SIMP-based Topological Optimization Design Method for Damping Materials

Abstract

The present invention provides a topology optimization design method for damping materials based on SIMP, which includes: determining the damping material setting range according to the plate and shell structure to generate boundary conditions, performing a force analysis on the plate and shell structure to determine the damping characteristic information of the damping material setting range to generate load conditions, dividing the damping material setting range into several unit areas, analyzing the force ratio corresponding to each unit area according to the damping characteristic information to generate constraint conditions, establishing a finite element model according to the boundary conditions and load conditions, constructing the initial unit density corresponding to each unit area in the finite element model according to the constraint conditions, performing SIMP iterative optimization on each initial unit density respectively within the specified density range, generating the optimal damping material layout of the damping material setting range, drawing and displaying the topology density cloud map, and being able to effectively optimize the layout of the damping material to reduce weight and maintain an efficient vibration damping effect.

Description

Technical Field

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

[0002] In contemporary engineering practices, especially in fields such as automobiles and civil engineering, effectively reducing and controlling vibration problems caused by external excitation forces is crucial for 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 the focus of attention in the engineering community.

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

[0004] The topology optimization design method of damping materials based on SIMP of the present invention can effectively optimize the layout of damping materials to reduce weight and maintain an efficient vibration damping effect.

[0005] The present invention provides a topology optimization design method of damping materials based on SIMP, including:

[0006] S1: Determine the boundary conditions by generating the damping material setting range according to the plate and shell structure, and determine the damping characteristic information of the damping material setting range to generate load conditions by performing a force analysis on the plate and shell structure;

[0007] S2: Divide the damping material setting range into several unit areas, and analyze the force ratio corresponding to each unit area according to the damping characteristic information to generate constraint conditions;

[0008] S3: Establish a finite element model according to the boundary conditions and the load conditions, and construct the initial unit density corresponding to each unit area in the finite element model according to the constraint conditions;

[0009] S4: Perform SIMP iterative optimization on each initial unit density within a specified density range to generate the optimal damping material layout of the damping material setting range, draw a topology density cloud map and display it.

[0010] In an implementable manner,

[0011] S4 includes:

[0012] S41: Generate the stiffness matrix for the damping material setting range according to the initial unit density corresponding to each unit area, analyze the displacement value corresponding to the stiffness matrix, and establish the topological optimization response for the damping material setting range according to the finite element model;

[0013] S42: Determine the adjustable density value corresponding to each initial unit density according to the specified density range, combine the adjustable density values to generate an optimized density distribution, and input the optimized density distribution into the stiffness matrix for displacement value analysis to obtain the displacement value;

[0014] S43: Use the topological optimization response to perform convergence analysis on the displacement value. When the displacement value is in a convergent state, form the optimal damping material layout for the damping material setting range according to the optimized density distribution. Otherwise, combine the adjustable density values to generate an iterative density distribution for displacement value analysis until the displacement value meets the preset convergence threshold;

[0015] S44: When the displacement value shows convergence, generate the optimal damping material layout for the damping material setting range according to the corresponding current iterative density distribution, draw and display the topological density nephogram.

[0016] In an implementable manner,

[0017] The process of performing a force analysis on the plate-shell structure includes:

[0018] Analyze the vibration excitation characteristics of the plate-shell structure according to formula (1);

[0019] (1)

[0020] Where, represents the vibration excitation characteristics of the plate-shell structure, represents the N-dimensional mass of the plate-shell structure, represents the initial damping of the plate-shell structure, represents the stiffness characteristics of the plate-shell structure, represents the displacement characteristic equation of the plate-shell structure, represents the velocity characteristic equation of the plate-shell structure, represents the acceleration characteristic equation of the plate-shell structure, represents the time duration;

[0021] Analyze the frequency response characteristics of the plate-shell structure according to formula (2);

[0022] (2)

[0023] Where, Represent the frequency response characteristics of the plate-shell structure Represent the amplitude characteristic equation of the plate-shell structure;

[0024] 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);

[0025] Determine the external force compression information of the plate-shell structure according to the vibration excitation characteristics and the frequency response characteristics, and determine the force value corresponding to each structural position in the plate-shell structure according to the external force compression information.

[0026] In an implementable manner,

[0027] The process of establishing a finite element model according to the boundary conditions and the load conditions includes:

[0028] Construct a model grid according to the boundary conditions in Optistruct;

[0029] Construct the load conditions to determine several load excitation points included in the model grid;

[0030] Obtain the frequency response characteristics of the plate-shell structure, construct a unit amplitude-frequency curve according to the frequency response characteristics, and analyze the frequency interval corresponding to each load excitation point in the model grid by using the unit amplitude-frequency curve;

[0031] Identify the real-time frequency response corresponding to each load excitation point respectively;

[0032] Construct the 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;

[0033] Arrange the load excitation points in the model grid, and use the frequency response function curve to perform vibration rendering on the model grid to generate a finite element model.

[0034] In an implementable manner,

[0035] It further includes:

[0036] Before performing S1, analyze the elastic modulus and damping density of each damping material according to formulas (3) and (4);

[0037] (3)

[0038] (4)

[0039] Wherein, Represents the elastic modulus of the damping material, Represents the damping density of the damping material, It is denoted as the elastic modulus optimization matrix for avoiding the singularity of the computational matrix, usually set to 0.001. It is denoted as the damping density optimization matrix for avoiding the singularity of the computational matrix, usually set to 0.001, and q represents the penalty factor, usually set to 3.

[0040] Analyze the elastic range and damping range of the damping material according to the calculation results of formulas (3) and (4).

[0041] Before performing S1, select the corresponding target damping material according to the basic parameters of the plate and shell structure.

[0042] In an implementable manner,

[0043] The process of generating the optimal damping material layout within the set range of the damping material includes:

[0044] Divide the set range of the damping material into several unit meshes according to the finite element model, and establish a SIMP mathematical optimization model using formula (5) according to the specifications of the unit meshes.

[0045] (5)

[0046] Wherein, X represents the fixed variable vector, represents the optimized response volume ratio, represents the area of the i-th unit mesh, represents the thickness of the i-th unit mesh, represents the volume of the i-th unit mesh, represents the frequency response amplitude, represents the modal weight, represents the set order of the optimized mode, represents the frequency response displacement, and respectively represent the i-th modal frequencies before and after optimization, and respectively represent the upper and lower limits of the i-th modal frequency after normalization processing, and respectively represent the minimum and maximum values of the optimized design, with values of 0.001 and 1 respectively;

[0047] Establish an iteration range condition according to the specified density range, input each unit mesh into the SIMP mathematical optimization model respectively, and perform iterative optimization on each unit mesh according to the iteration range condition to obtain the optimized damping material density corresponding to each unit mesh.

[0048] Determine the optimal damping material layout of the plate and shell structure according to the optimized damping material density corresponding to each unit grid.

[0049] In an implementable manner,

[0050] The process of obtaining the optimized damping material density corresponding to each unit grid includes:

[0051] Screen the load excitation points on the plate and shell structure where the excitation force is higher than the preset excitation force according to the load conditions;

[0052] Select several iterative optimization results that meet the constraint conditions, and obtain the displacement response values corresponding to the load excitation points for each iterative optimization result;

[0053] Generate response constraint conditions for the corresponding iterative optimization structure according to the displacement response values;

[0054] Feed the response constraint conditions back into the SIMP mathematical optimization model for displacement optimization to obtain several material layout results, and screen the target layout result with the smallest damping material volume;

[0055] Determine the optimized damping material density corresponding to each unit network according to the target layout result.

[0056] In an implementable manner,

[0057] It also includes:

[0058] Generate a damping material plate with a corresponding density distribution according to the topological density cloud map, and install the damping material plate at the corresponding shock-absorbing position of the plate and shell structure.

[0059] The achievable beneficial effects of the above technical solution are: In order to effectively damp the plate and shell structure and change the drawbacks of traditional damping materials, the damping characteristic information of the damping material setting range is determined according to the force-bearing situation of the plate and shell structure, so as to establish the load conditions. 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, so as to establish the constraint conditions. Further, a finite element model is built according to the existing load conditions and boundary conditions, and then the initial unit density corresponding to each unit area is determined by using the constraint conditions. Finally, the initial unit density is iteratively optimized within the range of [0, 1] to generate the optimal damping material layout of the damping material setting range. According to the damping density corresponding to each unit area in this layout, a topological density cloud map is generated. In this way, not only can suitable damping materials be set for different plate and shell structures, but also the self-mass of each unit density can be reduced, the damping effect can be improved, and the goals of high damping, low investment, high benefit, and low cost are achieved.

[0060] Other features and advantages of the present invention will be described in the following specification, and, in part, will become apparent from the specification, or will be understood by practicing the present invention. The objectives and other advantages of the present invention can be achieved and obtained by the structures particularly pointed out in the written specification, claims, and drawings.

[0061] The technical solution of the present invention will be further described in detail below through the drawings and embodiments. Description of the Drawings

[0062] The 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, but do not constitute a limitation to the present invention. In the drawings:

[0063] Figure 1 is a schematic diagram of the composition of the SIMP-based damping material topology optimization design method in the embodiment of the present invention;

[0064] Figure 2 is a schematic diagram of the damping material division of the SIMP-based damping material topology optimization design method in the embodiment of the present invention. Detailed Embodiments

[0065] The following describes the preferred embodiments of the present invention with reference to the 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.

[0066] Embodiment 1

[0067] This embodiment provides a SIMP-based damping material topology optimization design method, as Figure 1 shown, including:

[0068] S1: Determine the boundary conditions by generating the damping material setting range according to the plate and shell structure, and perform a force analysis on the plate and shell structure to determine the damping characteristic information of the damping material setting range to generate the load conditions;

[0069] S2: Divide the damping material setting range into several unit areas, and analyze the force ratio corresponding to each unit area according to the damping characteristic information to generate the constraint conditions;

[0070] S3: Establish a finite element model according to the boundary conditions and the load conditions, and construct the initial unit density corresponding to each unit area in the finite element model according to the constraint conditions;

[0071] S4: Perform SIMP iterative optimization on each of the initial unit densities within the specified density range to generate the optimal damping material layout of the damping material setting range, draw the topological density cloud map and display it.

[0072] In this example, the density range of the damping material per unit area is [0, 1];

[0073] In this example, the boundary condition represents the condition that needs to be executed when setting the outer frame of the damping material;

[0074] In this example, the setting range of the damping material is within the plate and shell structure and is used to place the damping material;

[0075] In this example, the load condition represents the pressure situation corresponding to each part of the plate and shell structure;

[0076] In this example, the stress 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;

[0077] In this example, the constraint condition represents the condition used to constrain the pressure range of a unit area;

[0078] In this example, the finite element model is an oSH model constructed using plate and shell elements and solid elements;

[0079] In this example, the initial unit density represents the result of randomly matching a damping density for a unit area from the range [0, 1] according to the stress ratio.

[0080] The working principle and beneficial effects of the above technical solution: In order to effectively damp the plate and shell structure and change the disadvantages of traditional damping materials, the damping characteristic information of the setting range of the damping material is determined according to the stress situation of the plate and shell structure, so as to establish the load condition. Then, the setting range of the damping material is divided into blocks, and the stress ratio between different unit areas is determined according to the damping characteristic information, so as to establish the constraint condition. Further, a finite element model is built according to the existing load condition and boundary condition, and then the constraint condition is used to determine the initial unit density corresponding to each unit area. Finally, the initial unit density is iteratively optimized within the range [0, 1] to generate the optimal damping material layout of the setting range of the damping material. According to the damping density corresponding to each unit area in this layout, a topological density cloud map is generated. In this way, not only can suitable damping materials be set for different plate and shell structures, but also the self-mass of each unit density can be reduced, the damping effect can be improved, and the goals of high damping, low investment, high benefit, and low cost are achieved.

[0081] Embodiment 2

[0082] Based on the Embodiment 1, for the topology optimization design method of the damping material based on SIMP, the S4 includes:

[0083] S41: Generate the stiffness matrix for the damping material setting range based on the initial unit density corresponding to each unit area, analyze the displacement values corresponding to the stiffness matrix, and establish the topology optimization response for the damping material setting range according to the finite element model;

[0084] S42: Determine the adjustable density value corresponding to each initial unit density according to the specified density range, combine the adjustable density values to generate an optimized density distribution, and input the optimized density distribution into the stiffness matrix for displacement value analysis to obtain displacement values;

[0085] S43: Use the topology optimization response to perform convergence analysis on the displacement values. When the displacement values are in a converged state, form the optimal damping material layout for the damping material setting range according to the optimized density distribution. Otherwise, combine the adjustable density values to generate an iterative density distribution for displacement value analysis until the displacement values meet the preset convergence threshold;

[0086] S44: When the displacement values show convergence, generate the optimal damping material layout for the damping material setting range according to the corresponding current iterative density distribution, draw and display the topology density contour map.

[0087] In this example, the stiffness matrix is a matrix used to represent the stiffness of each unit area in the damping material setting range;

[0088] In this example, the displacement values represent the response values corresponding to the displacement response of the plate and shell structure under the action of external loads presented in the stiffness matrix;

[0089] In this example, when the displacement values show convergence, it means that the damping material setting range can offset the pressure generated by the plate and shell structure;

[0090] In this example, the preset convergence threshold represents a point within the damping material setting range, that is, the damping material can share the pressure of the plate and shell structure.

[0091] Working principle and beneficial effects of the above technical solution: In order to set a damping material that can share the pressure of the plate-shell structure, a stiffness matrix is established according to the initial unit density corresponding to each unit area. By judging whether the displacement value of the stiffness matrix converges, it is determined whether the current density distribution is effective. When it is ineffective, a topological optimization response of the damping material setting range is established based on 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. By using the topological optimization response of the damping material setting range to analyze the displacement value of the optimized density distribution, the convergence of the current optimized density distribution is determined. By searching for the optimal damping material layout in the convergent state, a topological density nephogram is drawn. 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 suitable for the plate-shell structure.

[0092] Example 3

[0093] Based on the method for topological optimization design of damping materials based on SIMP in Example 1, the process of analyzing the force on the plate-shell structure includes:

[0094] Analyze the vibration excitation characteristics of the plate-shell structure according to formula (1);

[0095] (1)

[0096] Wherein, represents the vibration excitation characteristics of the plate-shell structure, represents the N-dimensional mass of the plate-shell structure, represents the initial damping of the plate-shell structure, represents the stiffness characteristics of the plate-shell structure, represents the displacement characteristic equation of the plate-shell structure, represents the velocity characteristic equation of the plate-shell structure, represents the acceleration characteristic equation of the plate-shell structure, represents the duration;

[0097] Analyze the frequency response characteristics of the plate-shell structure according to formula (2);

[0098] (2)

[0099] Wherein, represents the frequency response characteristics of the plate-shell structure, represents the amplitude characteristic equation of the plate-shell structure;

[0100] 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);

[0101] Determine the external force compression information of the plate-shell structure according to the vibration excitation characteristics and the frequency response characteristics, and determine the force value corresponding to each structural position in the plate-shell structure according to the external force compression information.

[0102] In this example, the external force compression information of the plate-shell structure is analyzed by analyzing the vibration excitation characteristics and frequency response characteristics of the plate-shell structure, so as to determine the force value corresponding to each structural position in the plate-shell structure, which is convenient for determining the damping characteristics corresponding to each unit area in subsequent work.

[0103] Example 4

[0104] On the basis of Example 1, in the method for topology optimization design of damping materials based on SIMP, the process of establishing a finite element model according to the boundary conditions and the load conditions includes:

[0105] Construct a model grid in Optistruct according to the boundary conditions;

[0106] Construct the load conditions to determine several load excitation points included in the model grid;

[0107] Obtain the frequency response characteristics of the plate-shell structure, construct a unit amplitude-frequency curve according to the frequency response characteristics, and analyze the frequency interval corresponding to each load excitation point in the model grid by using the unit amplitude-frequency curve;

[0108] Identify the real-time frequency response corresponding to each load excitation point respectively;

[0109] Construct the 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;

[0110] Arrange the load excitation points in the model grid, and use the frequency response function curve to perform vibration rendering on the model grid to generate a finite element model.

[0111] In this example, the load excitation points represent several points that bear load pressure in the model network;

[0112] In this example, the process of establishing the frequency response function curve is as follows: (1) Establish a model: Establish a 2D plate-shell grid and a 3D damping grid, connect the coplanar and co-nodal connections at the connection between the two, and assign material properties to both. In finite elements, the grid must be a continuous grid. If it is not a continuous grid, the two grids are independent calculation regions. For models that never separate or whose contacts do not change during the analysis, coplanar and co-nodal connections can be used.

[0113] (2)Establish load excitation: Define the load card DAREA and establish the load excitation points. DAREA is a note [A7]: Please give a specific calculation example. It is recommended to combine the application scenario with the location where the load will act, and the acting direction can also be set.

[0114] (3)Establish the solution frequency range: Create a unit amplitude-frequency curve LOADFREQ and define the frequency range 0 - 700 Hz used in the solution process.

[0115] (4)Define modal damping: Set the modal damping to 0.02.

[0116] (5)Create a frequency response analysis step: Create the analysis frequency points FREQ and the modal frequency response analysis step: In the finite element, the mesh must be a continuous mesh. If it is not a continuous mesh, the two meshes are independent calculation regions. For models that never separate or where the contact does not change during the analysis, coplanar and co - nodal points can be used. Freq.resp(modal), input the relevant card attributes.

[0117] The frequency response analysis step is mainly used to simulate the dynamic response of a structure under excitation at different frequencies. There are two types of Freq.resp, one is called Freq.resp(direct), and the other is called Freq.resp(modal). Direct is to obtain the frequency response by the direct method, and the disadvantage is that the computational amount is huge. Modal is to obtain the frequency response by the modal superposition method. First, find the modes of the system, and then calculate the response using the modal superposition principle. This algorithm has a relatively small computational amount and a faster calculation speed.

[0118] (6)Create a node set: Establish a node set SET_GRID, and the nodes are evenly arranged on the plate and shell.

[0119] (7)Create output parameters: Establish cards such as GLOBAL_OUTPUT_REQUEST and set the output parameters.

[0120] (8)Output the results, process the data and establish a frequency response function curve graph.

[0121] Working principle and beneficial effects of the above technical solution: In Optistruct, a model network is established according to the 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 interval of each load excitation point. Finally, the frequency response function curve of the plate and shell structure is constructed by identifying the actual frequency response of each load excitation point. Finally, a finite element model is constructed through vibration rendering. In this way, a model suitable for this plate and shell structure can be built, and better damping density analysis can be carried out.

[0122] Example 5

[0123] Based on Example 1, the SIMP-based damping material topology optimization design method further includes:

[0124] Before performing S1, analyze the elastic modulus and damping density of each damping material according to Formulas (3) and (4);

[0125] (3)

[0126] (4)

[0127] Where, represents the elastic modulus of the damping material, represents the damping density of the damping material, represents the elastic modulus optimization matrix to avoid the singularity of the calculation matrix, usually set to 0.001, represents the damping density optimization matrix to avoid the singularity of the calculation matrix, usually set to 0.001, and q represents the penalty factor, usually set to 3;

[0128] Analyze the elastic range and damping range of the damping material according to the calculation results of Formulas (3) and (4);

[0129] Before performing S1, select the corresponding target damping material according to the basic parameters of the plate and shell structure.

[0130] Working principle and beneficial effects of the above technical solution: Before setting the damping material density, first analyze the elastic modulus and damping density of each alternative damping material, so as to select a damping material suitable for this plate and shell structure. In this way, the later calculation amount can be reduced, the increase or decrease times of the damping density per unit area can be reduced, and the work efficiency and quality are improved.

[0131] Example 6

[0132] Based on Embodiment 1, in the topology optimization design method of the damping material based on SIMP, the process of generating the optimal damping material layout within the set range of the damping material includes:

[0133] Dividing the set range of the damping material into a number of unit meshes according to the finite element model, and establishing a SIMP mathematical optimization model using Equation (5) according to the specifications of the unit meshes;

[0134] (5)

[0135] where X represents the fixed variable vector, represents the optimized response volume ratio, represents the area of the i-th unit mesh, represents the thickness of the i-th unit mesh, represents the volume of the i-th unit mesh, represents the frequency response amplitude, represents the modal weight, represents the set order of the optimized mode represents the frequency response displacement, and respectively represent the i-th modal frequencies before and after optimization, and respectively represent the upper and lower limits of the i-th modal frequency after normalization processing, and respectively represent the minimum and maximum values of the optimized design, taking values of 0.001 and 1 respectively;

[0136] Establishing an iteration range condition according to the specified density range, inputting each unit mesh into the SIMP mathematical optimization model respectively, and performing iterative optimization on each unit mesh according to the iteration range condition to obtain the optimized damping material density corresponding to each unit mesh;

[0137] Determining the optimal damping material layout of the plate and shell structure according to the optimized damping material density corresponding to each unit mesh. The working principle and beneficial effects of the above technical solution: By using the SIMP mathematical optimization model to perform density optimization on the set range of the damping material, the optimized damping material density corresponding to each unit mesh is determined, thereby obtaining the optimal damping material layout of the plate and shell structure. Analyzing using the mathematical model can obtain more accurate density and improve the shock absorption performance of the optimal damping material layout.

[0138] Embodiment 7

[0139] Based on Embodiment 6, in the topology optimization design method of the damping material based on SIMP, the process of obtaining the optimized damping material density corresponding to each unit mesh includes:

[0140] Screen the load excitation points of the plate and shell structure where the excitation force is higher than the preset excitation force according to the load conditions;

[0141] Select several iterative optimization results that meet the constraint conditions, and obtain the displacement response values corresponding to the load excitation points for each iterative optimization result;

[0142] Generate response constraint conditions for the corresponding iterative optimization structure according to the displacement response values;

[0143] Feed the response constraint conditions back into the SIMP mathematical optimization model for displacement optimization to obtain several material layout results, and screen the target layout result with the smallest volume of damping material;

[0144] Determine the optimized damping material density corresponding to each unit cell according to the target layout result.

[0145] In this example, the preset excitation force is the average excitation force within the octagonal grid centered on a load excitation point;

[0146] In this example, the displacement response value represents the response of the load excitation point to an iterative optimization result.

[0147] The working principle and beneficial effects of the above technical solution: By iteratively optimizing the excitation force of each load excitation point in the plate and shell structure to establish response constraint conditions, and then performing displacement optimization in the SIMP mathematical optimization model according to the response constraint conditions to determine several material layout results, and finally screening the target layout result with the smallest volume of damping material to determine the optimized damping material density corresponding to each unit cell. In this way, the damping material density of each unit cell can be verified and adjusted multiple times, ensuring the shock absorption effect of each unit cell.

[0148] Example 8

[0149] Based on Example 1, the SIMP-based damping material topology optimization design method further includes:

[0150] Generate a damping material plate with a corresponding density distribution according to the topology density cloud map, and install the damping material plate on the plate and shell structure.

[0151] The working principle and beneficial effects of the above technical solution: The set damping material plate with a corresponding density distribution is used for shock absorption work on the plate and shell structure.

[0152] 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 equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A topology optimization design method of damping materials based on SIMP, characterized in that, Including: S1: Determine the damping material setting range based on the plate-shell structure to generate boundary conditions, and perform a force analysis on the plate-shell structure to determine the damping characteristic information of the damping material setting range to generate load conditions; S2: Divide the damping material setting range into several unit areas, and analyze the force ratio corresponding to each unit area according to the damping characteristic information to generate constraint conditions; S3: Establish a finite element model according to the boundary conditions and the load conditions, and construct the initial unit density corresponding to each unit area in the finite element model according to the constraint conditions; S4: Perform SIMP iterative optimization on each of the initial unit densities within the specified density range to generate the optimal damping material layout of the damping material setting range, draw and display a topological density contour map; The S4 includes: S41: Generate the stiffness matrix of the damping material setting range according to the initial unit density corresponding to each unit area, analyze the displacement value corresponding to the stiffness matrix, and establish the topological optimization response of the damping material setting range according to the finite element model; S42: Determine the adjustable density value corresponding to each initial unit density according to the specified density range, combine the adjustable density values to generate an optimized density distribution, input the optimized density distribution into the stiffness matrix for displacement value analysis to obtain a displacement value; S43: Use the topological optimization response to perform a convergence analysis on the displacement value. When the displacement value is in a converged state, form the optimal damping material layout of the damping material setting range according to the optimized density distribution. Otherwise, combine the adjustable density values to generate an iterative density distribution for displacement value analysis until the displacement value meets the preset convergence threshold; S44: When the displacement value shows convergence, generate the optimal damping material layout of the damping material setting range according to the corresponding current iterative density distribution, draw and display a topological density contour map.

2. The topology optimization design method of the damping material based on SIMP according to claim 1, wherein The process of performing a force analysis on the plate-shell structure includes: Analyze the vibration excitation characteristics of the plate-shell structure according to formula (1); （1） Among them, represents the vibration excitation characteristics of the plate-shell structure, represents the N-dimensional mass of the plate-shell structure, represents the initial damping of the plate-shell structure, represents the stiffness characteristics of the plate-shell structure, represents the displacement characteristic equation of the plate-shell structure, represents the velocity characteristic equation of the plate-shell structure, represents the acceleration characteristic equation of the plate-shell structure, represents the duration; Analyze the frequency response characteristics of the plate-shell structure according to formula (2); （2） Among them, represents the frequency response characteristics of the plate-shell structure, represents the amplitude characteristic equation of the plate-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); Determine the external force compression information of the plate-shell structure according to the vibration excitation characteristics and the frequency response characteristics, and determine the force value corresponding to each structural position in the plate-shell structure according to the external force compression information.

3. The topology optimization design method of the damping material based on SIMP according to claim 1, wherein The process of establishing a finite element model according to the boundary conditions and the load conditions includes: Construct a model grid in Optistruct according to the boundary conditions; Construct the load conditions to determine several load excitation points included in the model grid; Obtain the frequency response characteristics of the plate-shell structure, construct a unit amplitude-frequency curve according to the frequency response characteristics, and analyze the frequency interval corresponding to each load excitation point in the model grid by using the unit amplitude-frequency curve; Identify the real-time frequency response corresponding to each load excitation point respectively; Construct the frequency response function curve of the plate and shell structure according to the real-time frequency response corresponding to each load excitation point in the model grid; Arrange the load excitation points in the model grid, and use the frequency response function curve to perform vibration rendering on the model grid to generate a finite element model.

4. The topology optimization design method of the damping material based on SIMP according to claim 1, wherein It also includes: Before performing S1, analyze the elastic modulus and damping density of each damping material according to formulas (3) and (4); （3） （4） Among them, 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, and 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, select the corresponding target damping material according to the basic parameters of the plate and shell structure.

5. The topology optimization design method of the damping material based on SIMP according to claim 1, characterized in that The process of generating the optimal damping material layout within the set range of the damping material includes: Divide the set range of the damping material into several unit grids according to the finite element model, and establish a SIMP mathematical optimization model using formula (5) according to the specifications of the unit grids; （5） Wherein, 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, represents the frequency response amplitude, represents the modal weight, represents the set order of the optimized mode, represents the frequency response displacement, and respectively represent the i-th modal frequencies before and after optimization, and respectively represent the upper and lower limits of the i-th modal frequency after normalization processing, and respectively represent the minimum and maximum values of the optimized design, with values of 0.001 and 1 respectively; Establish an iteration range condition according to the specified density range, input each unit grid into the SIMP mathematical optimization model respectively, and perform iterative optimization on each unit grid according to the iteration range condition to obtain the optimized damping material density corresponding to each unit grid; Determine the optimal damping material layout of the plate and shell structure according to the optimized damping material density corresponding to each unit grid.

6. The topology optimization design method of the damping material based on SIMP according to claim 5, wherein The process of obtaining the optimized damping material density corresponding to each unit grid includes: Screen the load excitation points on the plate and shell structure where the excitation force is higher than the preset excitation force according to the load conditions; Select several iterative optimization results that meet the constraint conditions, and obtain the displacement response values corresponding to the load excitation points in each iterative optimization result respectively; Generate a response constraint condition for the corresponding iterative optimization structure according to the displacement response value; Feed the response constraint condition back into the SIMP mathematical optimization model for displacement optimization to obtain several material layout results, and screen the target layout result with the smallest volume of the damping material; Determine the optimized damping material density corresponding to each unit network according to the target layout result.

7. The topology optimization design method of the damping material based on SIMP according to claim 1, characterized in that It also includes: Generate a damping material plate with a corresponding density distribution according to the topological density cloud map, and install the damping material plate on the plate and shell structure.

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