Numerical modeling method for calculating electromagnetic scattering of honeycomb sandwich structure

Abstract

The invention provides a numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure. The method comprises the following steps: step 1, dividing the honeycomb sandwich structure into a honeycomb structure and dielectric layers located on two sides of the honeycomb structure; 2, obtaining a finite element grid information file in the honeycomb structure; step 3, acquiring surface grid vertex coordinate information and vertex number information of the outer surface; 4, performing modeling and surface mesh generation on the dielectric layer to obtain a corresponding surface mesh information file; 5, the finite element grid information files in the steps 2-4, the surface grid vertex coordinate information and vertex number information of the outer surface of the honeycomb structure and the surface grid information file of the dielectric layer are connected, global grid information of the honeycomb sandwich structure is obtained, and model construction is completed; and 6, performing electromagnetic scattering calculation according to the model. The modeling method provided by the invention can be used for efficiently calculating the large-size honeycomb sandwich structure.

Description

Technical Field

[0001] The invention relates to the field of electromagnetic scattering, and in particular to a numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure. Background Art

[0002] As part of the outer shell or internal components of a spacecraft, the shielding effectiveness of the honeycomb sandwich structure against electromagnetic interference and how to prevent the structure itself from becoming an interference source are the focus of electromagnetic simulation. In actual engineering applications, the honeycomb sandwich structure is usually designed into a standard square plate shape, and a series of standardized test methods are used to ensure that the material meets specific design requirements. In the field of military applications, the honeycomb sandwich structure has a certain absorption capacity for electromagnetic waves, making it one of the key technologies for reducing radar cross-section and achieving stealth effects when building stealth aircraft. Therefore, the optimization of its wave absorption performance is a top priority in research.

[0003] However, when exploring the specific effects of internal variables of honeycomb sandwich structures, such as the size of honeycomb units, the thickness of the wall, and the material of the core material on the absorbing performance, if we rely solely on actual measurement methods to tune the structure, we will face high-cost challenges, and it will take a lot of manpower and expensive experimental equipment to obtain the required parameters. Therefore, using computer numerical simulation technology to study honeycomb sandwich structures can not only help engineers quickly evaluate design solutions and shorten the design cycle, but also greatly reduce the cost of trial and error and improve design efficiency.

[0004] With the rapid development of computer technology, computational electromagnetics has been widely used in engineering practice, and a series of electromagnetic methods for simulation design have been generated, including finite element method (FEM), method of moments (MoM), finite difference time domain (FDTD), geometric optics (GO), physical optics (PO), etc. However, the complex electromagnetic scattering effects caused by the porous characteristics and anisotropic multilayer media unique to honeycomb sandwich structures require in-depth prediction and optimization using accurate simulation technology. Summary of the invention

[0005] The present invention provides an efficient numerical modeling method for calculating electromagnetic scattering of honeycomb sandwich structures. The technology is a hybrid solution technology based on finite element method, multilayer dielectric integral equation, and multilayer fast multipole technology, and proposes an efficient algorithm for electromagnetic scattering of honeycomb sandwich structures.

[0006] The modeling method provided by the present invention comprises the following steps:

[0007] Step 1: splitting and classifying the honeycomb sandwich structure according to whether it is easy to use the surface mesh division rule, and dividing the honeycomb sandwich structure into a honeycomb structure and a dielectric layer located on both sides of the honeycomb structure;

[0008] Step 2: Model the honeycomb structure as a uniform dielectric body with a series of impedance plate boundary conditions, and obtain the finite element mesh information file inside the honeycomb structure;

[0009] Step 3: Use a triangular surface mesh to divide the outer surface of the honeycomb structure, and obtain the vertex coordinate information and vertex number information of the surface mesh of the outer surface;

[0010] Step 4: Modeling and surface meshing the dielectric layer to obtain a corresponding surface mesh information file;

[0011] Step 5: Connect the finite element mesh information files in steps 2 to 4, the surface mesh vertex coordinate information and vertex number information of the outer surface of the honeycomb structure, and the surface mesh information file of the dielectric layer to obtain the global mesh information of the honeycomb sandwich structure and complete the construction of the model;

[0012] Step 6: Perform electromagnetic scattering calculations based on the model.

[0013] Furthermore, the honeycomb structure is mainly composed of a plurality of unit cells, each unit cell is connected by a unit wall, and the outer surface of the honeycomb structure includes a contact surface connected to the medium layer on both sides and a contact surface in contact with the air, wherein the outer surface is divided by a surface grid, and the interior of the honeycomb structure is divided by a volume grid.

[0014] Furthermore, the step 2 includes the following contents:

[0015] Step 2.1: Remove the honeycomb cell wall and fill the inner area of ​​the honeycomb structure with free space to simplify it into a uniform dielectric body model with a periodic zero-thickness impedance surface;

[0016] Step 2.2: Perform tetrahedral meshing on the simplified honeycomb structure, ensure that the cell wall mesh of each honeycomb unit is included in the tetrahedral mesh information, obtain the vertex coordinate information and vertex number information of the volume mesh discretization, store the vertex coordinate information in the filename.xyz file, and store the vertex number information in the filename.lv file;

[0017] Step 2.3: Partition the tetrahedral mesh of the honeycomb structure to obtain a filename.metis file containing the area where each tetrahedron is located;

[0018] Step 2.4: Extract the mesh information of each cell wall and save the triangle mesh vertex numbers of the cell wall into the filename.rsbc file;

[0019] Step 2.5: Assemble the filename.xyz, filename.lv, filename.metis and filename.rsbc files into the filename.fem file.

[0020] Furthermore, the step 3 comprises:

[0021] The outer surface of the honeycomb structure is divided into the contact surface with the air, the contact surface with the upper uniform medium and the contact surface with the lower uniform medium. The contact surfaces are divided separately. Then, the surface mesh vertex coordinate information and vertex number information of the outer surface of the honeycomb structure are stored in the newly created filename.bi_fe file.

[0022] Furthermore, the step 4 includes the following contents:

[0023] Step 4.1: Model the two dielectric layers, extract the outer surface of the model, perform surface meshing on the outer surface of the dielectric layer, and output the surfaces of the same type into the same surface mesh file;

[0024] Step 4.2: Partition each surface mesh file;

[0025] Step 4.3: Mark the surface mesh attributes and numbers, and set the material area information of the outer surface. These numbers correspond to the material areas one by one and are stored in the filename.sort file. The vertex coordinate information, vertex number information, surface number information and material information on both sides of the surface of the outer surface mesh of the dielectric layer are stored in a newly created filename.bi_bi file;

[0026] Step 4.4: Combine the contents of the filename.bi_fe file and the filename.bi_bi file into filename.bi.

[0027] Furthermore, the step 5 includes the following contents:

[0028] Step 5.1: Link the filename.fem and filename.bi.

[0029] For the partitioned grids in the finite element grid, the full second-order Robin type transmission condition is used to connect them; for the partitioned grids in the dielectric surface grid, the dielectric discontinuous Galerkin technique is used to connect them; and for the finite element grid and the external surface grid, the first-order Robin type transmission condition is used to connect them. By using appropriate transmission conditions between different grids, the partitioned grids are connected together to complete the overall continuity construction of the model;

[0030] Step 5.2: Set the material parameters for the solution. According to the material number sequence in filename.sort, create a new file containing material information: filename.mat file. Set the dielectric constant and magnetic permeability of the finite element area material in this filename.mat file.

[0031] Furthermore, in step 3, when performing surface meshing on the outer surface of the finite element, the normal direction needs to point in the opposite direction of the finite element region.

[0032] Furthermore, when modeling and meshing the two dielectric layers, the surface mesh normal direction is recorded to be outward, and the area to which the mesh normal vector points in the positive direction and the area to which the mesh normal vector points in the reverse direction are recorded at the same time.

[0033] Furthermore, the electromagnetic scattering calculation uses the Galerkin matching method to obtain a matrix system of hybrid finite element-multilayer medium integral equation based on domain decomposition:

[0034]

[0035] The matrix with superscript FE represents the matrix of the finite element region, the matrix with superscript BI represents the matrix of the dielectric integration region, C represents the coupling matrix, and its subscript FB or BF represents the coupling matrix of the finite element region and the dielectric integration region; the P and Q matrices are the coupling matrices of different dielectric regions, and B represents the coupling matrix of the finite element region and the dielectric integration region. m The (m=1,2) matrix is ​​a matrix block of different dielectric regions. This formula system is highly flexible and covers the traditional finite element polar equation system, multi-layer dielectric integral equation system, and hybrid finite element-multi-layer dielectric integral equation system based on regional decomposition.

[0036] The present invention has the following beneficial effects:

[0037] The honeycomb sandwich structure model is divided into an area that is not easy to model with surface integral equations and an area that is easy to model with surface integral equations. The area that is not easy to model with surface integral equations is the honeycomb core in the middle of the sandwich structure. The finite element method is used to perform volume discrete modeling in this area, and the extremely thin walls of the honeycomb unit are removed based on the impedance plate boundary condition technology, turning the entire honeycomb area into a uniform dielectric body with a series of impedance plate boundary conditions; the area that is easy to model with surface integral equations is the upper and lower thin dielectric plates, and the multi-layer dielectric target surface integral equation method is used for modeling. The surface integral equation can reduce the finite element calculation area as much as possible, thereby improving the modeling efficiency.

[0038] In order to improve the computing power of the hybrid solution technology and solve the problem of simulation of electrically large-sized honeycomb sandwich structures in actual engineering, a non-conformal domain decomposition method is introduced to improve the computing power of the method. The Schwarz-type domain decomposition finite element technology is used in the finite element calculation area, and the dielectric discontinuous Galerkin method is used in the surface integral calculation area. Based on the domain decomposition strategy, the sub-region fully sparse matrix diagonal block preconditioned matrix is ​​constructed to accelerate the solution of the matrix.

[0039] In addition, the multi-layer fast multipole technique is used to accelerate the matrix-vector multiplication operation in the multi-layer dielectric integral equation. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a mathematical model of multi-layer structure target;

[0041] Figure 2 It is a schematic diagram of the decomposition of the surface area of ​​the medium target;

[0042] Figure 3 Schematic diagram of the equivalent of extremely thin walls of honeycomb units;

[0043] Figure 4 Comparison of VV polarization and HH polarization bistatic RCS of a uniform dielectric coated sphere with Mie solution;

[0044] Figure 5 Schematic diagram and dimensional parameters of honeycomb sandwich structure;

[0045] Figure 6 Schematic diagram of the discretization of honeycomb sandwich structures using traditional hybrid methods;

[0046] Figure 7 Discrete schematic diagram of the honeycomb sandwich structure by the method of the present invention;

[0047] Figure 8 and Fig. 9 The dual station of the honeycomb sandwich structure calculated by the method of the present invention and the traditional FE-BI method;

[0048] Fig.10 Actual honeycomb structure materials;

[0049] Fig.11 Schematic diagram of mesh division before (upper figure) and after (lower figure) equivalence;

[0050] Fig.12 Schematic diagram of honeycomb wall mesh extraction;

[0051] Fig.13 Schematic diagram of the lost area of ​​the triangle mesh method;

[0052] Fig.14 The figure is a flowchart of the modeling method of the present invention. DETAILED DESCRIPTION

[0053] The following is a further detailed description of a numerical modeling method for calculating the electromagnetic scattering of a honeycomb sandwich structure proposed by the present invention in combination with the accompanying drawings and specific embodiments. According to the following description, the advantages and features of the present invention will be clearer. It should be noted that the drawings are in a very simplified form and use non-precise proportions, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention. In order to make the purposes, features and advantages of the present invention more obvious and easy to understand, please refer to the accompanying drawings. It should be noted that the structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the limiting conditions for the implementation of the present invention, so they have no technical substantive significance. Any structural modification, change in proportional relationship or adjustment of size, without affecting the effects that can be produced by the present invention and the purposes that can be achieved, should still fall within the scope of the technical content disclosed by the present invention.

[0054] 1. Integral equation of multilayer structure medium

[0055] For multi-layer structure target models, such as Figure 1 As shown, Ω0 represents the area outside the target, i.e., free space, and Ω m (m=1,2,…,N) represents different medium areas within the target, and the interface between adjacent areas is used In each dielectric region Ω m Using EFIE (electric field integral equation) and MFIE (magnetic field integral equation) we get:

[0056]

[0057] Among them J m and M m They represent the equivalent current and equivalent magnetic current on the medium surface, E m and H m represent the electric and magnetic fields in each region, respectively. Represents area Ω m The unit external normal of the internal interface points to the inside of the medium region, η m Representative area Ω m The characteristic impedance within and are two integro-differential operators defined as:

[0058]

[0059]

[0060] Among them, on means defined on the surface In the figure, PV represents the Cauchy principal value integral. For convenience, we define yes The principal value integral value of . Representative area Ω m The wave number within, ω = 2πf is expressed as the angular frequency. m (r,r′) is the Green’s function of free space, defined as:

[0061]

[0062] At the interface between adjacent regions, region Ω m and area Ω m+1 Combined with the integral equations in the interface The EFIE and MFIE equations on :

[0063]

[0064] in, and:

[0065]

[0066]

[0067] If and only if the integral surface is When m0 =1, at this time, e0 = -E inc , h0=-H inc , η0 represents the wave impedance of free space.

[0068] 2. Regional Decomposition Discontinuous Galerkin Technique

[0069] The relationship between electromagnetic flows on the boundaries of different dielectric regions is described using the normal continuity formula:

[0070]

[0071] Where C1 and C2 represent the boundary contours of the two sub-regions at the junction, such as Figure 2 As shown, is the unit normal vector of the contour line C1, and its direction is from S1 to S2. is the unit normal vector of the contour line C2, with the direction from S2 to S1, X i Represents C i The equivalent current or magnetic current on it.

[0072] Using the RWG basis function discretization formula (6), the semi-RWG basis function discretization formula (9), and the discrete formulas (6) and (9) together, the final domain decomposition multilayer medium integral equation is obtained.

[0073] 3. Efficient numerical modeling technology for honeycomb structures

[0074] After the honeycomb wall is equivalent to a surface with zero thickness, Figure 3 As shown, the electromagnetic fields on both sides of this surface are discontinuous, and the relationship between them can be characterized by a resistor sheet, satisfying the boundary condition

[0075]

[0076] in, Z0 is the characteristic impedance of free space, k0 is the wave number of free space, e is the number of cells that make up the entire honeycomb structure, and + and - refer to the inside and outside of the surface of the resistive sheet of a honeycomb structure cell. By using RSBC, the original area of ​​the cell thin wall is reduced to a zero-thickness surface. The thin-walled areas are replaced by filler material, i.e. free space. represents the outward unit normal vector, Z L is the surface impedance of the honeycomb cell wall, usually expressed as

[0077]

[0078] Among them, ε r and d are the relative dielectric constant and thickness of the honeycomb unit thin-wall material, respectively.

[0079] Therefore, the functional variation of the electromagnetic field in the finite element region of the sub-region obtained by further partitioning the middle layer honeycomb structure is

[0080]

[0081] in, E m Represent the internal sub-region Ω m The electric field in and are the sub-region interfaces Γ m The outer surface of the finite element region in contact with the dielectric integration region In addition, is an imaginary unit, is the wave number in free space, ω = 2πf is the angular frequency, and N is the number of regions where the outer boundary of the finite element region contacts the integral surface of different media.

[0082] A full second-order Robin transmission condition is used at the sub-region finite element interface:

[0083]

[0084] The first-order Robin transmission condition is used at the intersection of the sub-region finite element and the outer boundary:

[0085]

[0086] By combining equations (12), (13) and (14), the finite element equation of the honeycomb core region is obtained.

[0087] 4. Final Matrix System

[0088] Using the Galerkin matching method, the final matrix system of the hybrid finite element-multilayer dielectric integral equation based on domain decomposition is obtained. For the sake of simplicity, two sub-regions are taken as an example here, that is, the finite element region is divided into two sub-regions, and the multilayer dielectric integral equation is divided into two sub-regions:

[0089]

[0090] The matrix with superscript FE represents the matrix of the finite element region, that is, and represents the discretization matrix system of two adjacent finite element regions, and represents the unknowns in two adjacent finite element regions, and represents the plane wave excitation source of two adjacent finite element regions. The matrix with superscript BI is the matrix of the medium integration region, that is, and The discretized matrix system representing two adjacent dielectric integration regions, and represents the unknowns in the integration region of two adjacent media, and represents the plane wave excitation source of two adjacent dielectric integration regions. C represents the coupling matrix, and its subscript FB or BF represents the coupling matrix between the finite element region and the dielectric integration region. The P and Q matrices are the coupling matrices of different dielectric regions, and B m The (m=1,2) matrix is ​​a matrix block of different dielectric regions.

[0091] The final matrix system is preconditioned to speed up the solution. Formula (15) can be written in a more compact system matrix form:

[0092]

[0093] Among them, A FE The discrete matrix system representing the finite element domain, x FE represents the unknown number in the finite element region, b FE A represents the plane wave excitation source in the finite element region. mBI The discrete matrix system representing the multilayer dielectric integration region, x mBI represents the unknown number in the multilayer medium integration region, b mBI Represents the plane wave excitation source in the multilayer medium integration region. C FE,mBI , CmBI,FE Represents the mutual coupling matrix between the finite element region and the multilayer dielectric region.

[0094] When using the above formula for calculation, we can further extract the matrix blocks on the diagonal to construct a Schwarz-type preconditioning matrix to speed up the calculation of the matrix. -1 The form is as follows:

[0095]

[0096] For the BI matrix part in the above formula, sparse processing is used, that is, the number of non-zero elements in the matrix is ​​reduced as much as possible without affecting the accuracy and convergence. The phenomenon that the basis functions close to each other in the Green function have a strong effect, while the basis functions far away have a weak effect, is used to set a distance standard related to the wavelength of the medium to filter the matrix elements. That is,

[0097]

[0098] Among them, r i and r j are the positions of the basis function and the test function, respectively, m is the medium wavelength, σ is the distance coefficient,

[0099] Use the sparse preconditioning matrix to perform right preconditioning on equation (16) to obtain the final matrix system equation:

[0100]

[0101] The Krylov subspace method is used to iteratively solve formula (19). Due to the sparsity of the preconditioned matrix, the submatrix block dimension after domain decomposition is small. The MUMPS direct solver is used to calculate the inverse of the submatrix in the preconditioned matrix.

[0102] This example first studies the electromagnetic scattering of a uniform dielectric coated sphere to verify the accuracy of the method proposed in the present invention, which is abbreviated as FE-mBI. The radius of the inner metal sphere is 1m, the coating thickness on its surface is 0.1m, and the relative dielectric constant of the coating material is ε r =2.0, relative magnetic permeability is μ r=1.0. The plane wave is incident from the -z axis, and the calculated frequency is 0.3 GHz. In the method of the present invention, the dielectric-coated sphere is first decomposed into two regions: the finite element region and the dielectric integration region, and the mesh size of the two regions is λ0 / 20. Therefore, the final coating material region is discretized using 177,311 tetrahedral meshes and automatically partitioned into four sub-regions using Metis; the external dielectric integration surface is discretized using 15,738 triangular meshes and automatically partitioned into two sub-regions using Metis. The bistatic RCS of the VV polarization and HH polarization of the dielectric-coated sphere is calculated, as shown in Figure 4 To ensure the accuracy of the evaluation, the calculation results were compared with the Mie analytical solution. It can be seen that the calculation results of the method of the present invention are in good agreement with the calculation results of the analytical method of Mie series expansion.

[0103] Then calculate an Figure 5 The 100mm×100mm honeycomb sandwich structure shown in the figure has a thickness of t u =t d =15mm, the thickness of the middle honeycomb layer h=30mm, the side length of the honeycomb unit is 4mm, the wall thickness is 0.1mm, the dielectric parameter of the immersed absorbing liquid is ε=10-15j, the calculated frequency is 10GHz, and when the traditional hybrid finite element-boundary integral method (FE-BI) is used for modeling, the model is first divided into three parts, namely the upper layer, the middle layer and the lower layer. Only the surface mesh is used for discretization on the outer boundary of the model, and the tetrahedral mesh of the finite element method is used for discretization of the three inner layers, such as Figure 6 When the modeling method of the present invention is used, only the middle honeycomb structure is modeled using finite elements, and the rest of the area is modeled using dielectric integral equations, such as Figure 7 When using the medium integral equation modeling, different from Fig.11 The three sub-regions divided in the method of the present invention are divided into five independent sub-regions in total, with two more sub-regions on the upper and lower surfaces of the middle layer. The final finite element unknowns obtained by the traditional hybrid method are 1767488, the number of sub-regions of automatic partitioning is 35, the boundary integral unknowns are 17160, and the number of sub-regions is 3; the finite element unknowns obtained by the method of the present invention are 1077640, the number of sub-regions is 20, the boundary integral unknowns are 24876, and the number of sub-regions is 5.

[0104] A 10 GHz plane wave illuminates the model in the -z direction, and its electric field vector is polarized in the +x direction. Figure 8 and 9The results of the dual-station radar cross section of the model under VV polarization and HH polarization conditions are shown. The dual-station RCS curves obtained by the two different methods are consistent, showing a high degree of consistency. In addition, Table 1 lists in detail the resource consumption used by the two methods in the calculation process. It can be seen that when the method of the present invention is used, the memory is optimized by more than 40%, the calculation time is optimized by 30%, and the number of iterations is reduced compared to the traditional FEBI method. This result not only verifies the accuracy of the method of the present invention, but also highlights its significant advantages in terms of computing resource requirements.

[0105] Table 1: Computational resource statistics for simulating honeycomb sandwich structures using the traditional FE-BI method and the method of the present invention

[0106]

[0107] When constructing a honeycomb sandwich structure model, the first step is to classify the materials of each layer according to whether they are suitable for surface meshing. In view of the complexity and anisotropy of the intermediate honeycomb core structure, it is not suitable to use surface mesh processing, so tetrahedral mesh is used for fine discretization. In this process, the basic unit of the intermediate honeycomb core structure is constructed into a hexagonal solid column. While obtaining the tetrahedral mesh, the triangular mesh information located on the hexagonal wall is retained and the impedance sheet boundary condition is added to complete the mesh extraction of the honeycomb structure.

[0108] For the upper and lower layers of uniform medium areas of the structure, triangular surface meshes are used to accurately model their outer surfaces, mark the direction of the mesh normals, record the medium areas indicated by the forward and reverse normals, and store and mark the area information to complete the mesh extraction of the two thin plates.

[0109] After all meshing is completed, the volume mesh data file of the honeycomb structure and the surface mesh information files of the upper and lower structures are obtained. These files are connected to form a global model of the honeycomb sandwich structure. These modeling results are used to perform electromagnetic scattering calculations to evaluate and analyze the electromagnetic performance of the honeycomb sandwich structure.

[0110] The present invention provides a numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure, such as Fig.14 As shown, the following steps are included:

[0111] Step 1: Split and classify the model structure.

[0112] The honeycomb sandwich structure is split and classified into multilayer material regions according to the rules of whether it is easy to model with surface integral equations. Typical areas that are not easy to model with surface integral equations include antenna arrays, anisotropic honeycomb structures, etc. These areas are discretely modeled with volume meshes using the finite element method; while the homogeneous medium area belongs to the area that is easy to model with surface integral equations, and is discretely modeled using triangular surface meshes. Specifically, in the honeycomb sandwich structure, the honeycomb structure of the middle layer can only be discretely modeled using the finite element method according to the segmentation rules; while the upper and lower thin layers on both sides of the honeycomb structure are uniform and the material dielectric constants are isotropic, so the surface integral equation method is used for discrete modeling.

[0113] Step 2: Model the honeycomb structure as a uniform dielectric body with a series of impedance sheet boundary conditions (RSBC), including the following steps:

[0114] Step 2.1: Remove the honeycomb cell wall with very thin thickness and simplify it into a hexagonal solid column.

[0115] The honeycomb structure is composed of unit cells, which are separated by cell walls. The unit cells are generally hexagonal prisms, such as Fig.10 Usually the honeycomb cell wall is very thin, usually not more than 0.1 mm in actual engineering. Due to the limited resources of the computer used, the grid size cannot be set to a smaller value. Directly dividing the actual honeycomb structure will result in grid distortion, such as Fig.11 Therefore, the present invention removes the area corresponding to the honeycomb cell wall, retains the thin wall surface with zero thickness, and fills and models the internal area of ​​the entire honeycomb structure as a free space area, so that the mesh of the entire honeycomb structure model is very uniform, eliminating the bad mesh caused by the existence of the honeycomb cell wall, and finally simplifies it into a uniform dielectric body model containing a periodic zero thickness impedance surface.

[0116] Step 2.2: Perform tetrahedral meshing on the honeycomb structure simplified in the previous step, ensuring that each honeycomb cell wall mesh is included in the tetrahedral mesh information.

[0117] Use ANSYS, FEKO and other modeling software to build a solid hexagonal prism unit, and then obtain the actual size structure required for simulation through a series of Boolean operations, and set constraints on the honeycomb unit wall. Then use tetrahedral mesh to divide the structure, and set the mesh size to one twentieth of the wavelength at the solution frequency to obtain the vertex coordinate information and vertex number information of the discrete volume mesh. The coordinate information is stored in the filename.xyz file, and the vertex number information is stored in the filename.lv file.

[0118] Step 2.3, use the graph partitioning software Metis to partition the tetrahedral mesh of the honeycomb structure. According to experience, the calculation efficiency is optimal when the number of unknowns in each sub-region after partitioning is between 2w and 5w. The total number of unknowns in the honeycomb structure is roughly 1.5 times the total number of discrete tetrahedrons. By dividing the total number of unknowns by any number between 2w and 5w and rounding, partitioning is performed through the Metis model to obtain a file containing the area where each tetrahedron is located, that is, the filename.metis file, which is used to store the tetrahedron area number information.

[0119] Step 2.4: Extract the honeycomb cell wall grid information.

[0120] like Fig.12 As shown, a two-dimensional framework with periodic hexagonal distribution is established on a two-dimensional plane. The framework corresponds to the mapping of the hexagonal wall of the three-dimensional honeycomb structure on the plane one by one. The same hexagonal unit side length and periodic distribution characteristics as the three-dimensional honeycomb structure are set. The two-dimensional framework is used to extract the unit wall mesh information from the tetrahedral mesh of the simplified honeycomb structure, and a file filename.rsbc storing the triangular mesh vertex numbers of all the unit walls of the honeycomb structure is obtained. Generally speaking, the entire two-dimensional framework needs to be set larger than the mapping area of ​​the three-dimensional honeycomb model on the plane so that the triangular mesh information of all the honeycomb unit walls can be extracted.

[0121] Step 2.5, obtain the internal finite element mesh information file of the honeycomb structure. After obtaining the information files storing the honeycomb structure, namely the filename.xyz file, the filename.lv file, the filename.metis file, and the filename.rsbc file, the information in these files is collected into a total file, namely the filename.fem file, which contains the coordinates of each tetrahedron vertex, the global vertex number, the tetrahedron region number, and the triangle mesh vertex number of the honeycomb unit wall.

[0122] Step 3: Divide the outer surface of the honeycomb structure using a triangular face mesh, with the mesh size set to one tenth of the wavelength at the frequency being solved. When the face mesh is divided, the direction of the face mesh normal is always outward, and it is necessary to record the area to which the mesh normal vector points in the positive direction and the area in the reverse direction. The outer surface of the honeycomb structure is divided according to the contact surfaces with different media. In the present invention, it is divided into the contact surface with the air, the contact surface with the upper uniform medium, and the contact surface with the lower uniform medium, and these contact surfaces are divided separately. Then, the face mesh vertex coordinate information and vertex number information of the outer surface of the honeycomb structure are stored in the newly created filename.bi_fe file.

[0123] Step 4: Model and mesh the upper and lower uniform medium structures to obtain the corresponding surface mesh information file.

[0124] Step 4.1, use CATIA and other commercial CAD software to model the upper and lower structures, extract the outer surface of the model, classify the surfaces with the same medium area on both sides as the same type of surface, combine and segment them together. At the same time, when using commercial CAD software to segment the surface, it is necessary to record the area pointed by the positive normal and the area pointed by the negative normal according to the normal direction of the grid, such as Fig.13 In the figure, the positive normal area is area 1, and the negative normal area is area 2. Output the same type of surface into a mesh file. Since the meshing of the contact surface between the upper and lower layers and the middle layer (i.e., the honeycomb structure) was completed in step 3, there is no need to mesh these two contact surfaces in this step.

[0125] Step 4.2: Use the graph partitioning software Metis to partition the mesh file of each surface. Use the graph partitioning software Metis to partition the surface mesh. According to experience, the surface mesh of each sub-area is about 0.5w~1w, which has the best efficiency and memory consumption. The number of partitions is obtained by dividing the total number of surface meshes by 0.5w~1w and rounding.

[0126] Step 4.3, mark the surface mesh attributes and numbers, and set the material area information on both sides of the different medium contact surfaces (i.e., including the contact surface between air and upper medium, the contact surface between air and middle medium, the contact surface between air and lower medium, the contact surface between upper and middle medium, and the contact surface between lower and middle medium). When reading the contact surface mesh between the upper and lower medium and the middle medium, the surface mesh needs to be marked as the finite element outer boundary surface (FE-BI surface), and when reading the remaining surface meshes (i.e., the contact surface mesh with the upper medium, the middle medium, the lower medium and the air), it is marked as the medium boundary surface (BI-BI surface). Then the surface numbering starts from the outer boundary of the honeycomb layer, and the same type of surface meshes, that is, meshes with the same material on both sides, use the same number. These numbers are matched one by one with the material area, and stored in the filename.sort file, which contains the surface number and the material area on both sides of the surface. Finally, the vertex coordinate information, vertex number information, surface number information and material information on both sides of the surface of the upper and lower outer surface meshes are stored in a newly created filename.bi_bi file.

[0127] Step 4.4, obtain all the external surface mesh information files of the entire model. Collect the surface mesh information obtained in the above steps 3 and 4 (i.e. the contents of the filename.bi_fe file and the filename.bi_bi file) into the total file filename.bi, which contains the vertex coordinates, vertex global number, triangle unit area number and mesh material number of each triangle unit.

[0128] Step 5: Connect the honeycomb internal finite element mesh file filename.fem and the surface triangle mesh file filename.bi in steps 2 and 4 to obtain the global mesh information of the honeycomb sandwich structure and complete the model construction.

[0129] Step 5.1. After the above steps are completed, the tetrahedral mesh file filename.fem of the middle layer honeycomb structure and the outer surface mesh file filename.bi of the entire dielectric structure are obtained. In steps 2.3 and 4.2, the graphic partitioning software Metis is used to partition the mesh, that is, both filename.fem and filename.bi contain partition information. For the partitioned meshes in the finite element mesh, the full second-order Robin-type transmission condition is used for connection; for the partitioned meshes in the dielectric surface mesh, the dielectric discontinuous Galerkin technique is used for connection; and for the finite element mesh and the outer surface mesh, the first-order Robin-type transmission condition is used for connection. By using suitable transmission conditions between different meshes, the partitioned meshes are connected together to complete the overall continuity construction of the model.

[0130] Step 5.2, set the material parameters to be solved. According to the material number sequence in filename.sort, create a new file containing material information: filename.mat. The dielectric constant and magnetic permeability of the finite element region material are set in the filename.mat file. The dielectric constant and magnetic permeability of the finite element region medium material in the present invention are set to the dielectric constant and magnetic permeability of air.

[0131] Step 6: Perform electromagnetic scattering calculation on all the grid information files obtained according to the above modeling steps.

[0132] The first-order edge element basis function is used to expand the electric field in the finite element region in the middle honeycomb core area using tetrahedral meshing. The RWG basis function is used to expand the surface electromagnetic current in the uniform medium area using triangular meshing. The semi-RWG basis function is used to expand the electromagnetic current on the boundary line at the boundary contour of the dielectric integral sub-region. The Schwarz-type regional decomposition finite element technique is used in the finite element calculation area, and the regional decomposition discontinuous Galerkin method is used in the surface integral calculation area. Based on the regional decomposition strategy, the sub-region full sparse matrix diagonal block preconditioning matrix is ​​constructed to accelerate the matrix solution. In addition, the multi-layer fast multipole technology is used to accelerate the matrix-vector multiplication operation in the dielectric integral equation.

[0133] The present invention proposes an efficient numerical modeling method for calculating electromagnetic scattering of honeycomb sandwich structures. From the perspective of numerical calculation, the model shown in the embodiment is compared with the Mie analytical solution and the traditional hybrid method, and the calculation results are consistent, which proves the accuracy of the method of the present invention. From the perspective of application, the calculation of the scattering characteristics of the honeycomb sandwich composite structure shown in the embodiment proves the practicality of the method of the present invention in calculating the honeycomb sandwich structure and the flexibility of model processing, and can perform efficient calculations on honeycomb sandwich structures of large electrical sizes.

[0134] Although the content of the present invention has been described in detail through the above preferred embodiments, it should be appreciated that the above description should not be considered as a limitation of the present invention. After reading the above content, it will be apparent to those skilled in the art that various modifications and substitutions of the present invention will occur. Therefore, the protection scope of the present invention should be limited by the appended claims.

Claims

1. A numerical modeling method for calculating electromagnetic scattering of honeycomb sandwich structures, characterized in that: The following steps are involved: Step 1: splitting and classifying the honeycomb sandwich structure according to whether it is easy to use the surface mesh division rule, and dividing the honeycomb sandwich structure into a honeycomb structure and a dielectric layer located on both sides of the honeycomb structure; Step 2: Model the honeycomb structure as a uniform dielectric body with a series of impedance plate boundary conditions, and obtain the finite element mesh information file inside the honeycomb structure; Step 3: Use a triangular surface mesh to divide the outer surface of the honeycomb structure, and obtain the vertex coordinate information and vertex number information of the surface mesh of the outer surface; Step 4: Modeling and surface meshing the dielectric layer to obtain a corresponding surface mesh information file; Step 5: Connect the finite element mesh information files in steps 2 to 4, the surface mesh vertex coordinate information and vertex number information of the outer surface of the honeycomb structure, and the surface mesh information file of the dielectric layer to obtain the global mesh information of the honeycomb sandwich structure and complete the construction of the model; Step 6: Perform electromagnetic scattering calculations based on the model.

2. The numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure according to claim 1, characterized in that: The honeycomb structure is mainly composed of a plurality of unit cells, each of which is connected by a unit wall. The outer surface of the honeycomb structure includes a contact surface connected to the medium layers on both sides and a contact surface in contact with the air, wherein the outer surface is divided by a surface grid, and the interior of the honeycomb structure is divided by a volume grid.

3. The numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure according to claim 2, characterized in that: The step 2 includes the following contents: Step 2.1: Remove the honeycomb cell wall and fill the inner area of ​​the honeycomb structure with free space to simplify it into a uniform dielectric body model with a periodic zero-thickness impedance surface; Step 2.2: Perform tetrahedral meshing on the simplified honeycomb structure, ensure that the cell wall mesh of each honeycomb unit is included in the tetrahedral mesh information, obtain the vertex coordinate information and vertex number information of the volume mesh discretization, store the vertex coordinate information in the filename.xyz file, and store the vertex number information in the filename.lv file; Step 2.3: Partition the tetrahedral mesh of the honeycomb structure to obtain a filename.metis file containing the area where each tetrahedron is located; Step 2.4: Extract the mesh information of each cell wall and save the triangle mesh vertex number of the cell wall into the filename.rsbc file; Step 2.5: Assemble the filename.xyz, filename.lv, filename.metis and filename.rsbc files into the filename.fem file.

4. The numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure according to claim 3, characterized in that: The step 3 comprises: The outer surface of the honeycomb structure is divided into the contact surface with the air, the contact surface with the upper uniform medium and the contact surface with the lower uniform medium. The contact surfaces are divided separately. Then, the surface mesh vertex coordinate information and vertex number information of the outer surface of the honeycomb structure are stored in the newly created filename.bi_fe file.

5. The numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure according to claim 4, characterized in that: The step 4 includes the following contents: Step 4.1: Model the two dielectric layers, extract the outer surface of the model, perform surface meshing on the outer surface of the dielectric layer, and output the surfaces of the same type into the same surface mesh file; Step 4.2: Partition each surface mesh file; Step 4.3: Mark the surface mesh attributes and numbers, and set the material area information of the outer surface. These numbers correspond to the material areas one by one and are stored in the filename.sort file. The vertex coordinate information, vertex number information, surface number information and material information on both sides of the surface of the outer surface mesh of the dielectric layer are stored in a newly created filename.bi_bi file; Step 4.4: Combine the contents of the filename.bi_fe file and the filename.bi_bi file into filename.bi.

6. The numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure according to claim 5, characterized in that: The step 5 includes the following contents: Step 5.1: Link the filename.fem and filename.bi. For the partitioned grids in the finite element grid, the full second-order Robin type transmission condition is used to connect them; for the partitioned grids in the dielectric surface grid, the dielectric discontinuous Galerkin technique is used to connect them; and for the finite element grid and the external surface grid, the first-order Robin type transmission condition is used to connect them. By using appropriate transmission conditions between different grids, the partitioned grids are connected together to complete the overall continuity construction of the model; Step 5.2: Set the material parameters for the solution. According to the material number sequence in filename.sort, create a new file containing material information: filename.mat file. Set the dielectric constant and magnetic permeability of the finite element area material in this filename.mat file.

7. The numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure according to claim 1, characterized in that: In step 3, when performing surface meshing on the outer surface of the finite element, the normal direction needs to point in the opposite direction of the finite element region.

8. The numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure according to claim 1, characterized in that: When modeling and meshing the two dielectric layers, the surface mesh normal direction is recorded outward, and the area to which the mesh normal vector points in the positive direction and the area in the reverse direction are recorded at the same time.

9. The numerical modeling method for calculating electromagnetic scattering of a honeycomb sandwich structure according to claim 1, characterized in that: The electromagnetic scattering calculation uses the Galerkin matching method to obtain a matrix system of hybrid finite element-multilayer medium integral equation based on domain decomposition: The matrix with superscript FE represents the matrix of the finite element region, the matrix with superscript BI represents the matrix of the dielectric integration region, C represents the coupling matrix, and its subscript FB or BF represents the coupling matrix of the finite element region and the dielectric integration region; the P and Q matrices are the coupling matrices of different dielectric regions, and B represents the coupling matrix of the finite element region and the dielectric integration region. m The (m=1,2) matrix is ​​a matrix block for different dielectric regions. This formula system is highly flexible and covers the traditional finite element polar equation system, multi-layer dielectric integral equation system, and hybrid finite element-multi-layer dielectric integral equation system based on regional decomposition.

Images