Topology and morphology integrated optimization design method for thin-walled structure

Abstract

The invention provides a topology and morphology integrated optimization design method for a thin-walled structure. The method comprises the steps that 1, a finite element model is established according to design requirements; 2, extracting a thin-wall structure morphology distribution field # imgabs0 # through two-step partial differential equation filtering and Heavide projection operation; 3, constructing a material attribute rational approximation model in combination with the thin-wall morphology distribution field # imgabs1 # and the topological density field v obtained in the step 2, thereby obtaining an elastic modulus E and mass rho in a design domain; 4, performing finite element analysis in combination with the material interpolation model, and calculating the flexibility of the structure; 5, solving to obtain the sensitivity of the structure flexibility and the quality relative to the design variables; step 6, updating the morphology design variable mu and the topology design variable v of the thin plate by adopting a moving asymptote method; and step 7, when a convergence condition is satisfied, stopping optimization iteration and outputting an optimization result. According to the method, the maximum forming angle of the thin-wall structure is controlled by adjusting the filtering radius of the anisotropic filter, and the stamping forming process is met.

Description

Technical Field

[0001] The present invention relates to the field of ultra-lightweight structure design methods, and in particular to a method for integrated optimization design of thin-wall structure topology and morphology. Background Art

[0002] Thin-walled structure is a lightweight structure with a high stiffness-to-mass ratio. Combined with the stamping forming process, it can realize the manufacture of complex thin-walled shapes. It has the advantages of high material utilization, large production scale and low economic cost. It is widely used in the automotive, shipbuilding and aerospace industries.

[0003] In recent years, electric vehicle technology has flourished. However, due to powertrain mass limitations, electric vehicles typically weigh 200-400kg more than similarly sized fuel-powered vehicles. Research shows that for every 10kg reduction in vehicle weight, driving range increases by approximately 2.5km. To ensure vehicle range, electrification faces increasingly stringent lightweighting requirements. In automobile manufacturing, over 65% of components are stamped thin-walled structures. Therefore, achieving lightweight thin-walled design and reducing vehicle weight are crucial for enhancing the international competitiveness of the automotive industry and safeguarding national energy security.

[0004] Thin-walled structures are often discretized using shell elements due to their large surface characteristics, and lightweight design of thin-walled structures can be achieved by optimizing the thickness of the shell elements and the control points. However, the problem of fuzzy force transmission path identification and the inability to eliminate redundant materials by optimizing the control points alone has resulted in limited lightweighting capabilities of thin-walled structures. In order to address the above difficulties, the present invention proposes a method for integrated topology and morphology optimization design of thin-walled structures. This method extracts thin-walled morphology based on a two-step filtering and projection method, couples topological characterization variables, and constructs a material interpolation model that uniformly describes morphology and topology, thereby achieving integrated topology and morphology optimization design of thin-walled structures. This method expands the design freedom of thin-walled structures, improves the lightweight design level of thin-walled structures, and is expected to provide technical support for the high performance and lightweight design of vehicle structures. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for integrated optimization design of thin-walled structure topology and morphology, which identifies the morphology of thin-walled structures through two-step PDE filtering and Heaviside projection, constructs a material interpolation model describing the thin-walled morphology and topology based on the RAMP model, and realizes the integrated optimization design of thin-walled structure topology and morphology through the coordinated optimization of thin-walled morphology and topology, thereby maximizing the mechanical properties and lightweight level of the structure.

[0006] To achieve the above objectives, the specific technical solution of the present invention is as follows: A method for optimizing the topology and morphology of a thin-walled structure, characterized by:

[0007] Step 1: Establish a finite element model according to the design requirements, determine the design domain, and establish a topology optimization model with structural flexibility as the target and mass fraction as the constraint. Initialize the physical parameters, optimization parameters, and thin-wall thickness t of the optimization model. The topology optimization model is as follows:

[0008]

[0009] Where st represents the constraint condition, T represents the transpose of the matrix; K represents the total stiffness matrix of the structure, U and F represent the global displacement and load vectors; u e represents the unit node displacement vector, k e Represents the element stiffness matrix, e is the element number; N represents the number of design domain elements; μ e represents the cell density before filtering, v e represents the cell density of the topological field; μ is μ e The vector composed of v is v e The vector composed of g volf represents the mass fraction constraint; frac is the mass fraction, which is equal to the ratio of the structural mass ρ(μ,v) to the total mass ρ0 of the initial design domain; frac * represents a predetermined threshold;

[0010] Step 2: Extract the thin-walled structure morphology distribution field through two-step partial differential equation filtering and Heaviside projection operation

[0011] Step 3: Combine the thin-wall morphology distribution field obtained in step 2 and the topological density field v, constructing a rational approximation model of material properties, thereby obtaining the elastic modulus E and mass ρ in the design domain;

[0012] Step 4: Perform finite element analysis based on the material interpolation model to calculate the flexibility of the structure.

[0013] Step 5: Solve to obtain the sensitivity of structural flexibility and mass to design variables;

[0014] Step 6: Use the moving asymptote method to update the thin plate morphology design variable μ and topology design variable v;

[0015] Step 7: When the convergence condition is met, the optimization iteration stops and the optimization results are output. Otherwise, repeat steps 2 to 6.

[0016] Furthermore, in step 2, the mathematical expression of the partial differential equation filtering is:

[0017]

[0018] Where, is the gradient operator, μ is the density field before filtering, is the density field after filtering, and the coefficient matrix C is defined as:

[0019]

[0020] Where, are the three basis vectors of the three-dimensional stamping coordinate system, V is the matrix composed of the three basis vectors, is the filter radius corresponding to the three basis vector directions, r is the diagonal matrix corresponding to the three-directional filter radius; if If they are equal to each other, it is an isotropic filter, otherwise it is an anisotropic filter.

[0021] Furthermore, in step 2, the mathematical expression of the Heaviside projection is:

[0022]

[0023] Where β is the sharpness of the projection, η is the threshold of the projection, Represents the unit density after filtering of the i-th unit The cell density obtained after projection;

[0024] Through two filtering and projection operations, the thin-walled structure morphology distribution field can be obtained

[0025] Furthermore, in step 3, according to the derived sensitivity formula, the elastic modulus E and density ρ in the design domain are:

[0026]

[0027] Where, E min To avoid numerical singularities in the minimum elastic modulus, E0 is the elastic modulus of the solid element, q is the penalty factor, and ρ is the element mass.

[0028] Furthermore, in step 5, the sensitivity of the flexibility c and mass ρ to the design parameters can be obtained by the following formula:

[0029]

[0030] Beneficial effects of the present invention:

[0031] 1. The present invention realizes the coordinated optimization of the morphology and topology of the thin-walled structure, expands the design freedom of the thin-walled structure, and improves the mechanical properties of the thin-walled structure.

[0032] 2. The present invention uses an anisotropic filter to extract the neutral plane of the thin-walled structure, and adjusts the filter radius of the anisotropic filter on this basis, thereby controlling the maximum forming angle of the thin-walled structure to meet the stamping forming process.

[0033] 3. The present invention adopts two-step PDE filtering and Heaviside projection method to extract the thin-wall morphology distribution in space, which not only ensures the continuity of material distribution but also realizes the control of uniform and variable thin-wall thickness.

[0034] 4. The present invention constructs a functional mapping between the topological density of thin-walled structures and the elastic modulus of materials based on a rational approximation model of material properties, which improves the accuracy and reliability of structural design while ensuring clear definition of boundaries during the topological optimization process.

[0035] 5. The present invention adopts PDE filtering to replace the density filtering used in the existing method, which not only simplifies the definition of filtering boundary conditions and the calculation process of spatial gradients, but also can be extended to parallel computing, which helps to handle large-scale optimization tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A flow chart of a thin-walled structure topology and morphology integrated optimization design method constructed by the present invention;

[0037] Figure 2 The present invention extracts a schematic diagram of uniform thin walls of equal thickness through two-step PDE filtering and Heaviside projection operations;

[0038] Figure 3 A schematic diagram of a three-dimensional cantilever beam implementation example of the present invention;

[0039] Figure 4 For the present invention Figure 3 Example: Topology optimization results with the goal of minimizing flexibility;

[0040] Figure 5 For the present invention Figure 4 Schematic cross-section of the topology optimization results. DETAILED DESCRIPTION

[0041] The following is combined with Figure 1-5 The technical solution of the present invention is described in detail.

[0042] like Figure 1 As shown, this embodiment provides a method for optimizing the topology and morphology of a thin-walled structure, which specifically includes the following steps:

[0043] Step 1: Establish a finite element model according to the design requirements and determine the design domain. Establish a topology optimization model with structural flexibility as the target and mass fraction as the constraint. Initialize the physical parameters, optimization parameters, and plate thickness t of the optimization model.

[0044] In this implementation, the topology optimization model with structural flexibility as the target and mass fraction as the constraint is as follows:

[0045]

[0046]

[0047] Where st represents the constraint condition, T represents the transpose of the matrix; K represents the total stiffness matrix of the structure, U and F represent the global displacement and load vectors; u e represents the unit node displacement vector, k e Represents the element stiffness matrix, e is the element number; N represents the number of design domain elements; μ e is the cell density that characterizes the thin-wall morphology, v e is the cell density that characterizes the thin-wall topology; μ is μ e The vector composed of v is v e The vector composed of g volf represents the mass fraction constraint; frac is the mass fraction, which is equal to the ratio of the structural mass ρ(μ,v) to the total mass ρ0 of the initial design domain; frac * Indicates a predetermined threshold.

[0048] Step 2: Extract the thin-walled structure morphology distribution field through two-step PDE filtering and Heaviside projection operation

[0049] First, anisotropic PDE filtering is used to extract the neutral surface of the thin-walled structure. Isotropic PDE filtering is used to avoid checkerboard phenomenon and grid dependence, and it helps to obtain spatial gradient information. The solution format of PDE filtering is as follows:

[0050]

[0051] Where, is the gradient operator, μ is the density field before filtering, is the density field after filtering, and the coefficient matrix C is defined as:

[0052]

[0053] Where, are the three basis vectors of the three-dimensional stamping coordinate system, and B is the matrix composed of the three basis vectors. is the filter radius corresponding to the three basis vector directions, and r is the diagonal matrix corresponding to the three-directional filter radius. If they are equal to each other, it is an isotropic filter, otherwise it is an anisotropic filter.

[0054] On the basis of filtering, combined with Heaviside projection, a clear 0-1 distribution topological configuration can be obtained. The unit density after filtering of the i-th unit is The cell density obtained after projection for:

[0055]

[0056] Where β is the sharpness of the projection, η is the threshold of the projection, Represents the unit density after filtering of the i-th unit The cell density obtained after projection.

[0057] Through two filtering and projection operations, the thin-wall morphology distribution field can be obtained Specifically, the design variable μ is Anisotropic PDE filtering is performed on the radius to obtain the cell density According to the stamping coordinate system, in the stamping direction n i (i=1,2 or 3) Set the filter radius tends to infinity; then With sharpness β s , threshold η s Project the parameters to get In the thought Radius pair Perform isotropic filtering to obtain cell density The filtering radius in each direction satisfies beg The spatial gradient norm field of ( is the gradient operator) and multiplied by the normalization factor The normalized spatial gradient norm field can be obtained Then again With sharpness β g , threshold η h Project the parameters to get

[0058] Step 3: Combine the thin-wall morphology distribution field obtained in step 2 And the topological density field v, based on the RAMP model to build a material interpolation model, calculate the elastic modulus E and mass ρ:

[0059]

[0060] Where, E min To avoid numerical singularities in the minimum elastic modulus, E0 is the elastic modulus of the solid element, q is the penalty factor, and ρ is the element mass.

[0061] Step 4: Perform finite element analysis based on the material interpolation model to calculate the flexibility of the structure.

[0062] Step 5: Based on the derived sensitivity formula, the sensitivity of the structural flexibility c and mass ρ to the design variables is obtained, which can be obtained by the following formula:

[0063]

[0064] in, It can be expanded using the chain rule:

[0065]

[0066] Will Substitution have to:

[0067]

[0068] At this point, the sensitivity expressions of structural flexibility and structural mass with respect to the design variables μ,v have been derived.

[0069] Step 6: Use the moving asymptotes method (MMA) to update the thin plate morphology design variable μ and topology design variable v.

[0070] Step 7: If at the kth iteration, the projection sharpness β s and β g Achieve maximum sharpness β max If the maximum change of the design variable is less than 0.01, the convergence condition is considered to be met, the optimization iteration stops and the optimization results are output; otherwise, steps 2 to 6 are repeated.

[0071] The technical implementation method disclosed in the present invention is as follows:

[0072] This embodiment is a common 3D cantilever beam, and its loading and constraint conditions are as follows Figure 3 As shown in Figure 3, the filtering boundary condition adopts the Dirichlet boundary condition.

[0073] Step 1: Determine the design domain of the 3D cantilever beam and divide the finite element mesh into 45×18×30; set the elastic modulus E0 of the material to 1 and Poisson's ratio ξ to 0.3; set the z-axis stamping direction and the sheet thickness t to 2; control the density range of the morphology variable μ and the topology variable v within [0,1], and the upper limit of the structural mass fraction frac * is 0.15, and a mathematical model of the optimization problem is established with flexibility as the objective function.

[0074] Step 2: If Figure 2 As shown, the thin-wall morphology distribution field is obtained through two-step PDE filtering and Heaviside projection. Let n1 represent the z-direction punching direction, then the filter radius of the anisotropic filter is r1 = [10000, 5, 5], and the filter radius of the isotropic filter is r2 = [5, 5, 5]. The boundary conditions of the isotropic filter are set as follows: Figure 3 As shown. Projection sharpness β s and β g The initial value is 4, multiplied by 2 every 30 steps of iteration, and the upper limit is 64; the projection threshold η s is the relative height of the unit in the stamping direction, and the projection threshold η g Set to 0.5.

[0075] Step 3: According to the interpolation model of elastic modulus E and mass ρ, it can be based on and v assemble the interpolation function to describe the distribution of the thin-walled structure in the design domain.

[0076] Step 4-5: Perform finite element analysis in conjunction with the material interpolation model to calculate the flexibility of the structure. Based on the derived sensitivity formula, the sensitivity of the structural flexibility c and mass ρ to the design variables are respectively calculated and sensitivity analysis is performed.

[0077] Step 6-7: Submit the sensitivity analysis results to the MMA solver to update the design variables. If at the kth iteration, the projection sharpness β s and β g Achieve maximum sharpness β max =64 and the maximum change of the design variable is less than 0.01, the convergence condition is considered to be met, the optimization iteration stops and the optimization results are output; otherwise, steps 2 to 6 are repeated.

[0078] The present invention is not limited to the above-mentioned specific embodiments. A person skilled in the art can implement the present invention in a variety of other specific embodiments based on the embodiments and the contents disclosed in the drawings. Therefore, any design that adopts the design structure and ideas of the present invention and makes some simple transformations or changes falls within the scope of protection of the present invention.

Claims

1. A method for integrated optimization design of thin-walled structure topology and morphology, characterized by: Step 1: Establish a finite element model according to the design requirements, determine the design domain, and establish a topology optimization model with structural flexibility as the target and mass fraction as the constraint. Initialize the physical parameters, optimization parameters, and thin-wall thickness t of the optimization model. The topology optimization model is as follows: stKU=F 0≤μ e ≤1 0≤v e ≤1 Where st represents the constraint condition, T represents the transpose of the matrix; K represents the total stiffness matrix of the structure, U and F represent the global displacement and load vectors; u e represents the unit node displacement vector, k e Represents the element stiffness matrix, e is the element number; N represents the number of design domain elements; μ e represents the cell density before filtering, v e represents the cell density of the topological field; μ is μ e The vector composed of v is v e The vector composed of g volf represents the mass fraction constraint; frac is the mass fraction, which is equal to the ratio of the structural mass ρ(μ,v) to the total mass ρ0 of the initial design domain; frac* represents the predetermined threshold; Step 2: Extract the thin-walled structure morphology distribution field through two-step partial differential equation filtering and Heaviside projection operation Step 3: Combine the thin-wall morphology distribution field obtained in step 2 and the topological density field v, constructing a rational approximation model of material properties, thereby obtaining the elastic modulus E and mass ρ in the design domain; Step 4: Perform finite element analysis based on the material interpolation model to calculate the flexibility of the structure. Step 5: Solve to obtain the sensitivity of structural flexibility and mass to design variables; Step 6: Use the moving asymptote method to update the thin plate morphology design variable μ and topology design variable v; Step 7: When the convergence condition is met, the optimization iteration stops and the optimization results are output. Otherwise, repeat steps 2 to 6.

2. The method for integrated optimization design of thin-walled structure topology and morphology according to claim 1, characterized in that: In step 2, the mathematical expression of the partial differential equation filtering is: Where, is the gradient operator, μ is the density field before filtering, is the density field after filtering, and the coefficient matrix C is defined as: Where, are the three basis vectors of the three-dimensional stamping coordinate system, V is the matrix composed of the three basis vectors, is the filter radius corresponding to the three basis vector directions, r is the diagonal matrix corresponding to the three-directional filter radius; if If they are equal to each other, it is an isotropic filter, otherwise it is an anisotropic filter.

3. The method for integrated optimization design of thin-walled structure topology and morphology according to claim 1, characterized in that: In step 2, the mathematical expression of the Heaviside projection is: Where β is the sharpness of the projection, η is the threshold of the projection, Represents the unit density after filtering of the i-th unit The cell density obtained after projection; Through two filtering and projection operations, the thin-walled structure morphology distribution field can be obtained 4. The method for integrated optimization design of thin-walled structure topology and morphology according to claim 1, characterized in that: In step 3, according to the derived sensitivity formula, the elastic modulus E and density ρ in the design domain are: Where, E min To avoid numerical singularities in the minimum elastic modulus, E0 is the elastic modulus of the solid element, q is the penalty factor, and ρ is the element mass.

5. The method for integrated optimization design of thin-walled structure topology and morphology according to claim 4, characterized in that: In step 5, the sensitivity of the flexibility c and mass ρ to the design parameters can be obtained by the following formula:

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