Damping material topological optimization design method based on SIMP

Abstract

The invention provides a damping material topological optimization design method based on SIMP. The method comprises the steps of determining a damping material setting range according to a plate shell structure to generate boundary conditions, performing stress analysis on the plate shell structure to determine damping characteristic information of the damping material setting range to generate load conditions, and dividing the damping material setting range into a plurality of unit areas, analyzing a stress ratio corresponding to each unit area according to the damping characteristic information to generate a constraint condition, establishing a finite element model according to a boundary condition and a load condition, and constructing an initial unit density corresponding to each unit area in the finite element model according to the constraint condition, according to the method, SIMP iterative optimization is performed on each initial unit density in a specified density range, an optimal damping material layout of a damping material setting range is generated, and a topological density cloud picture is drawn and displayed, so that the layout of the damping material can be effectively optimized, the weight is reduced, and an efficient vibration reduction effect is maintained.

Description

Technical Field

[0001] The invention relates to the technical field of damping material topology optimization, and in particular to a damping material topology optimization design method based on SIMP. Background Art

[0002] In contemporary engineering practice, especially in the fields of automobiles and civil engineering, effectively mitigating and controlling vibration problems caused by external excitation forces is crucial to improving structural performance, enhancing stability and improving noise control. Given that the stiffness of existing structures is often difficult to adjust, increasing damping has become an effective way to improve vibration characteristics. However, simply adding damping materials will bring additional weight and cost burdens. Therefore, how to optimize the structural layout of damping materials to achieve lightweight and maximize cost-effectiveness has become a focus of attention in the engineering community.

[0003] Therefore, the present invention provides a damping material topology optimization design method based on SIMP. Summary of the invention

[0004] The present invention provides a damping material topology optimization design method based on SIMP, which can effectively optimize the layout of the damping material to reduce weight and maintain a high-efficiency vibration reduction effect.

[0005] The present invention provides a damping material topology optimization design method based on SIMP, comprising: S1: Determine the setting range of the damping material according to the plate-shell structure to generate boundary conditions, and perform force analysis on the plate-shell structure to determine the damping characteristic information of the setting range of the damping material to generate load conditions; S2: dividing the damping material setting range into a plurality of unit areas, and generating constraint conditions by analyzing the force ratio corresponding to each unit area according to the damping characteristic information; S3: establishing a finite element model according to the boundary conditions and the load conditions, and constructing an initial unit density corresponding to each unit area in the finite element model according to the constraint conditions; S4: performing SIMP iterative optimization on each of the initial unit densities within a specified density range, generating an optimal damping material layout within the damping material setting range, and drawing and displaying a topological density cloud map.

[0006] In one practicable manner, The S4 comprises: S41: generating a stiffness matrix of the damping material setting range according to the initial unit density corresponding to each unit area, analyzing the displacement value corresponding to the stiffness matrix, and establishing a topology optimization response of the damping material setting range according to the finite element model; S42: determining an adjustable density value corresponding to each of the initial unit densities according to the specified density range, combining the adjustable density values ​​to generate an optimized density distribution, and inputting the optimized density distribution into the stiffness matrix to perform displacement value analysis to obtain a displacement value; S43: performing convergence analysis on the displacement value using the topology optimization response, and when the displacement value is in a convergence state, an optimal damping material layout within the damping material setting range is formed according to the optimized density distribution; otherwise, the adjustable density values ​​are combined to generate an iterative density distribution for displacement value analysis until the displacement value meets a preset convergence threshold; S44: When the displacement value converges, an optimal damping material layout of the damping material setting range is generated according to the corresponding current iterative density distribution, and a topological density cloud map is drawn and displayed.

[0007] In one practicable manner, The process of performing stress analysis on the plate and shell structure includes: The vibration excitation characteristics of the plate-shell structure are analyzed according to formula (1); (1) in, represents the vibration excitation characteristics of the plate and shell structure, represents the N-dimensional mass of the plate and shell structure, represents the initial damping of the plate and shell structure, represents the stiffness characteristics of the plate and shell structure, represents the displacement characteristic equation of the plate and shell structure, The velocity characteristic equation representing the plate and shell structure is, The characteristic equation for the acceleration of the plate and shell structure is represented by, Indicates duration; The frequency response characteristics of the plate-shell structure are analyzed according to formula (2); (2) in, The frequency response characteristics of the plate and shell structure are represented by A characteristic equation representing the amplitude of the plate and shell structure; Determine the vibration excitation characteristics of the plate-shell structure according to formula (1), and determine the frequency response characteristics of the plate-shell structure according to formula (2); The external force pressure information of the plate-shell structure is determined according to the vibration excitation characteristics and the frequency response characteristics, and the force value corresponding to each structural position in the plate-shell structure is determined according to the external force pressure information.

[0008] In one practicable manner, The process of establishing a finite element model according to the boundary conditions and the load conditions includes: constructing a model grid in Optistruct according to the boundary conditions; Constructing the load condition to determine a number of load excitation points included in the model grid; Acquire the frequency response characteristics of the plate-shell structure, construct a unit amplitude-frequency curve according to the frequency response characteristics, and use the unit amplitude-frequency curve to analyze the frequency interval corresponding to each load excitation point in the model grid; Respectively identifying the real-time frequency response corresponding to each of the load excitation points; Constructing a frequency response function curve of the plate-shell structure according to the real-time frequency response corresponding to each load excitation point in the model grid; The load excitation points are distributed and arranged in the model grid, and the model grid is vibrated and rendered using the frequency response function curve to generate a finite element model.

[0009] In one practicable manner, Also includes: Before performing S1, the elastic modulus and damping density of each damping material are analyzed according to formulas (3) and (4); (3) (4) in, represents the elastic modulus of the damping material, represents the damping density of the damping material, In order to avoid affecting the calculation matrix and causing singular elastic modulus optimization matrix, it is usually set to 0.001. In order to avoid the occurrence of singular damping density optimization matrix in the calculation matrix, it is usually set to 0.001. q represents the penalty factor, which is usually set to 3. Analyze the elastic range and damping range of the damping material according to the calculation results of formulas (3) and (4); Before performing S1, a corresponding target damping material is selected according to the basic parameters of the plate-shell structure.

[0010] In one practicable manner, The process of generating an optimal damping material layout for the damping material setting range comprises: Dividing the damping material setting range into a plurality of unit grids according to the finite element model, and establishing a SIMP mathematical optimization model using formula (5) according to the specifications of the unit grids; (5) Where X represents a fixed variable vector, represents the optimized response volume ratio, represents the area of ​​the i-th unit grid, represents the thickness of the i-th unit grid, represents the volume of the i-th unit grid, Indicates the frequency response amplitude, represents the modal weight, represents the setting order of the optimization mode, represents the frequency response displacement, and Respectively represent the i-th order modal frequency before and after optimization, and Respectively represent the upper and lower limits of the i-th order modal frequency after normalization, and They represent the minimum and maximum values ​​of the optimized design, and their values ​​are 0.001 and 1 respectively; Establishing an iteration range condition according to the specified density range, inputting each of the unit grids into the SIMP mathematical optimization model respectively, and iteratively optimizing each of the unit grids according to the iteration range condition respectively to obtain an optimized damping material density corresponding to each unit grid; The optimal damping material layout of the plate-shell structure is determined according to the optimized damping material density corresponding to each unit grid.

[0011] In one practicable manner, The process of obtaining the optimized damping material density corresponding to each unit grid includes: Selecting, according to the load condition, a load excitation point where the excitation force of the plate-shell structure is higher than a preset excitation force; Selecting a number of iterative optimization results that meet the constraint conditions, and obtaining a displacement response value corresponding to the load excitation point in each iterative optimization result; Generate response constraint conditions corresponding to the iterative optimization structure according to the displacement response value; Feeding back the response constraint condition to the SIMP mathematical optimization model to perform displacement optimization, obtaining a number of material layout results, and selecting a target layout result with the smallest damping material volume; The optimized damping material density corresponding to each of the unit networks is determined according to the target layout result.

[0012] In one practicable manner, Also includes: A damping material plate with corresponding density distribution is generated according to the topological density cloud map, and the damping material plate is installed at a shock absorbing position corresponding to the plate-shell structure.

[0013] The achievable beneficial effects of the above technical solution are as follows: in order to effectively reduce the shock of the plate and shell structure and change the drawbacks of traditional shock-absorbing materials, the damping characteristic information of the damping material setting range is determined according to the stress conditions of the plate and shell structure, thereby establishing the load conditions, and then the damping material setting range is divided into blocks, and the force ratio between different unit areas is determined according to the damping characteristic information, thereby establishing the constraint conditions, and further building a finite element model according to the existing load conditions and boundary conditions, and then using the constraint conditions to determine the initial unit density corresponding to each unit area, and finally iteratively optimizing the initial unit density within the range of [0, 1] to generate the optimal damping material layout of the damping material setting range, and generating a topological density cloud map according to the damping density corresponding to each unit area in the layout, in this way, not only can suitable damping materials be set for different plate and shell structures, but also the mass of each unit density itself can be reduced, thereby improving the shock absorption effect, and achieving the goals of high shock absorption, low investment, high efficiency and low cost.

[0014] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description, claims, and drawings.

[0015] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings: Figure 1 Schematic diagram of the composition of the damping material topology optimization design method based on SIMP in an embodiment of the present invention; Figure 2 Schematic diagram of damping material division in the damping material topology optimization design method based on SIMP in an embodiment of the present invention. DETAILED DESCRIPTION

[0017] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0018] Example 1 This embodiment provides a damping material topology optimization design method based on SIMP, such as Figure 1 As shown, including: S1: Determine the setting range of the damping material according to the plate-shell structure to generate boundary conditions, and perform force analysis on the plate-shell structure to determine the damping characteristic information of the setting range of the damping material to generate load conditions; S2: dividing the damping material setting range into a plurality of unit areas, and generating constraint conditions by analyzing the force ratio corresponding to each unit area according to the damping characteristic information; S3: establishing a finite element model according to the boundary conditions and the load conditions, and constructing an initial unit density corresponding to each unit area in the finite element model according to the constraint conditions; S4: performing SIMP iterative optimization on each of the initial unit densities within a specified density range, generating an optimal damping material layout within the damping material setting range, and drawing and displaying a topological density cloud map.

[0019] In this example, the density of the damping material per unit area ranges from [0,1]; In this example, the boundary condition represents the condition that needs to be executed when setting the outer border of the damping material; In this example, the damping material setting range is in the plate-shell structure and is used to place the damping material; In this example, the load conditions represent the pressure conditions corresponding to each part of the plate and shell structure; In this example, the force ratio represents the ratio between the pressure borne by a unit area and the total pressure borne by the setting range of the damping material; In this example, the constraint condition represents a condition used to constrain the pressure range per unit area; In this example, the finite element model is an oSH model constructed using plate and shell elements and solid elements; In this example, the initial unit density represents the result of randomly matching a damping density to a unit area in the range of [0, 1] according to the force ratio.

[0020] The working principle and beneficial effects of the above technical solution: In order to effectively reduce the shock of plate and shell structures and change the drawbacks of traditional shock-absorbing materials, the damping characteristic information of the damping material setting range is determined according to the stress conditions of the plate and shell structures, thereby establishing load conditions, and then the damping material setting range is divided into blocks, and the force ratio between different unit areas is determined according to the damping characteristic information, thereby establishing constraint conditions, and further building a finite element model according to the existing load conditions and boundary conditions, and then using the constraint conditions to determine the initial unit density corresponding to each unit area, and finally iteratively optimizing the initial unit density within the range of [0, 1] to generate the optimal damping material layout of the damping material setting range, and generating a topological density cloud map according to the damping density corresponding to each unit area in the layout. In this way, not only can suitable damping materials be set for different plate and shell structures, but also the mass of each unit density itself can be reduced, thereby improving the shock absorption effect, and achieving the goals of high shock absorption, low investment, high efficiency and low cost.

[0021] Example 2 On the basis of Example 1, the damping material topology optimization design method based on SIMP, S4, comprises: S41: generating a stiffness matrix of the damping material setting range according to the initial unit density corresponding to each unit area, analyzing the displacement value corresponding to the stiffness matrix, and establishing a topology optimization response of the damping material setting range according to the finite element model; S42: determining an adjustable density value corresponding to each of the initial unit densities according to the specified density range, combining the adjustable density values ​​to generate an optimized density distribution, and inputting the optimized density distribution into the stiffness matrix to perform displacement value analysis to obtain a displacement value; S43: performing convergence analysis on the displacement value using the topology optimization response, and when the displacement value is in a convergence state, an optimal damping material layout within the damping material setting range is formed according to the optimized density distribution; otherwise, the adjustable density values ​​are combined to generate an iterative density distribution for displacement value analysis until the displacement value meets a preset convergence threshold; S44: When the displacement value converges, an optimal damping material layout of the damping material setting range is generated according to the corresponding current iterative density distribution, and a topological density cloud map is drawn and displayed.

[0022] In this example, the stiffness matrix represents a matrix used to present the stiffness of each unit area in the setting range of the damping material; In this example, the displacement value represents the response value corresponding to the displacement response of the plate and shell structure when it is subjected to external loads, as presented in the stiffness matrix; In this example, when the displacement value shows convergence, it means that the damping material setting range can offset the pressure generated by the plate and shell structure; In this example, the preset convergence threshold represents a point within the setting range of the damping material, that is, the damping material can share the pressure of the plate and shell structure.

[0023] The working principle and beneficial effects of the above technical solution are as follows: in order to set up a damping material that can share the pressure of the plate and shell structure, a stiffness matrix is ​​established according to the initial unit density corresponding to each unit area, and whether the current density distribution is valid is determined by judging whether the displacement value of the stiffness matrix converges. When it is invalid, a topological optimization response of the damping material setting range is established according to the finite element model, and then the adjustable density value corresponding to each initial unit density is further determined, so as to perform density optimization and generate an optimized density distribution. The convergence of this optimized density distribution is determined by analyzing the displacement value of the optimized density distribution using the topological optimization response of the damping material setting range, and a topological density cloud map is drawn by searching for the optimal damping material layout in a convergent state. In this way, the damping density of each unit area can be planned to ensure that the damping material can achieve the purpose of shock absorption and build a damping material layout that is suitable for the plate and shell structure.

[0024] Example 3 On the basis of Example 1, the damping material topology optimization design method based on SIMP, the process of performing force analysis on the plate-shell structure, includes: The vibration excitation characteristics of the plate-shell structure are analyzed according to formula (1); (1) in, represents the vibration excitation characteristics of the plate and shell structure, represents the N-dimensional mass of the plate and shell structure, represents the initial damping of the plate and shell structure, represents the stiffness characteristics of the plate and shell structure, represents the displacement characteristic equation of the plate and shell structure, The velocity characteristic equation representing the plate and shell structure is, The characteristic equation for the acceleration of the plate and shell structure is represented by, Indicates duration; The frequency response characteristics of the plate-shell structure are analyzed according to formula (2); (2) in, represents the frequency response characteristics of the plate-shell structure, A characteristic equation representing the amplitude of the plate and shell structure; Determine the vibration excitation characteristics of the plate-shell structure according to formula (1), and determine the frequency response characteristics of the plate-shell structure according to formula (2); The external force pressure information of the plate-shell structure is determined according to the vibration excitation characteristics and the frequency response characteristics, and the force value corresponding to each structural position in the plate-shell structure is determined according to the external force pressure information.

[0025] In this example, the external force compressive information of the plate and shell structure is analyzed by analyzing the vibration excitation characteristics and frequency response characteristics of the plate and shell structure, thereby determining the force value corresponding to each structural position in the plate and shell structure, which facilitates the determination of the damping characteristics corresponding to each unit area in subsequent work.

[0026] Example 4 On the basis of Example 1, the damping material topology optimization design method based on SIMP, the process of establishing a finite element model according to the boundary conditions and the load conditions includes: constructing a model grid in Optistruct according to the boundary conditions; Constructing the load condition to determine a number of load excitation points included in the model grid; Acquire the frequency response characteristics of the plate-shell structure, construct a unit amplitude-frequency curve according to the frequency response characteristics, and use the unit amplitude-frequency curve to analyze the frequency interval corresponding to each load excitation point in the model grid; Respectively identifying the real-time frequency response corresponding to each of the load excitation points; Constructing a frequency response function curve of the plate-shell structure according to the real-time frequency response corresponding to each load excitation point in the model grid; The load excitation points are distributed and arranged in the model grid, and the model grid is vibrated and rendered using the frequency response function curve to generate a finite element model.

[0027] In this example, the load excitation points represent several points in the model network that are subject to load pressure; In this example, the process of establishing the frequency response function curve is as follows: (1) Establish the model: establish a 2D plate and shell mesh and a 3D damping mesh, connect the two with coplanar and co-node connections, and assign material properties to both. In the finite element method, the mesh must be a continuous mesh. If it is not a continuous mesh, the two meshes are independent calculation areas. For models that never separate or whose contact does not change during the analysis process, coplanar and co-node connections can be used.

[0028] (2) Establish load excitation: define the load card DAREA and establish the load excitation point. DAREA is a comment [A7]: Please give a specific calculation example and suggest the location where the load will act in combination with the application scenario. At the same time, you can set the direction of action.

[0029] (3) Establish the solution frequency range: Create a unit amplitude-frequency curve LOADFREQ and define the frequency range used in the solution process (0-700 Hz).

[0030] (4) Define modal damping: Set the modal damping to 0.02.

[0031] (5) Create frequency response analysis step: Create analysis frequency points FREQ and modal frequency response analysis step: In finite element analysis, the mesh must be a continuous mesh. If it is not a continuous mesh, the two meshes are independent calculation areas. For models that never separate or whose contact does not change during the analysis, coplanar and co-node can be used. Freq.resp(modal), enter the relevant card properties.

[0032] The frequency response analysis step is mainly used to simulate the dynamic response of a structure under excitations of different frequencies. There are two types of Freq.resp, one is Freq.resp (direct) and the other is Freq.resp (modal). Direct is a direct method for obtaining frequency response, but the disadvantage is that the amount of calculation is huge. Modal is a modal superposition method for obtaining frequency response, which first finds the mode of the system and then calculates the response using the modal superposition principle. This algorithm has a relatively small amount of calculation and a fast calculation speed.

[0033] (6) Create a node set: Create a node set SET_GRID, and the nodes are evenly arranged on the plate and shell.

[0034] (7) Create output parameters: Create cards such as GLOBAL_OUTPUT_REQUEST and set output parameters.

[0035] (8) Output the results, process the data and create a frequency response function graph.

[0036] The working principle and beneficial effects of the above technical solution are as follows: in Optistruct, a model network is established according to boundary conditions, and then the load excitation points of the model network are established according to the load conditions. The frequency response characteristics of the plate and shell structure are further analyzed to establish the unit amplitude-frequency curve of each load excitation point and the frequency range of each load excitation point. Finally, the frequency response function curve of the plate and shell structure is constructed by identifying the trial frequency response of each load excitation point. Finally, a finite element model is constructed through vibration rendering. In this way, a model suitable for the plate and shell structure can be built, which can better perform damping density analysis.

[0037] Example 5 On the basis of Example 1, the damping material topology optimization design method based on SIMP further includes: Before performing S1, the elastic modulus and damping density of each damping material are analyzed according to formulas (3) and (4); (3) (4) in, represents the elastic modulus of the damping material, represents the damping density of the damping material, In order to avoid affecting the calculation matrix and causing singular elastic modulus optimization matrix, it is usually set to 0.001. In order to avoid the occurrence of singular damping density optimization matrix in the calculation matrix, it is usually set to 0.001. q represents the penalty factor, which is usually set to 3. Analyze the elastic range and damping range of the damping material according to the calculation results of formulas (3) and (4); Before performing S1, a corresponding target damping material is selected according to the basic parameters of the plate-shell structure.

[0038] The working principle and beneficial effects of the above technical solution are as follows: before setting the density of the damping material, the elastic modulus and damping density of each candidate damping material are analyzed first, so as to select a damping material suitable for the plate and shell structure. This can reduce the amount of subsequent calculations, reduce the number of increases or decreases in the damping density per unit area, and improve work efficiency and quality.

[0039] Example 6 On the basis of Example 1, the damping material topology optimization design method based on SIMP generates the process of the optimal damping material layout of the damping material setting range, including: Dividing the damping material setting range into a plurality of unit grids according to the finite element model, and establishing a SIMP mathematical optimization model using formula (5) according to the specifications of the unit grids; (5) Where X represents a fixed variable vector, represents the optimized response volume ratio, represents the area of ​​the i-th unit grid, represents the thickness of the i-th unit grid, represents the volume of the i-th unit grid, Indicates the frequency response amplitude, represents the modal weight, Indicates the set order of the optimized mode represents the frequency response displacement, and Respectively represent the i-th order modal frequency before and after optimization, and Respectively represent the upper and lower limits of the i-th order modal frequency after normalization, and They represent the minimum and maximum values ​​of the optimized design, and their values ​​are 0.001 and 1 respectively; Establishing an iteration range condition according to the specified density range, inputting each of the unit grids into the SIMP mathematical optimization model respectively, and iteratively optimizing each of the unit grids according to the iteration range condition respectively to obtain an optimized damping material density corresponding to each unit grid; According to the optimized damping material density corresponding to each unit grid, the optimal damping material layout of the plate-shell structure is determined. The working principle and beneficial effects of the above technical solution are as follows: by using the SIMP mathematical optimization model to optimize the density of the damping material setting range, the optimized damping material density corresponding to each unit grid is determined, thereby obtaining the optimal damping material layout of the plate-shell structure. The use of mathematical models for analysis can obtain more accurate density and improve the shock absorption of the optimal damping material layout.

[0040] Example 7 On the basis of Example 6, the damping material topology optimization design method based on SIMP, the process of obtaining the optimized damping material density corresponding to each unit grid includes: Selecting, according to the load condition, a load excitation point where the excitation force of the plate-shell structure is higher than a preset excitation force; Selecting a number of iterative optimization results that meet the constraint conditions, and obtaining a displacement response value corresponding to the load excitation point in each iterative optimization result; Generate response constraint conditions corresponding to the iterative optimization structure according to the displacement response value; Feeding back the response constraint condition to the SIMP mathematical optimization model to perform displacement optimization, obtaining a number of material layout results, and selecting a target layout result with the smallest damping material volume; The optimized damping material density corresponding to each of the unit networks is determined according to the target layout result.

[0041] In this example, the preset excitation force is the average excitation force within an eight-square grid centered at a load excitation point; In this example, the displacement response values ​​represent the response of the load excitation point to an iterative optimization result.

[0042] The working principle and beneficial effects of the above technical solution are as follows: the response constraint condition is established by iteratively optimizing the excitation force of each load excitation point in the plate-shell structure, and then the displacement optimization is performed according to the response constraint condition in the SIMP mathematical optimization model to determine several material layout results, and finally the target layout result with the smallest damping material volume is screened to determine the optimized damping material density corresponding to each unit grid. In this way, the damping material density of each unit grid can be verified and adjusted multiple times to ensure the shock absorption effect of each unit grid.

[0043] Example 8 On the basis of Example 1, the damping material topology optimization design method based on SIMP further includes: A damping material plate with corresponding density distribution is generated according to the topological density cloud map, and the damping material plate is installed on the plate-shell structure.

[0044] The working principle and beneficial effects of the above technical solution are as follows: the set density-distributed damping material plate is used to perform shock absorption work on the plate-shell structure.

[0045] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A damping material topology optimization design method based on SIMP, characterized in that: include: S1: Determine the setting range of the damping material according to the plate-shell structure to generate boundary conditions, and perform force analysis on the plate-shell structure to determine the damping characteristic information of the setting range of the damping material to generate load conditions; S2: dividing the damping material setting range into a plurality of unit areas, and generating constraint conditions by analyzing the force ratio corresponding to each unit area according to the damping characteristic information; S3: establishing a finite element model according to the boundary conditions and the load conditions, and constructing an initial unit density corresponding to each unit area in the finite element model according to the constraint conditions; S4: performing SIMP iterative optimization on each of the initial unit densities within a specified density range, generating an optimal damping material layout within the damping material setting range, and drawing and displaying a topological density cloud map; The S4 includes: S41: generating a stiffness matrix of the damping material setting range according to the initial unit density corresponding to each unit area, analyzing the displacement value corresponding to the stiffness matrix, and establishing a topology optimization response of the damping material setting range according to the finite element model; S42: determining an adjustable density value corresponding to each of the initial unit densities according to the specified density range, combining the adjustable density values ​​to generate an optimized density distribution, and inputting the optimized density distribution into the stiffness matrix to perform displacement value analysis to obtain a displacement value; S43: performing convergence analysis on the displacement value using the topology optimization response, and when the displacement value is in a convergence state, an optimal damping material layout within the damping material setting range is formed according to the optimized density distribution; otherwise, the adjustable density values ​​are combined to generate an iterative density distribution for displacement value analysis until the displacement value meets a preset convergence threshold; S44: When the displacement value converges, an optimal damping material layout of the damping material setting range is generated according to the corresponding current iterative density distribution, and a topological density cloud map is drawn and displayed.

2. The damping material topology optimization design method based on SIMP according to claim 1, characterized in that: The process of performing stress analysis on the plate and shell structure includes: The vibration excitation characteristics of the plate-shell structure are analyzed according to formula (1); （1） in, represents the vibration excitation characteristics of the plate and shell structure, represents the N-dimensional mass of the plate and shell structure, represents the initial damping of the plate and shell structure, represents the stiffness characteristics of the plate and shell structure, represents the displacement characteristic equation of the plate and shell structure, The velocity characteristic equation representing the plate and shell structure is, The characteristic equation for the acceleration of the plate and shell structure is represented by, Indicates duration; The frequency response characteristics of the plate-shell structure are analyzed according to formula (2); （2） in, represents the frequency response characteristics of the plate-shell structure, A characteristic equation representing the amplitude of the plate and shell structure; Determine the vibration excitation characteristics of the plate-shell structure according to formula (1), and determine the frequency response characteristics of the plate-shell structure according to formula (2); The external force pressure information of the plate-shell structure is determined according to the vibration excitation characteristics and the frequency response characteristics, and the force value corresponding to each structural position in the plate-shell structure is determined according to the external force pressure information.

3. The damping material topology optimization design method based on SIMP according to claim 1, characterized in that: The process of establishing a finite element model according to the boundary conditions and the load conditions includes: constructing a model grid in Optistruct according to the boundary conditions; Constructing the load condition to determine a number of load excitation points included in the model grid; Acquire the frequency response characteristics of the plate-shell structure, construct a unit amplitude-frequency curve according to the frequency response characteristics, and use the unit amplitude-frequency curve to analyze the frequency interval corresponding to each load excitation point in the model grid; Respectively identifying the real-time frequency response corresponding to each of the load excitation points; Constructing a frequency response function curve of the plate-shell structure according to the real-time frequency response corresponding to each load excitation point in the model grid; The load excitation points are distributed and arranged in the model grid, and the model grid is vibrated and rendered using the frequency response function curve to generate a finite element model.

4. The damping material topology optimization design method based on SIMP according to claim 1, characterized in that: Also includes: Before performing S1, the elastic modulus and damping density of each damping material are analyzed according to formulas (3) and (4); （3） （4） in, represents the elastic modulus of the damping material, represents the damping density of the damping material, is the elastic modulus optimization matrix, is the damping density optimization matrix, q represents the penalty factor; Analyze the elastic range and damping range of the damping material according to the calculation results of formulas (3) and (4); Before performing S1, a corresponding target damping material is selected according to the basic parameters of the plate-shell structure.

5. The damping material topology optimization design method based on SIMP according to claim 1, characterized in that: The process of generating an optimal damping material layout for the damping material setting range comprises: Dividing the damping material setting range into a plurality of unit grids according to the finite element model, and establishing a SIMP mathematical optimization model using formula (5) according to the specifications of the unit grids; （5） Where X represents a fixed variable vector, represents the optimized response volume ratio, represents the area of ​​the i-th unit grid, represents the thickness of the i-th unit grid, represents the volume of the i-th unit grid, Indicates the frequency response amplitude, represents the modal weight, represents the setting order of the optimization mode, represents the frequency response displacement, and Respectively represent the i-th order modal frequency before and after optimization, and Respectively represent the upper and lower limits of the i-th order modal frequency after normalization, and They represent the minimum and maximum values ​​of the optimized design, and their values ​​are 0.001 and 1 respectively; Establishing an iteration range condition according to the specified density range, inputting each of the unit grids into the SIMP mathematical optimization model respectively, and iteratively optimizing each of the unit grids according to the iteration range condition respectively to obtain an optimized damping material density corresponding to each unit grid; The optimal damping material layout of the plate-shell structure is determined according to the optimized damping material density corresponding to each unit grid.

6. The damping material topology optimization design method based on SIMP according to claim 5, characterized in that: The process of obtaining the optimized damping material density corresponding to each unit grid includes: Selecting, according to the load condition, a load excitation point where the excitation force of the plate-shell structure is higher than a preset excitation force; Selecting a number of iterative optimization results that meet the constraint conditions, and obtaining a displacement response value corresponding to the load excitation point in each iterative optimization result; Generate response constraint conditions corresponding to the iterative optimization structure according to the displacement response value; Feeding back the response constraint condition to the SIMP mathematical optimization model to perform displacement optimization, obtaining a number of material layout results, and selecting a target layout result with the smallest damping material volume; The optimized damping material density corresponding to each of the unit networks is determined according to the target layout result.

7. The damping material topology optimization design method based on SIMP according to claim 1, characterized in that: Also includes: A damping material plate with corresponding density distribution is generated according to the topological density cloud map, and the damping material plate is installed on the plate-shell structure.

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