary conditions adopt Dirichlet boundary conditions.

[0176] Step 1: Determine the design domain of the 3D motor suspension bracket and divide it into finite element meshes with a unit size of 2mm; Under braking conditions, the suspension bracket is subjected to a horizontal force of 8000N; Initialize the thin-wall thickness field. Thin-walled morphology field and reinforced variable field The range is within [0,1]; set the elastic modulus of the material. Poisson's ratio Set the z-axis as the rib-raising direction, and the minimum thin-wall thickness. and maximum thin wall thickness Upper limit of structural volume fraction With a value of 0.6, a mathematical model for the optimization problem is established with compliance as the objective function.

[0177] Steps 2-3: For thin-walled thickness fields Perform filtering radius Isotropic PDE filtering, establishing the filter field With thin wall thickness The interpolation function is used to construct the isotropic filter radius. and thin wall thickness The relational expression. Based on the established filter radius. and thin wall thickness The relational expression is used, combined with numerical discretization methods, to obtain the isotropic filtering matrix in the second step. .

[0178] Step 4: As Figure 2 As shown, the intermediate field is obtained through two-step anisotropic-isotropic PDE filtering and sigmoid projection. and the morphology field of thickened thin walls .use If the Y-axis is the rib-forming direction, then the filter radius of the anisotropic filter is taken as... The isotropic filter has been defined in steps 2-3. Projection sharpness. and The initial value is 4, multiplied by 2 every 50 iterations, with an upper limit of 64; projection threshold. The relative height of the element in the rib direction, and the projection threshold. Set it to 0.5.

[0179] Step 5: By analyzing the reinforced variable field Perform anisotropic filtering and sharpness 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, using... If the z-axis is the rib-forming direction, then the filtering radius of the anisotropic filter is taken as... ; and sharpness The update strategy is the same as the projection sharpness in step 4. and threshold It is a vector consisting of the normalized height of the element along the stiffening direction.

[0180] Step 6: Combine the intermediate fields obtained in steps 4 and 5 thin-walled field and tendon field Construct a material interpolation model and set a penalty factor. , Thus, the elastic modulus within the design domain is obtained. and density .

[0181] Steps 7-8: Perform finite element analysis using the material interpolation model to calculate the structural flexibility, and determine the structural flexibility based on the derived sensitivity formula. and quality Sensitivity analysis was performed on the design variables.

[0182] Steps 9-10: Submit the sensitivity analysis results to the MMA solver to update the design variables. If the... During the iteration step, the projection sharpness , Achieve maximum sharpness If the maximum change in the design variable is less than 0.01, the convergence condition is considered met, the optimization iteration stops, and the optimization result is output; otherwise, steps 2 to 9 are repeated. The final optimization result is as follows. Figure 5 and Figure 6 As shown; where, Figure 5 The overall optimization of the thin-walled reinforced suspension bracket is demonstrated. Figure 6 This indicates the morphology and thickness distribution of the thin-walled structure.

[0183] This invention is not limited to the specific embodiments described above. Those skilled in the art can implement this invention using various other specific embodiments based on the disclosed content of the embodiments and accompanying drawings. Therefore, any design that adopts the design structure and concept of this invention and makes some simple changes or modifications falls within the protection scope of this invention.

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. 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.

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 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.

4. 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. .

5. The integrated optimization design method for thin-walled reinforced structures according to claim 4, 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. .

6. 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.

7. 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.

8. 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 area. For 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 rib 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.

Images