Lightweight design method of structure based on modified equivalent static load method
By modifying the modulus proportionality coefficient and strain matrix coefficient of the equivalent static load method, the error problem of the equivalent static load method under plastic deformation is solved, and nonlinear topology optimization and lightweight structural design are realized.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- YANSHAN UNIV
- Filing Date
- 2022-09-07
- Publication Date
- 2026-04-24
AI Technical Summary
The classic equivalent static load method is difficult to handle errors caused by plastic deformation in nonlinear dynamic analysis of materials, and cannot achieve nonlinear topology optimization design.
The equivalent static load method is modified by modulus proportionality coefficient and strain matrix correction coefficient, and a nonlinear topology optimization method is established to reconstruct the three-dimensional model of the energy-absorbing lattice cell configuration.
Nonlinear topology optimization design was achieved, and lightweight structural design was completed, satisfying the optimization of lattice structure under compression conditions.
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Figure CN116484659B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of lightweight structural design, and specifically to a lightweight structural design method based on the modified equivalent static load method. Background Technology
[0002] With the increasing demands for lightweight structures and improved structural performance in fields such as automotive, shipbuilding, and aerospace, topology optimization has gained favor among scholars and designers for achieving disruptive designs during the conceptual design phase. Currently, dynamic structural optimization methods mainly include the approximate surrogate model method, the Inertia Relief Method (IRM), the Hybrid Cellar Automata (HCA) method, and the Equivalent Static Loads Method (ESLM). The Equivalent Static Loads Method transforms the dynamic optimization process into a static optimization process, resulting in high computational efficiency. Furthermore, it enhances optimization stability through multiple iterations and allows for more diverse optimization objectives, better aligning with practical engineering needs.
[0003] Classical ESLM topology optimization is suitable for linear elastic analysis, where the equivalent static load analysis calculated by ESLM is identical to the displacement response of the linear elastic dynamic analysis. This is because the linear elastic deformation of the structure is recoverable, the structural stiffness does not change (i.e., the structural stiffness matrix calculated by ESLM at different sampling times is a constant), the loading and unloading paths remain unchanged, and there is no influence between the equivalent static loads at different times in the dynamic analysis. However, in the nonlinear dynamic analysis process, when the structure yields, irreversible plastic deformation occurs, causing a change in stiffness. If the equivalent static load is still calculated using the linear elastic stiffness matrix, the static analysis system response will inevitably have a large error compared to the system response of the nonlinear dynamic analysis at the corresponding time. The greater the plastic deformation of the structure, the greater the error between the two. Therefore, classical ESLM is difficult to handle material and geometric nonlinearities in the plastic stage and cannot realize the conceptual design of nonlinear topology optimization. Therefore, it is necessary to consider the impact of plastic deformation on the ESLM equivalent accuracy and to numerically correct the static load calculated by linear elastic ESLM. Summary of the Invention
[0004] To overcome the shortcomings of existing technologies, this invention is based on the material and geometric nonlinear numerical correction equivalent static load method. The equivalent static load method is corrected by modulus proportionality coefficient and strain matrix correction coefficient to complete the structural optimization. Based on the nonlinear topology optimization results, the three-dimensional model of the energy-absorbing lattice cell configuration is reconstructed to obtain the geometric parameterized model of the lattice cell configuration, which is used for the lightweight design of lattice structures under compression load conditions.
[0005] To achieve the above objectives, the solution adopted by the present invention is as follows:
[0006] A lightweight structural design method based on the modified equivalent static load method, characterized by comprising the following steps:
[0007] Step 1: Establish the initial finite element model of the structure to be optimized and calculate the linear equivalent static load;
[0008] Nonlinear dynamic finite element analysis is performed on the structure to be optimized. The equivalent static load in the z-axis direction is calculated using the linear elastic equivalent static load method, as shown below:
[0009] F i,t =K L z D (t);
[0010] In the formula: F i,t K represents the equivalent static load at sampling time t along the i-th direction during the dynamic analysis process. L Represents the structural stiffness moment
[0011] array; z D (t) represents the displacement vector dynamically analyzed at sampling time t; t represents the sampling time; i represents the coordinate number, which is x, y or z respectively;
[0012] Step 2: Calculate the modulus proportion coefficient of the structure to be optimized during the plastic deformation stage;
[0013] Step 21: Based on the results of the nonlinear dynamic finite element analysis of the structure, extract the stress and strain of the structural elements to obtain the stress increment and strain increment of the structural elements, as shown below:
[0014]
[0015] In the formula: Δσ(t) represents the stress increment at sampling time t; Δε(t) represents the strain increment at sampling time t; Δσ x (t), Δσ y (t) and Δσ z (t) represents the stress increment at sampling time t in the x, y, and z directions, respectively; Δε x (t), Δε y (t) and Δε z (t) represents the strain increment at sampling time t in the x, y, and z directions, respectively;
[0016] The methods for obtaining the numerical values of stress increment and strain increment are as follows:
[0017]
[0018] In the formula: σ i(t-1) represents the structural element stress in the direction of coordinate i at sampling time t-1; ε i (t-1) represents the strain of the structural element in the direction of coordinate i at sampling time t-1.
[0019] Step 22: Determine the relationship between stress and strain to obtain the equivalent plastic modulus of the structural element;
[0020] Step 23: Calculate the equivalent plastic modulus in the z-direction at sampling time t. The ratio of the linear elastic Young's modulus E to the modulus proportionality coefficient is obtained as follows:
[0021]
[0022] In the formula: λ z (t) represents the modulus scaling factor at sampling time t in the z-direction; The equivalent plastic modulus of the structural element at sampling time t in the z-axis direction is represented by E; the linear elastic Young's modulus is represented by m; the number of solid elements whose strain increment is not zero at sampling time t-1 is represented by m; and the number of the structural element is represented by j. and These represent the stress increments of the j-th structural element at sampling time t in the x, y, and z directions, respectively. This represents the strain increment of the j-th structural element at sampling time t in the z-direction;
[0023] Step 3: Correct the equivalent static load of the structure based on the calculated modulus scaling factor;
[0024] Step 31: Correct the equivalent static load using an incremental method based on the calculated modulus scaling factor. The correction expression is as follows:
[0025]
[0026] In the formula: This represents the corrected equivalent static load corresponding to sampling time t in the direction of coordinate i; λ represents the corrected equivalent static load corresponding to sampling time t-1 in the direction of coordinate i; i (t) represents the correction coefficient at sampling time t in the direction of coordinate i; F i,t F represents the equivalent static load corresponding to sampling time t in the direction of coordinate i; i,t-1 This represents the equivalent static load corresponding to sampling time t-1 in the direction of coordinate i. When t is 0, the initial load is...
[0027] Step 32: Establish the relationship between structural element strain and nodal displacement through the strain matrix, extract the strain matrix coefficients, and obtain the strain matrix correction coefficients based on the ratio of the strain matrix coefficients in the elastoplastic and linear elastic stages; calculate the strain matrix correction coefficient β(t), as shown below:
[0028]
[0029] In the formula: β(t) represents the strain matrix correction coefficient; Represents the strain matrix coefficients in the elastoplastic stage; Represents the strain matrix coefficients in the linear elastic stage;
[0030] Step 33; Based on the calculated strain matrix correction coefficients, adjust the equivalent static load for the modulus scaling factor. Further numerical corrections were made, as shown below:
[0031]
[0032] In the formula: This represents the equivalent static load after secondary correction in the direction of coordinate i at sampling time t;
[0033] Step 4: Perform nonlinear topology optimization calculations based on the corrected equivalent static load, reconstruct the topology-optimized structure to obtain the energy-absorbing lattice cell configuration, and realize the lightweight design of the structure;
[0034] The corrected equivalent static load from step 33 is obtained as the output result. The optimization result of the nonlinear topology optimization is reconstructed to obtain the geometric parameterized model of the new lattice cell configuration, thereby realizing the lightweight design of the structure.
[0035] Step 21 involves extracting the stress and strain of structural elements based on the results of the nonlinear dynamic finite element analysis of the structure, and obtaining the stress increment and strain increment of the structural elements. Specifically:
[0036] The method for obtaining the stress of the structural unit is as follows:
[0037] σ(t)=[σ x (t),σ y (t),σ z (t)] T ;
[0038] In the formula: σ(t) represents the stress of the structural element at sampling time t; σ x (t), σ y (t) and σ z (t) represents the stress at sampling time t in the x, y, and z directions, respectively;
[0039] The method for obtaining the strain of the structural unit is as follows:
[0040] ε(t)=[ε x (t),ε y (t),ε z (t)] T ;
[0041] In the formula: ε(t) represents the strain of the structural element at sampling time t; ε x (t), ε y (t) and ε z (t) represents the strain at sampling time t in the x, y and z directions, respectively.
[0042] In step 22, the relationship between stress and strain is determined, and the equivalent plastic modulus of the structural element is obtained using the incremental form principle, specifically:
[0043] The relationship between stress and strain is determined as follows:
[0044]
[0045] Where: ε x ε y and ε z σ represents the strain of the structural element in the x, y, and z directions, respectively; x σ y and σ z These represent the stresses of the structural element in the x, y, and z directions, respectively; μ represents the material's Poisson's ratio.
[0046] Linearizing the nonlinear stress-strain process transforms it into a series of linear relationships. The physical meaning of the equivalent plastic modulus at each moment under uniaxial stress is the slope of the tangent line between adjacent moments on the stress-strain curve during the plastic stage. The equivalent plastic modulus of the element at each moment is calculated by the ratio of the stress increment to the strain increment. As shown below:
[0047]
[0048] In the formula: Δσ represents the equivalent plastic modulus of the structural element at coordinate i at sampling time t; i (t) represents the stress increment in the direction of coordinate i at sampling time t; Δε i (t) represents the strain increment in the direction of coordinate i at sampling time t;
[0049] Further calculations yielded the equivalent plastic modulus of the structure at various times along the x, y, and z coordinate axes, as shown below:
[0050]
[0051] In the formula: and Let Δσ represent the equivalent plastic modulus of the structure at sampling time t at coordinates x, y, and z, respectively; x (t), Δσ y (t) and Δσ z (t) represents the stress increments of the structure at sampling time t on coordinates x, y, and z, respectively; Δε x (t), Δε y (t) and Δε z (t) represents the strain increment of the structure at sampling time t at coordinates x, y and z, respectively.
[0052] Step 32, the strain matrix coefficients for the elastoplastic and linear elastic stages, are as follows:
[0053] Based on the nonlinear dynamic analysis results, the strain of the element and the displacement of the element nodes at each time step are extracted. The equivalent strain and the mean value of the displacement vector magnitude of the element nodes are calculated. The method for obtaining the strain matrix coefficients in the elastoplastic stage is as follows:
[0054]
[0055] In the formula: u x,h (t), u y,h (t) and u z,h (t) represents the displacement values of the h-th node of the structural unit at sampling time t in the x, y, and z directions, respectively; γ xy (t), γ yz (t) and γ zx (t) represents the shear strain of the structural element in the xy, yz, and zx directions at sampling time t, respectively; k represents the number of nodes in the structural element;
[0056] Linear elastic dynamic analysis was performed on the structure to extract the strain of the elements and the displacement of the element nodes at each time step. The mean values of the equivalent strain and the displacement vector magnitude of the element nodes were calculated. The method for obtaining the strain matrix coefficients in the linear elastic stage is as follows:
[0057]
[0058] Where: n t This indicates the number of units at sampling time t.
[0059] Preferably, the energy-absorbing lattice cell configuration in step 4 is as follows:
[0060] The energy-absorbing lattice cell configuration consists of eight tilted symmetrical pillars and a central cross-shaped thin-walled structure; the geometric parameters are parameterized models of pillar widths L1 and L2, cell heights h1 and h2, and thin-wall spacing a1 and a2; it is suitable for working conditions where the load-bearing environment is compression.
[0061] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0062] (1) This invention is based on the equivalent static load method with material and geometric nonlinear numerical correction. The equivalent static load method is corrected by modulus proportionality coefficient and strain matrix correction coefficient, which completes the linearization of the nonlinear problem of material and geometry and realizes nonlinear topology optimization design.
[0063] (2) Based on the analysis results, the present invention reconstructs the three-dimensional model of the energy-absorbing lattice cell configuration and obtains the geometric parameterized model of the lattice cell configuration, which is used to bear the working conditions of the compression environment, and realizes the lightweight design of the lattice structure. Attached Figure Description
[0064] Figure 1 This is a control block diagram of the structural lightweight design method based on the modified equivalent static load method according to an embodiment of the present invention;
[0065] Figure 2 This is a general flowchart of the lightweight structural design method according to an embodiment of the present invention;
[0066] Figure 3 A finite element model diagram established for an embodiment of the present invention;
[0067] Figure 4 This is a schematic diagram showing the relationship between the equivalent plastic modulus and the linear elastic Young's modulus in an embodiment of the present invention;
[0068] Figure 5 This is a graph showing the change of the z-direction modulus proportionality coefficient over time, calculated in an embodiment of the present invention.
[0069] Figure 6 This is a schematic diagram of the method for correcting the equivalent static load using the modulus scaling factor in an embodiment of the present invention;
[0070] Figure 7 This is a graph showing the change of the z-direction strain rectangular correction coefficient over time, calculated in an embodiment of the present invention.
[0071] Figure 8 This is a graph showing the change of the objective function of the outer loop optimization results in an embodiment of the present invention.
[0072] Figure 9 This is a diagram showing the final optimized result in an embodiment of the present invention. Detailed Implementation
[0073] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.
[0074] This invention proposes a nonlinear topology optimization method based on the equivalent static load method to optimize material distribution. By modifying the equivalent static load method with modulus proportionality coefficients and strain matrix correction coefficients, nonlinear topology optimization design is achieved, optimizing the material distribution and completing the lightweight design of the structure. Based on the topology optimization results, the three-dimensional configuration and geometric parameterized model of the energy-absorbing lattice cell are reconstructed, as shown in the attached figure. This model is mainly used for working conditions where the load environment is compressive, completing the lightweight design of the lattice structure while ensuring structural strength. Figure 1 The diagram shown is a control block diagram of the structural lightweight design method based on the modified equivalent static load method according to an embodiment of the present invention.
[0075] The structural lightweight design method based on the modified equivalent static load method provided in this invention embodiment, such as... Figure 2 The diagram shown is a general flowchart of the lightweight structural design method according to an embodiment of the present invention. To demonstrate the applicability of the present invention, it is applied to an example, specifically including the following steps:
[0076] S1: Establish the initial finite element model of the structure to be optimized and calculate the linear equivalent static load;
[0077] This method designs a lattice cell configuration that maximizes energy absorption per unit mass under dynamic loads. Most classic lattice cell configurations are symmetrical structures with regular cubic circumscribed structures. Since the cell, as the smallest unit of a lattice structure, has a regular circumscribed shape that facilitates the regular arrangement of the lattice, an initial topology optimization model of a cubic lattice cell is established in the finite element software, as follows: Figure 3 The diagram shows the finite element model established in this embodiment of the invention; the dimensions of the lattice cell finite element optimization model are: length 10mm, width 10mm, height 12mm. The velocity of the analytical rigid body 1 is set to 5m / s. The optimization model is divided into a design domain 2 and a non-design region 3. The design domain uses elastoplastic materials, and the non-design region elements use rigid body models. The initial optimization parameters are set as follows: volume constraint V* = 0.4, evolution rate ER = 0.02, AR = 0.05, filter radius r = 3, and inner loop convergence τ. int =0.1%, outer loop converges τ out =0.5%. A nonlinear dynamic finite element analysis was performed on the optimized structure. The equivalent static load in the z-axis direction was calculated using the linear elastic equivalent static load method, as shown below:
[0078] F i,t =K L z D (t);
[0079] In the formula: F i,tK represents the equivalent static load at sampling time t along the i-th direction during the dynamic analysis process. L The stiffness matrix represents the structural stiffness moment; z D (t) represents the displacement vector of the dynamic analysis at sampling time t; t represents the sampling time; i represents the coordinate number, which is x, y or z respectively.
[0080] S2: Calculate the modulus proportion coefficient of the structure to be optimized during the plastic deformation stage;
[0081] S21: Extract the stress and strain of the structural elements based on the results of the nonlinear dynamic finite element analysis of the structure;
[0082] The method for obtaining the stress of structural elements is as follows:
[0083] σ(t)=[σ x (t),σ y (t),σ z (t)] T ;
[0084] In the formula: σ(t) represents the stress of the structural element at sampling time t; σ x (t), σ y (t) and σ z (t) represents the stress at sampling time t in the x, y, and z directions, respectively;
[0085] The method for obtaining the strain of the structural unit is as follows:
[0086] ε(t)=[ε x (t),ε y (t),ε z (t)] T ;
[0087] In the formula: ε(t) represents the strain of the structural element at sampling time t; ε x (t), ε y (t) and ε z (t) represents the strain at sampling time t in the x, y, and z directions, respectively;
[0088] The methods for obtaining the numerical values of stress increment and strain increment are as follows:
[0089]
[0090] In the formula: σ i (t-1) represents the structural element stress in the direction of coordinate i at sampling time t-1; ε i (t-1) represents the strain of the structural element in the direction of coordinate i at sampling time t-1.
[0091] The stress increments and strain increments of the structural elements are obtained as follows:
[0092]
[0093] In the formula: Δσ x (t), Δσ y (t) and Δσ z (t) represents the stress increment at sampling time t in the x, y, and z directions, respectively; Δε x (t), Δε y (t) and Δε z (t) represents the strain increment at sampling time t in the x, y and z directions, respectively.
[0094] S22: Based on the generalized Hooke's law, the relationship between stress and strain is determined, and the equivalent plastic modulus of the structural element is obtained using the incremental form principle; the relationship between stress and strain determined according to the generalized Hooke's law is shown below:
[0095]
[0096] Where: ε x ε y and ε z σ represents the strain of the structural element in the x, y, and z directions, respectively; x σ y and σ z These represent the stresses of the structural element in the x, y, and z directions, respectively; μ represents the Poisson's ratio of the material.
[0097] The incremental approach linearizes the nonlinear stress-strain process, transforming it into a series of linear relationships. The equivalent plastic modulus at each moment under uniaxial stress is physically represented by the slope of the tangent line between adjacent moments on the stress-strain curve during the plastic stage. It is calculated as the ratio of the stress increment to the strain increment. The equivalent plastic modulus of the calculation unit at each moment is then determined. As shown below:
[0098]
[0099] In the formula: Δσ represents the equivalent plastic modulus of the structural element at coordinate i at sampling time t; i (t) represents the stress increment in the direction of coordinate i at sampling time t; Δε i (t) represents the strain increment in the direction of coordinate i at sampling time t.
[0100] Further calculations yielded the equivalent plastic modulus of the element at each time step along the x, y, and z coordinate axes, as shown below:
[0101]
[0102] In the formula: and Let Δσ represent the equivalent plastic modulus of the structure at sampling time t at coordinates x, y, and z, respectively; x (t), Δσ y (t) and Δσ z (t) represents the stress increments of the structure at sampling time t on coordinates x, y, and z, respectively; Δε x (t), Δε y (t) and Δε z (t) represents the strain increment of the structure at sampling time t at coordinates x, y and z, respectively.
[0103] S23: Calculate the equivalent plastic modulus in the z-direction at sampling time t. The ratio of the linear elastic Young's modulus E to the modulus proportionality coefficient is obtained as follows:
[0104]
[0105] In the formula: λ z (t) represents the modulus scaling factor at sampling time t in the z-direction; The equivalent plastic modulus of the structural element at sampling time t in the z-axis direction is represented by E; the linear elastic Young's modulus is represented by m; the number of solid elements whose strain increment is not zero at sampling time t-1 is represented by m; and the number of the structural element is represented by j. and These represent the stress increments of the j-th structural element at sampling time t in the x, y, and z directions, respectively. This represents the strain increment of the j-th structural element at sampling time t in the z-direction;
[0106] like Figure 5 The figure shown is a curve of the z-direction modulus proportional coefficient calculated in this embodiment of the invention changing with time; it is also a schematic diagram of the changes in the optimization process in this step.
[0107] S3: Correct the equivalent static load of the structure based on the calculated modulus scaling factor;
[0108] S31: The equivalent static load is corrected incrementally based on the calculated modulus proportionality coefficient. The correction expression is as follows:
[0109]
[0110] In the formula: This represents the corrected equivalent static load corresponding to sampling time t in the direction of coordinate i; λ represents the corrected equivalent static load corresponding to sampling time t-1 in the direction of coordinate i; i (t) represents the correction coefficient at sampling time t in the direction of coordinate i; F i,t F represents the equivalent static load corresponding to sampling time t in the direction of coordinate i; i,t-1 This represents the equivalent static load corresponding to sampling time t-1 in the direction of coordinate i. When t is 0, the initial load is...
[0111] S32: The relationship between structural element strain and nodal displacement is established through the strain matrix, and the strain matrix coefficients are proposed. Based on the nonlinear dynamic analysis results, the strain of the element and the displacement of the element nodes at each time step are extracted, and the mean values of the equivalent strain and the vector magnitude of the element nodal displacement are calculated. The method for obtaining the strain matrix coefficients in the elastoplastic stage is as follows:
[0112]
[0113] In the formula: u x,h (t), u y,h (t) and u z,h (t) represents the displacement values of the h-th node of the structural unit at sampling time t in the x, y, and z directions, respectively; γ xy (t), γ yz (t) and γ zx (t) represents the shear strain of the structural element in the xy, yz, and zx directions at sampling time t, respectively; k represents the number of nodes in the structural element;
[0114] Linear elastic dynamic analysis was performed on the structure to extract the strain of the elements and the displacement of the element nodes at each time step. The mean values of the equivalent strain and the displacement vector magnitude of the element nodes were calculated. The method for obtaining the strain matrix coefficients in the linear elastic stage is as follows:
[0115]
[0116] Where: n t This indicates the number of units at sampling time t.
[0117] The strain matrix correction coefficient is obtained based on the ratio of the strain matrix coefficients in the elastoplastic and linear elastic stages; the strain matrix correction coefficient β(t) is calculated as follows:
[0118]
[0119] In the formula: β(t) represents the strain matrix correction coefficient; Represents the strain matrix coefficients in the elastoplastic stage; Represents the strain matrix coefficients in the linear elastic stage;
[0120] S33; Equivalent static load corrected for modulus scaling factor based on calculated strain matrix correction coefficient. Further numerical corrections were made, as shown below:
[0121]
[0122] In the formula: This represents the equivalent static load after secondary correction in the direction of coordinate i at sampling time t;
[0123] S4: Perform nonlinear topology optimization based on the corrected equivalent static load, reconstruct the topology optimization results to obtain the energy-absorbing lattice cell configuration, and realize the lightweight design of the structure.
[0124] Obtain the corrected equivalent static load in S33 as the output result, such as Figure 8 The figure shows the objective function variation curve of the outer loop optimization result in this embodiment of the invention; it can be seen from the figure that the optimization process of this invention has a good optimization convergence effect. The topology optimization result is reconstructed to obtain a geometric parameterized model of the energy-absorbing lattice cell configuration. The energy-absorbing lattice cell configuration consists of eight tilted symmetrical pillars and a central cross-shaped thin-walled structure; the geometric parameters are the parameterized models of pillar widths L1 and L2, cell heights h1 and h2, and thin-wall spacing a1 and a2; it is used to withstand compression conditions, realizing a lightweight design of the lattice structure. Figure 9 The figure shown is the final optimization result diagram in the embodiment of the present invention; the figure also illustrates the optimization result of the material structure in the embodiment of the present invention.
[0125] In summary, the results of this case study demonstrate the effectiveness of the lightweight structural design method based on the modified equivalent static load method.
[0126] (1) The embodiments of the present invention are based on the material and geometric nonlinear numerical correction equivalent static load method. The equivalent static load method is corrected by modulus proportionality coefficient and strain matrix correction coefficient, the material structure is distributed and optimized, and nonlinear topology optimization design is realized, thereby completing the lightweight design of the structure.
[0127] (2) The embodiment of the present invention reconstructs the geometric parameterization model of the energy-absorbing lattice cell configuration based on the topology optimization results, as shown in the figure. This model can be used for working conditions where the bearing environment is compression, and the lightweight design of the lattice structure is completed while ensuring the structural strength.
[0128] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims
1. A structural lightweight design method based on the modified equivalent static load method, characterized in that, It includes the following steps: Step 1: Establish the initial finite element model of the structure to be optimized and calculate the linear equivalent static load; Nonlinear dynamic finite element analysis is performed on the structure to be optimized. The equivalent static load in the z-axis direction is calculated using the linear elastic equivalent static load method, as shown below: F i,t =K L z D (t); In the formula: F i,t K represents the equivalent static load at sampling time t along the i-th direction during the dynamic analysis process. L Represents the structural stiffness matrix; z D (t) represents the displacement vector dynamically analyzed at sampling time t; t represents the sampling time; i represents the coordinate number, which is x, y or z respectively; Step 2: Calculate the modulus proportion coefficient of the structure to be optimized during the plastic deformation stage; Step 21: Based on the results of the nonlinear dynamic finite element analysis of the structure, extract the stress and strain of the structural elements to obtain the stress increment and strain increment of the structural elements, as shown below: In the formula: Δσ(t) represents the stress increment at sampling time t; Δε(t) represents the strain increment at sampling time t; Δσ x (t), Δσ y (t) and Δσ z (t) represents the stress increment at sampling time t in the x, y, and z directions, respectively; Δε x (t), Δε y (t) and Δε z (t) represents the strain increment at sampling time t in the x, y, and z directions, respectively; The methods for obtaining stress increments and strain increments are as follows: In the formula: σ i (t-1) represents the structural element stress in the i-direction at sampling time t-1; ε i (t-1) represents the strain of the structural element in the direction of coordinate i at sampling time t-1; Step 22: Determine the relationship between stress and strain to obtain the equivalent plastic modulus of the structural element; Step 23: Calculate the equivalent plastic modulus in the z-direction at sampling time t. The ratio of the linear elastic Young's modulus E to the modulus proportionality coefficient is obtained as follows: In the formula: λ z (t) represents the modulus scaling factor at sampling time t in the z-direction; The equivalent plastic modulus of the structural element at sampling time t in the z-axis direction is represented by E; the linear elastic Young's modulus is represented by m; the number of solid elements whose strain increment is not zero at sampling time t-1 is represented by m; and the number of the structural element is represented by j. and These represent the stress increments of the j-th structural element at sampling time t in the x, y, and z directions, respectively. This represents the strain increment of the j-th structural element at sampling time t in the z-direction; Step 3: Correct the equivalent static load of the structure based on the calculated modulus scaling factor; Step 31: Correct the equivalent static load using an incremental method based on the calculated modulus scaling factor. The correction expression is as follows: In the formula: This represents the corrected equivalent static load corresponding to sampling time t in the direction of coordinate i; This represents the corrected equivalent static load corresponding to sampling time t-1 in the direction of coordinate i; λ i (t) represents the correction coefficient at sampling time t in the direction of coordinate i; F i,t F represents the equivalent static load corresponding to sampling time t in the direction of coordinate i; i,t-1 This represents the equivalent static load corresponding to sampling time t-1 in the direction of coordinate i. When t is 0, the initial load is... Step 32: Establish the relationship between structural element strain and nodal displacement through the strain matrix, extract the strain matrix coefficients, and obtain the strain matrix correction coefficients based on the ratio of the strain matrix coefficients in the elastoplastic and linear elastic stages; calculate the strain matrix correction coefficient β(t), as shown below: In the formula: β(t) represents the strain matrix correction coefficient; Represents the strain matrix coefficients in the elastoplastic stage; Represents the strain matrix coefficients in the linear elastic stage; Step 33; Based on the calculated strain matrix correction coefficients, adjust the equivalent static load for the modulus scaling factor. Further numerical corrections were made, as shown below: In the formula: This represents the equivalent static load after secondary correction in the direction of coordinate i at sampling time t; Step 4: Perform nonlinear topology optimization calculations based on the corrected equivalent static load, reconstruct the topology-optimized structure to obtain the energy-absorbing lattice cell configuration, and realize the lightweight design of the structure; The equivalent static load corrected in step 33 is obtained as the output result. The optimization result of nonlinear topology optimization is reconstructed to obtain the geometric parameterization model of the novel lattice cell configuration, thereby realizing the lightweight design of the structure.
2. The structural lightweight design method based on the modified equivalent static load method according to claim 1, characterized in that, Step 21, which involves extracting the stress and strain of structural elements based on the results of the nonlinear dynamic finite element analysis of the structure, and obtaining the stress increment and strain increment of the structural elements, specifically involves: The method for obtaining the stress of the structural unit is as follows: σ(t)=[σ x (t),σ y (t),σ z (t)] T ; In the formula: σ(t) represents the stress of the structural element at sampling time t; σ x (t), σ y (t) and σ z (t) represents the stress at sampling time t in the x, y, and z directions, respectively; The method for obtaining the strain of the structural unit is as follows: ε(t)=[ε x (t),e y (t),e z (t)] T ; In the formula: ε(t) represents the strain of the structural element at sampling time t; ε x (t), ε y (t) and ε z (t) represents the strain at sampling time t in the x, y and z directions, respectively.
3. The structural lightweight design method based on the modified equivalent static load method according to claim 1, characterized in that, In step 22, the relationship between stress and strain is determined, and the equivalent plastic modulus of the structural element is obtained using the incremental form principle, specifically as follows: The relationship between stress and strain is determined as follows: Where: ε x ε y and ε z σ represents the strain of the structural element in the x, y, and z directions, respectively; x σ y and σ z These represent the stresses of the structural element in the x, y, and z directions, respectively; μ represents the material's Poisson's ratio. Linearizing the nonlinear stress-strain process transforms it into a series of linear relationships. The physical meaning of the equivalent plastic modulus at each moment under uniaxial stress is the slope of the tangent line between adjacent moments on the stress-strain curve during the plastic stage. The equivalent plastic modulus of the element at each moment is calculated by the ratio of the stress increment to the strain increment. As shown below: In the formula: Δσ represents the equivalent plastic modulus of the structural element at coordinate i at sampling time t; i (t) represents the stress increment in the direction of coordinate i at sampling time t; Δε i (t) represents the strain increment in the direction of coordinate i at sampling time t; Further calculations yielded the equivalent plastic modulus of the structure at various times along the x, y, and z coordinate axes, as shown below: In the formula: and Let Δσ represent the equivalent plastic modulus of the structure at sampling time t at coordinates x, y, and z, respectively; x (t), Δσ y (t) and Δσ z (t) represents the stress increments of the structure at sampling time t on coordinates x, y, and z, respectively; Δε x (t), Δε y (t) and Δε z (t) represents the strain increment of the structure at sampling time t at coordinates x, y and z, respectively.
4. The structural lightweight design method based on the modified equivalent static load method according to claim 1, characterized in that, The strain matrix coefficients for the elastoplastic and linear elastic stages in step 32 are specifically as follows: Based on the nonlinear dynamic analysis results, the strain of the element and the displacement of the element nodes at each time step are extracted. The equivalent strain and the mean value of the displacement vector magnitude of the element nodes are calculated. The method for obtaining the strain matrix coefficients in the elastoplastic stage is as follows: In the formula: u x,h (t), u y,h (t) and u z,h (t) represents the displacement values of the h-th node of the structural unit at sampling time t in the x, y, and z directions, respectively; γ xy (t), γ yz (t) and γ zx (t) represents the shear strain of the structural element in the xy, yz, and zx directions at sampling time t, respectively; k represents the number of nodes in the structural element; Linear elastic dynamic analysis was performed on the structure to extract the strain of the elements and the displacement of the element nodes at each time step. The mean values of the equivalent strain and the displacement vector magnitude of the element nodes were calculated. The method for obtaining the strain matrix coefficients in the linear elastic stage is as follows: Where: n t This indicates the number of units at sampling time t.
5. The structural lightweight design method based on the modified equivalent static load method according to claim 1, characterized in that, The energy-absorbing lattice cell configuration in step 4 is specifically as follows: The energy-absorbing lattice cell configuration consists of eight tilted symmetrical pillars and a central cross-shaped thin-walled structure; the geometric parameters are parameterized models of pillar widths L1 and L2, cell heights h1 and h2, and thin-wall spacing a1 and a2; it is suitable for working conditions where the load-bearing environment is compression.