A method for rapidly and automatically generating a finite element mesh of a parallelepiped target plate

Abstract

The present invention discloses a method for quickly and automatically generating a finite element mesh of a parallelepiped target plate. First, the geometric parameters of the parallelepiped target plate are determined, including thickness, height, width, orientation, offset distance, and inclination angle. The parallelepiped target plate is divided into hexahedrons with specific shapes. Then, the number of meshes on the edges of each hexahedron with a specific shape is determined and the corresponding node coordinates are determined. Subsequently, the node coordinates are supplemented by mirroring. After that, it is extended to the node coordinates of the parallelepiped target plate and output as a structured finite element mesh. Finally, the structured mesh node coordinates are sorted and organized and output as an unstructured finite element mesh for use in calculations such as penetration, loading, and contact, without the need to rely on existing finite element mesh generation software, significantly reducing the workload of relevant technical personnel and improving the calculation efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of finite element numerical simulation, and particularly relates to a method for quickly and automatically generating finite element meshes of a parallelepiped target plate. Background Technique

[0002] The parallelepiped target plate is a very common damage target for penetration, explosion, and collision simulation calculations. The commonly used finite element simulation calculation programs in the military industry are mainly AUTODYN and LS-DYNA. The former mostly calculates based on structured finite element meshes, and the latter mostly calculates based on unstructured finite element meshes. The node sorting of structured finite element meshes has a specific format and does not require additional indication of the connection between nodes. The node sorting of unstructured finite element meshes is arbitrary and requires additional indication of the nodes constituting the mesh and their order. For some academic research or engineering projects with a parallelepiped target plate as the damage target, they often face working conditions based on parallelepiped target plates with different thicknesses, heights, widths, inclinations, orientations, and offset distances. In this case, finite element mesh generation software that draws meshes through the GUI, such as HYPERMESH and ICEM, needs to continuously draw different parallelepiped target plates, going through a series of steps such as modeling, importing, drawing, exporting, and re-importing. Finite element mesh generation software that can be programmed to model and draw meshes, such as TrueGrid, requires manual continuous calculation of the normal vector of the target plate generated by the inclination angle, with low work efficiency, time-consuming and laborious, increasing the workload of relevant technical personnel. To solve the above problems, a method for quickly and automatically generating finite element meshes of a parallelepiped target plate that can simultaneously generate structured finite element meshes suitable for use in the AUTODYN program and unstructured finite element meshes suitable for use in the LS-DYNA program is proposed. Summary of the Invention

[0003] The purpose of the present invention is to overcome the problems of repeated finite element mesh generation process, low calculation efficiency, and large workload of parallelepiped target plates under the condition of a large number of working conditions, and to provide a method for quickly and automatically generating finite element meshes of parallelepiped target plates, with a simple process and easy to be extended to other structures.

[0004] The technical solution for achieving the purpose of the present invention is as follows: A method for quickly and automatically generating finite element meshes of a parallelepiped target plate, the steps are as follows:

[0005] Step S1, determine the geometric parameters of the parallelepiped target plate, including thickness, height, width, orientation, offset distance, and inclination angle, divide the parallelepiped target plate into 4 sub-target plates along the reference direction, which are the first sub-target plate, the second sub-target plate, the third sub-target plate, and the fourth sub-target plate in sequence, divide the first sub-target plate into 6 hexahedrons with specific shapes along the reference direction, and transfer to step S2.

[0006] Step S2, determine the number of grid cells on a pair of opposite sides on the front face of six hexahedrons with specific shapes and determine the corresponding edge node coordinates, then proceed to Step S3.

[0007] Step S3, perform mirror supplementation on the edge node coordinates of a pair of opposite sides on the front face of six hexahedrons with specific shapes to obtain the edge node coordinates of the front face of the parallelepiped target board, then proceed to Step S4.

[0008] Step S4, expand the edge node coordinates of the front face of the target board to the face node coordinates of the front face of the target board, and supplement the edge node coordinates of the planar parallelepiped target board along the reference direction, then proceed to Step S5.

[0009] Step S5, by setting a matrix sorting function, obtain the volume node coordinates of the structured grid of the parallelepiped target board from the face node coordinates of the front face of the parallelepiped target board and the edge node coordinates of the planar parallelepiped target board along the reference direction according to the orientation of the parallelepiped target board, and then obtain the structured finite element grid of the parallelepiped target board, then proceed to Step S6.

[0010] Step S6, by setting a three-dimensional serial number matrix, obtain an unstructured grid matrix, sort and organize the volume node coordinates of the structured finite element grid of the parallelepiped target board to obtain the unstructured finite element grid of the parallelepiped target board.

[0011] Compared with the prior art, the remarkable advantages of the present invention are as follows: The present invention does not need to rely on commercial modeling software and finite element grid drawing software. By inputting the geometric parameters of the target board, such as the height, width, thickness, inclination angle, orientation, and deviation position of the target board, and determining the number of grid cells on each side, the finite element grid can be generated. Moreover, the internal grid can be further adjusted through the geometric parameters of the hexahedron with a specific shape. It can generate both a structured finite element grid suitable for use in the AUTODYN program and an unstructured finite element grid suitable for use in the LS-DYNA program. Furthermore, the nodes of the unstructured finite element grid and the combination of nodes for generating each grid directly originate from the structured finite element grid, greatly improving the efficiency of generating both grids simultaneously. Combining the advantages of matrix calculation, compared with finite element grid generation software such as HYPERMESH and ICEM that draw grids through the GUI, it does not require continuously drawing different parallelepiped target boards and does not need to go through a series of steps such as modeling, importing, drawing, exporting, and re-importing. Compared with the finite element grid generation software such as TrueGrid that can perform programmable modeling and drawing of grids, it does not require manual calculation of the normal vector of the target board, and the time required to generate a grid of millions of levels is only less than 30% of it. The overall idea is simple and clear, the implementation difficulty is low, it can effectively improve work efficiency, and significantly reduce the workload of relevant technical personnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1This is the flow chart of the present invention.

[0013] Figure 2 This is the schematic diagram of the target plate segmentation of the present invention.

[0014] Figure 3 This is the schematic diagram of each line segment of the target plate segmentation of the present invention.

[0015] Figure 4 This is the schematic diagram of the geometric parameters of the target plate of the present invention.

[0016] Figure 5 This is the schematic diagram of the grid parameters of the target plate of the present invention.

[0017] Figure 6 This is the example diagram of the present invention. Detailed implementation manners

[0018] The present invention will be further described in detail below with reference to the accompanying drawings.

[0019] Combined with Figures 1 to 6 , a method for quickly and automatically generating a finite element mesh of a parallelepiped target plate is as follows:

[0020] Step S1, determine the geometric parameters of the parallelepiped target plate, including thickness, height, width, orientation, offset distance, and inclination angle. Divide the parallelepiped target plate into 4 sub-target plates along the reference direction, which are the first sub-target plate, the second sub-target plate, the third sub-target plate, and the fourth sub-target plate in sequence. Divide the first sub-target plate into 6 hexahedrons with specific shapes along the reference direction, specifically as follows:

[0021] Taking the direction of the projectile, shock wave, and other incoming objects as the reference direction, the surface of the parallelepiped target plate that bears the projectile, shock wave, and other incoming objects is the front of the target plate, and its reverse side is the back of the target plate. The other four sides are the top surface of the target plate, the bottom surface of the target plate, the left side surface of the target plate, and the right side surface of the target plate respectively.

[0022] The distance between the front of the target plate and the back of the target plate is the thickness L4 of the parallelepiped target plate. The distance between the top surface of the target plate and the bottom surface of the target plate is 2*L2, where L2 is half of the height of the parallelepiped target plate. The distance between the left side surface of the target plate and the right side surface of the target plate is 2*L3, where L3 is half of the width of the parallelepiped target plate. The ratio of the height of the target plate to the width of the target plate is not less than 0.5 and not greater than 2. The reverse direction of the reference direction is the orientation of the parallelepiped target plate. The translation length of the parallelepiped target plate along the reference direction is the offset distance L5. The line-plane angle between the parallelepiped target plate and the reference direction is the inclination angle α of the parallelepiped target plate, and the inclination angle α is not less than 30 degrees and not greater than 90 degrees.

[0023] All points equidistant from the top surface and the bottom surface of the target plate form the first mid-plane of the parallelepiped target plate. All points equidistant from the left side surface and the right side surface of the target plate form the second mid-plane of the parallelepiped target plate.

[0024] The parallelepiped target plate is divided into four sub-target plates by the first mid-plane and the second mid-plane along the reference direction. The sub-target plate that simultaneously contacts the top surface and the right side surface of the target plate is the first sub-target plate. Starting from the first sub-target plate in the direction of the equivalent thickness and moving clockwise, the other sub-target plates are sequentially defined as the second sub-target plate, the third sub-target plate, and the fourth sub-target plate.

[0025] Define the projection plane of the surface of the first sub-target plate that coincides with the front surface of the target plate along the reference direction as the pre-partition plane, and the projection plane of the front surface of the target plate along the reference direction is the projected front surface of the target plate. The pre-partition plane is exactly the part of the front surface of the target plate surrounded by the first mid-plane, the second mid-plane, the top surface of the target plate, and the right side surface of the target plate.

[0026] With the intersection point of the pre-partition plane, the first mid-plane, and the second mid-plane as the center, draw a 1 / 4 arc with a radius of R within the pre-partition plane, which is called the in-plane arc, where 0.1L2 ≤ R ≤ 0.7L2 and 0.1L3 ≤ R ≤ 0.7L3.

[0027] The in-plane arc divides the pre-partition plane into an inner-arc plane and an outer-arc plane. The midpoint of the in-plane arc divides the in-plane arc into two parts. The part intersecting with the first mid-plane is the in-plane first arc, and the part intersecting with the second mid-plane is the in-plane second arc. Determine a face center point within the inner-arc plane. The face center point is equidistant from the first mid-plane and the second mid-plane, and the distance from the face center point to the center of the circle is not less than 0.2 times the radius R and not greater than 0.75 times the radius R.

[0028] Along the reference direction, on the inner-arc plane, rotate the perpendicular line from the face center point to the first mid-plane clockwise by the inner-arc angle θ to draw a line segment connecting the face center point to the first mid-plane, which is the inner-arc first line, where 0° ≤ θ ≤ 32.5°. The distance from the intersection point of the inner-arc first line and the first mid-plane to the center of the circle is L1, and 0.1L1 ≤ R ≤ 0.7L1.

[0029] Along the reference direction, on the inner-arc plane, rotate the perpendicular line from the face center point to the second mid-plane counterclockwise by the inner-arc angle to draw a line segment connecting the face center point to the second mid-plane, which is the inner-arc second line. The distance from the intersection point of the inner-arc second line and the second mid-plane to the center of the circle is equal to the distance L1 from the intersection point of the inner-arc first line and the first mid-plane to the center of the circle. Along the reference direction, on the inner-arc plane, rotate the perpendicular line from the face center point to the second mid-plane counterclockwise by an inner-arc angle equal to θ.

[0030] Draw a perpendicular line from the face center point to the in-plane arc, and the intersection point with the in-plane arc is the arc midpoint. This perpendicular line is the inner-arc third line.

[0031] Along the reference direction, on the outer-arc plane, rotate the perpendicular line from the arc midpoint to the top surface of the parallelepiped target plate clockwise by the outer-arc angle Draw a line segment connecting the midpoint of the arc to the top surface of the parallelepiped target plate, which is a line outside the arc. Among them,

[0032] Rotate the outer arc angle counterclockwise along the reference direction on the outer surface of the arc with respect to the perpendicular line from the midpoint of the arc to the right side surface of the parallelepiped target plate, and draw a line segment connecting the midpoint of the arc to the right side surface of the parallelepiped target plate, which is the second line outside the arc. Rotate the outer arc angle counterclockwise along the reference direction on the outer surface of the arc with respect to the perpendicular line from the midpoint of the arc to the right side surface of the parallelepiped target plate, and the rotation angle is equal to

[0033] The first sub-target plate is divided into 6 parallelepipeds with specific shapes by the inner arc on the surface, the first line inside the arc, the second line inside the arc, the third line inside the arc, the first line outside the arc, and the second line outside the arc along the reference direction.

[0034] The pre-divided surface is divided into 6 sub-surfaces by the inner arc on the surface, the first line inside the arc, the second line inside the arc, the third line inside the arc, the first line outside the arc, and the second line outside the arc along the reference direction. Among these sub-surfaces, the sub-surface with the first line inside the arc and the second line inside the arc as its sides is the first sub-surface, the sub-surface with the first line inside the arc and the third line inside the arc as its sides is the second sub-surface, the sub-surface with the second line inside the arc and the third line inside the arc as its sides is the third sub-surface, the sub-surface with the inner arc on the surface and the second line outside the arc as its sides is the fourth sub-surface, the sub-surface with the first line outside the arc and the second line outside the arc as its sides is the fifth sub-surface, and the sub-surface with the inner arc on the surface and the first line outside the arc as its sides is the sixth sub-surface.

[0035] The parallelepiped with a specific shape that coincides with the first sub-surface along the reference direction is the first parallelepiped, and the first sub-surface is the front face of the first parallelepiped. The parallelepiped with a specific shape that coincides with the second sub-surface along the reference direction is the second parallelepiped, and the second sub-surface is the front face of the second parallelepiped. The parallelepiped with a specific shape that coincides with the third sub-surface along the reference direction is the third parallelepiped, and the third sub-surface is the front face of the third parallelepiped. The parallelepiped with a specific shape that coincides with the fourth sub-surface along the reference direction is the fourth parallelepiped, and the fourth sub-surface is the front face of the fourth parallelepiped. The parallelepiped with a specific shape that coincides with the fifth sub-surface along the reference direction is the fifth parallelepiped, and the fifth sub-surface is the front face of the fifth parallelepiped. The parallelepiped with a specific shape that coincides with the sixth sub-surface along the reference direction is the sixth parallelepiped, and the sixth sub-surface is the front face of the sixth parallelepiped.

[0036] Step S2: Determine the number of grids of a set of opposite sides on the front faces of the 6 parallelepipeds with specific shapes and determine the corresponding edge node coordinates, specifically as follows:

[0037] Set the edge node ratio matrix G(m,q), where m represents the number of grids set on the edge of the parallelepiped with a specific shape, q represents the ratio of the distance between two adjacent nodes, and q is a positive number. i represents the node number, and the value of the i-th element G(m,q) i is:

[0038]

[0039] In the first sub - surface, the length of the opposite side of the line inside the arc is equal to L1, the number of grids is determined to be n1, and the upper - side node coordinates of the opposite side of the line inside the arc are composed of the node abscissa matrix x1 and the node ordinate matrix y1, respectively:

[0040]

[0041] The upper - side node coordinates of the line inside the arc are composed of the node abscissa matrix x2 and the node ordinate matrix y2, respectively:

[0042]

[0043] Among them, represents a 1*(n1 + 1) all - one matrix.

[0044] In the second sub - surface, the upper - side node coordinates of the arc inside the surface are composed of the node abscissa matrix x3 and the node ordinate matrix y3, respectively:

[0045]

[0046] In the third sub - surface, the length of the opposite side of the second line inside the arc is equal to L1, the number of grids is determined to be n2, and the upper - side node coordinates of the opposite side of the second line inside the arc are composed of the node abscissa matrix x4 and the node ordinate matrix y4, respectively:

[0047]

[0048] Among them, represents a 1*(n2 + 1) all - one matrix.

[0049] The upper - side node coordinates of the second arc inside the surface are composed of the node abscissa matrix x5 and the node ordinate matrix y5, respectively:

[0050]

[0051] In the fourth sub - surface, the upper - side node coordinates of the opposite side of the second arc inside the surface are composed of the node abscissa matrix x6 and the node ordinate matrix y6, respectively:

[0052]

[0053] In the fifth sub - surface, the number of grids on the first line outside the arc is determined to be n3, and the upper - side node coordinates of the first line outside the arc are composed of the node abscissa matrix x7 and the node ordinate matrix y7, respectively:

[0054]

[0055] Among them, represents a 1*(n3 + 1) all - one matrix.

[0056] The upper edge node coordinates of the opposite side of a line outside the arc are composed of the node abscissa matrix x8 and the node ordinate matrix y8, respectively, as follows:

[0057]

[0058] In the sixth sub-surface, the upper edge node coordinates of the opposite side of an arc within the surface are composed of the node abscissa matrix x9 and the node ordinate matrix y9, respectively, as follows:

[0059]

[0060] The number of grids on the edges of each hexahedron with a specific shape and the corresponding edge node coordinates have been determined.

[0061] Step S3: Mirror and supplement the edge node coordinates of a set of opposite sides on the front of the 6 hexahedrons with specific shapes to obtain the edge node coordinates of the front of the parallelepiped target plate, specifically as follows:

[0062] On each sub-surface, a set of opposite sides is assigned a node abscissa matrix and a node ordinate matrix. For any set of opposite sides: the node abscissa matrix of any one edge is the first horizontal matrix x s , and the node ordinate matrix is the first vertical matrix y s . The node abscissa matrix of the other edge is the second horizontal matrix x t , and the node ordinate matrix is the second vertical matrix y t .

[0063] The first horizontal matrix, the first vertical matrix, the second horizontal matrix, and the second vertical matrix are concatenated in order from top to bottom into a first-order node matrix coor with 4 rows and the number of nodes on the edge as the number of columns (1) :

[0064] coor (1) =[x s T y s T x t T y t T T (11)

[0065] Among them, the superscript T is the matrix transpose symbol.

[0066] Mirror and supplement the edge node coordinates of the 6 sub-surfaces to obtain the mirror-supplemented node coordinates of each sub-surface. Take the first-order middle surface as the symmetry plane and mirror the first-order node matrix to obtain the second-order node matrix coor (2) . In the first-order node matrix coor (1) ​Exchange x in the middle s with x t positions, and exchange y s with y t positions to obtain a new primary node matrix coor (1.5) , mirror the edge node coordinates of the 6 sub - surfaces with the intersection line of the primary mid - surface and the secondary mid - surface as the axis of symmetry to the new primary node matrix to obtain the tertiary node matrix coor (3) . Mirror the edge node coordinates of the 6 sub - surfaces with the secondary mid - surface as the symmetric plane to the new primary node matrix to obtain the quaternary node matrix coor (4) . Thus, the edge node coordinates of the front surface of the parallelepiped target plate have all been obtained.

[0067] Step S4: Expand the edge node coordinates of the front surface of the target plate to the face node coordinates of the front surface of the target plate, and supplement the edge node coordinates of the parallelepiped target plate along the reference direction, specifically as follows:

[0068] Step S4 - 1: The abscissa matrix X′ and the ordinate matrix Y′ of the face node coordinates of the front surface of the parallelepiped target plate are calculated from the primary node matrix of each sub - surface and its mirror image, supplemented with node coordinates and the boundary point ratio matrix, as follows:

[0069]

[0070] For the first sub - surface, the horizontal matrix subscript s = 1, the vertical matrix subscript t = 2, and the first grid variable n = n2.

[0071] For the second sub - surface, the horizontal matrix subscript s = 2, the vertical matrix subscript t = 3, n = n4, and n4 is the number of grids determined on the three - line inside the arc.

[0072] For the third sub - surface, the horizontal matrix subscript s = 4, the vertical matrix subscript t = 5, n = n4.

[0073] For the fourth sub - surface, the horizontal matrix subscript s = 5, the vertical matrix subscript t = 6, n = n5, and n5 is the number of grids determined on the two - line outside the arc.

[0074] For the fifth sub - surface, the horizontal matrix subscript s = 7, the vertical matrix subscript t = 8, n = n5.

[0075] For the sixth sub - surface, the horizontal matrix subscript s = 3, the vertical matrix subscript t = 9, n = n3. Proceed to step S4 - 2.

[0076] Step S4 - 2: If the number of grids determined on the edge of the parallelepiped target plate along the reference direction is n6, then the node value matrix Z′ of the node coordinates of each node along the reference direction is:

[0077]

[0078] Among them, represents a matrix of all 1s with a size of 1*(n6 + 1).

[0079] Step S5: By setting up a matrix arrangement function, based on the face node coordinates on the front surface of the parallelepiped target plate and the edge node coordinates of the parallelepiped target plate along the reference direction, and according to the orientation of the parallelepiped target plate, obtain the body node coordinates of the structured grid of the parallelepiped target plate, and then obtain the structured finite element grid of the parallelepiped target plate, specifically as follows:

[0080] Step S5-1: Set three matrix arrangement functions:

[0081] The first matrix arrangement function Re(A) represents a matrix with a column number of 1 formed by splicing the elements with column numbers greater than 1 in matrix A below the first column elements in ascending order of column numbers.

[0082] The second matrix arrangement function De(A, p) represents a matrix formed by repeating each element in matrix A p times and placing them sequentially below the elements.

[0083] The third matrix arrangement function Dm(A, p) represents a matrix formed by repeating matrix A as a whole p times and placing them sequentially below matrix A. Proceed to step 5-2.

[0084] Step S5-2: Determine the orientation of the parallelepiped target plate in the X-Y-Z coordinate system. If it is in the positive X-axis direction, then:

[0085] The matrix of all body node coordinates (X″, Y″, Z″) of the first hexahedron, the second hexahedron, and the sixth hexahedron is:

[0086]

[0087] For the first hexahedron, the second grid variable b1 = n2.

[0088] For the second hexahedron, b1 = n4.

[0089] For the sixth hexahedron, b1 = n3.

[0090] The matrix of all body node coordinates of the third hexahedron, the fourth hexahedron, and the fifth hexahedron is:

[0091]

[0092] For the third hexahedron, the third grid variable b2 = n2, and the fourth grid variable b3 = n4. For the fourth hexahedron, b2 = n2, b3 = n5.

[0093] For the fifth hexahedron, b2 = n3, b3 = n5.

[0094] If it is the positive direction of the Y-axis, then:

[0095] The total body node coordinate matrices of the first hexahedron, the second hexahedron, and the sixth hexahedron are:

[0096]

[0097] For the first hexahedron, the fifth grid variable b4 = n2.

[0098] For the second hexahedron, b4 = n4.

[0099] For the sixth hexahedron, b4 = n3.

[0100] The total body node coordinate matrices of the third hexahedron, the fourth hexahedron, and the fifth hexahedron are:

[0101]

[0102] For the third hexahedron, the fifth grid variable b5 = n2, and the sixth grid variable b6 = n4. For the fourth hexahedron, b5 = n2, b6 = n5.

[0103] For the fifth hexahedron, b5 = n3, b6 = n5.

[0104] If it is the positive direction of the Z-axis, then:

[0105] The total body node coordinate matrices of the first hexahedron, the second hexahedron, and the sixth hexahedron are:

[0106]

[0107] For the first hexahedron, the seventh grid variable b7 = n2.

[0108] For the second hexahedron, b7 = n4.

[0109] For the sixth hexahedron, b7 = n3.

[0110] The total body node coordinate matrices of the third hexahedron, the fourth hexahedron, and the fifth hexahedron are:

[0111]

[0112] For the third hexahedron, the eighth grid variable b8 = n2, and the ninth grid variable b9 = n4.

[0113] For the fourth hexahedron, b8 = n2, b9 = n5.

[0114] For the fifth hexahedron, b8 = n3, b9 = n5. Proceed to step S5-3.

[0115] Step S5-3: Obtain the structured grid node coordinate distribution matrix S:

[0116] S = [X″ Y″ Z″] (20)

[0117] Proceed to Step S5-4.

[0118] Step S5-4: According to the quadratic node matrix, cubic node matrix, and quartic node matrix, repeat Step S5-2 once respectively to obtain the quadratic structured grid node coordinate distribution matrix, cubic structured grid node coordinate distribution matrix, and quartic structured grid node coordinate distribution matrix, and then proceed to Step S5-5.

[0119] Step S5-5: Stack the obtained structured grid node coordinate distribution matrix, quadratic structured grid node coordinate distribution matrix, cubic structured grid node coordinate distribution matrix, and quartic structured grid node coordinate distribution matrix vertically in sequence to obtain the structured finite element grid of the parallelepiped target plate.

[0120] Step S6: By setting a three-dimensional serial number matrix, obtain the unstructured grid matrix, sort and organize the body node coordinates of the structured finite element grid of the parallelepiped target plate to obtain the unstructured finite element grid of the parallelepiped target plate, specifically as follows:

[0121] The structured grid node coordinate distribution matrix, quadratic structured grid node coordinate distribution matrix, cubic structured grid node coordinate distribution matrix, and quartic structured grid node coordinate distribution matrix contain the body node coordinates of all the structured finite element grids of the parallelepiped target plate. The above four matrices have the same number of rows, which is the number of rows of the structured grid matrix.

[0122] Establish a three-dimensional serial number matrix B0, and use B0(u, v, w) to represent the element in the u-th row, v-th column, and w-th layer of the three-dimensional serial number matrix B0.

[0123] Judge the orientation of the parallelepiped target plate. If it is in the positive X-axis direction, then:

[0124] B0(u, v, w) = u + f2(v - 1) + f2f1(w - 1) + h, u ∈ [1, f2], v ∈ [1, f1], w ∈ [1, f3] (21)

[0125] Subsequently, exchange the first and second dimensions of the three-dimensional serial number matrix.

[0126] If it is in the positive Y-axis direction, then:

[0127] B0(u, v, w) = u + f1(v - 1) + f1f3(w - 1) + h, u ∈ [1, f1], v ∈ [1, f3], w ∈ [1, f2] (22)

[0128] Subsequently, the second and third dimensions of the three-dimensional serial number matrix are exchanged.

[0129] If it is the positive direction of the Z-axis, then:

[0130] B0(u, v, w) = u + f3(v - 1) + f2f3(w - 1) + h, u ∈ [1, f3], v ∈ [1, f2], w ∈ [1, f1] (23)

[0131] Subsequently, the first and third dimensions of the three-dimensional serial number matrix are exchanged.

[0132] Among them, the value of h is 0. For the first hexahedron, the first-order quantity f1 = n2, the second-order quantity f2 = n1, and the third-order quantity f3 = n6.

[0133] For the second hexahedron, f1 = n4, f2 = n1, f3 = n6. For the third hexahedron, f1 = n2, f2 = n4, f3 = n6.

[0134] For the fourth hexahedron, f1 = n2, f2 = n5, f3 = n6. For the fifth hexahedron, f1 = n3, f2 = n5, f3 = n6.

[0135] For the sixth hexahedron, f1 = n3, f2 = n1, f3 = n6. Proceed to step S6-2.

[0136] Step S6-2: Obtain the three-dimensional serial number processing matrix B1. Proceed to step S6-3.

[0137] Step S6-3: Remove all elements corresponding to the maximum number of rows, columns, and layers from the three-dimensional serial number processing matrix B1 to obtain the three-dimensional serial number unstructured matrix B', and arrange the three-dimensional serial number unstructured matrix B' in ascending order from smallest to largest according to the order of row serial number, then column serial number, and finally layer serial number to obtain the unstructured row matrix C. Proceed to step S6-4.

[0138] Step S6-4: Obtain the unstructured grid information matrix D through the unstructured row matrix C. The unstructured grid information matrix D represents each unstructured finite element grid information composed of structured finite element grid nodes. Determine the orientation of the parallelepiped target plate. If it is the positive direction of the X-axis, then:

[0139]

[0140] If it is the positive direction of the Y-axis, then:

[0141]

[0142] If it is the positive direction of the Z-axis, then:

[0143]

[0144] Transfer to step S6-5.

[0145] Step S6-5: Construct a column of elements on the left side of the unstructured grid information matrix D. The value of each element is the row number of the row where it is located. The new matrix formed is the unstructured finite element grid node coordinate distribution matrix E2. Then transfer to step S6-6.

[0146] Step S6-6: Supplement a column of elements on the left side of the structured grid node coordinate distribution matrix, which is the row number of the element in the matrix where it is located, to obtain the unstructured finite element grid node coordinate distribution matrix E1. Arrange the unstructured finite element grid distribution matrix E2 below the unstructured finite element grid node coordinate distribution matrix E1 to obtain the unstructured finite element grid.

[0147] Change the value of h to the number of rows of the structured grid matrix, repeat steps S6-1 to S6-4 once to obtain the quadratic unstructured finite element grid node coordinate distribution matrix E4. Supplement a column of elements on the left side of the quadratic structured grid node coordinate distribution matrix, which is the row number of the element in the matrix where it is located plus the number of rows of the structured grid matrix, to obtain the quadratic unstructured finite element grid node coordinate distribution matrix E3. Arrange the quadratic unstructured finite element grid distribution matrix E4 below the quadratic unstructured finite element grid node coordinate distribution matrix E3 to obtain the quadratic unstructured finite element grid.

[0148] Change the value of h to twice the number of rows of the structured grid matrix, repeat steps S6-1 to S6-4 once to obtain the cubic unstructured finite element grid node coordinate distribution matrix E6. Supplement a column of elements on the left side of the cubic structured grid node coordinate distribution matrix, which is the row number of the element in the matrix where it is located plus the number of rows of the structured grid matrix, to obtain the cubic unstructured finite element grid node coordinate distribution matrix E5. Arrange the cubic unstructured finite element grid distribution matrix E6 below the cubic unstructured finite element grid node coordinate distribution matrix E5 to obtain the cubic unstructured finite element grid.

[0149] Change the value of h to three times the number of rows of the structured grid matrix, repeat steps S6-1 to S6-4 once. Obtain the quartic unstructured finite element grid node coordinate distribution matrix E8. Supplement a column of elements on the left side of the quartic structured grid node coordinate distribution matrix, which is the row number of the element in the matrix where it is located plus the number of rows of the structured grid matrix, to obtain the quartic unstructured finite element grid node coordinate distribution matrix E7. Arrange the quartic unstructured finite element grid distribution matrix E8 below the quartic unstructured finite element grid node coordinate distribution matrix E7 to obtain the quartic unstructured finite element grid, then transfer to step S6-7.

[0150] Step S6-7: Place the unstructured finite element mesh, quadratic unstructured finite element mesh, cubic unstructured finite element mesh, and quartic unstructured finite element mesh in a text file in sequence to obtain the unstructured finite element mesh of the parallelepiped target plate.

[0151] According to the above steps, the rapid automatic generation of the finite element mesh of the parallelepiped target plate can be realized.

[0152] Embodiment

[0153] Combined with Figures 1 to 6 , a method for rapid automatic generation of the finite element mesh of a parallelepiped target plate is as follows:

[0154] First, set up the calculation example and draw a target plate with a thickness of 80 mm, a height and width of 800 mm, an inclination angle of 45°, a facing direction of the positive x-axis, and an offset distance of 300 mm.

[0155] Input the geometric parameter values of the target plate as follows:

[0156]

[0157] Input the mesh parameter values of the target plate as follows:

[0158] <![CDATA[n1]]> <![CDATA[n2]]> <![CDATA[n3]]> <![CDATA[n 4 > <![CDATA[n 5 > <![CDATA[n 6 > q 20 20 40 30 40 30 1

[0159] Step S1: Taking the direction of the projectile, shock wave, and other incoming objects as the reference direction, the surface of the parallelepiped target plate that bears the projectile, shock wave, and other incoming objects is the front surface of the target plate, and its opposite surface is the back surface of the target plate. The other four surfaces are the top surface, bottom surface, left side surface, and right side surface of the target plate respectively.

[0160] The distance between the front surface and the back surface of the target plate is the thickness L4 of the parallelepiped target plate. The distance between the top surface and the bottom surface of the target plate is 2*L2, where L2 is half of the height of the parallelepiped target plate. The distance between the left side surface and the right side surface of the target plate is 2*L3, where L3 is half of the width of the parallelepiped target plate. The opposite direction of the reference direction is the facing direction of the parallelepiped target plate. The translation length of the parallelepiped target plate along the reference direction is the offset distance L5. The line-plane angle between the parallelepiped target plate and the reference direction is the inclination angle α of the parallelepiped target plate.

[0161] All the points with equal distances from the top surface to the bottom surface of the target plate form the first mid-plane of the parallelepiped target plate. All the points with equal distances from the left side surface to the right side surface of the target plate form the second mid-plane of the parallelepiped target plate.

[0162] The parallelepiped target plate is divided into four sub-target plates by the first middle plane and the second middle plane along the reference direction. The sub-target plate that synchronously contacts the top surface and the right side surface of the target plate is the first sub-target plate, and the other sub-target plates are sequentially defined as the second sub-target plate, the third sub-target plate, and the fourth sub-target plate in a clockwise direction starting from the first sub-target plate along the equivalent thickness direction.

[0163] The projection plane of the surface on the first sub-target plate that coincides with the front surface of the target plate along the reference direction is defined as the pre-partition plane, and the projection plane of the front surface of the target plate along the reference direction is the projected front surface of the target plate. The pre-partition plane is exactly the part of the front surface of the target plate surrounded by the first middle plane, the second middle plane, the top surface of the target plate, and the right side surface of the target plate.

[0164] Taking the intersection point of the pre-partition plane, the first middle plane, and the second middle plane as the center, a 1 / 4 circular arc with a radius of R is drawn within the pre-partition plane, which is called the in-plane arc.

[0165] The in-plane arc divides the pre-partition plane into the arc-inner surface and the arc-outer surface. The midpoint of the in-plane arc divides the in-plane arc into two parts, intersecting with the first middle plane to form the in-plane first arc and intersecting with the second middle plane to form the in-plane second arc. A face center point is determined within the arc-inner surface, and the distances from the face center point to the first middle plane and the second middle plane are equal.

[0166] Along the reference direction, on the arc-inner surface, a line segment is drawn from the face center point to the first middle plane by clockwise rotating the arc inner angle θ along the perpendicular line from the face center point to the first middle plane, which is the arc-inner first line. The distance from the intersection point of the arc-inner first line and the first middle plane to the center of the circle is L1.

[0167] Along the reference direction, on the arc-inner surface, a line segment is drawn from the face center point to the second middle plane by counterclockwise rotating the arc inner angle along the perpendicular line from the face center point to the second middle plane, which is the arc-inner second line. The distance from the intersection point of the arc-inner second line and the second middle plane to the center of the circle is equal to the distance L1 from the intersection point of the arc-inner first line and the first middle plane to the center of the circle. Along the reference direction, on the arc-inner surface, the counterclockwise rotation angle of the arc inner angle along the perpendicular line from the face center point to the second middle plane is equal to θ.

[0168] A perpendicular line is drawn from the face center point to the in-plane arc, intersecting the in-plane arc at the arc midpoint, and this perpendicular line is the arc-inner third line.

[0169] Along the reference direction, on the arc-outer surface, the arc outer angle is clockwise rotated along the perpendicular line from the arc midpoint to the top surface of the parallelepiped target plate A line segment is drawn from the arc midpoint to the top surface of the parallelepiped target plate, which is the arc-outer first line.

[0170] Along the reference direction, on the arc-outer surface, a line segment is drawn from the arc midpoint to the right side surface of the parallelepiped target plate by counterclockwise rotating the arc outer angle along the perpendicular line from the arc midpoint to the right side surface of the parallelepiped target plate, which is the arc-outer second line. Along the reference direction, on the arc-outer surface, the counterclockwise rotation angle of the arc outer angle along the perpendicular line from the arc midpoint to the right side surface of the parallelepiped target plate is equal to

[0171] The first sub-target board is divided into six hexahedrons with specific shapes by the in-plane arc, the first line inside the arc, the second line inside the arc, the third line inside the arc, the first line outside the arc, and the second line outside the arc along the reference direction.

[0172] The pre-divided plane is divided into six sub-planes by the in-plane arc, the first line inside the arc, the second line inside the arc, the third line inside the arc, the first line outside the arc, and the second line outside the arc along the reference direction. Among these sub-planes, the one with the first line inside the arc and the second line inside the arc as its sides is the first sub-plane, the one with the first line inside the arc and the third line inside the arc as its sides is the second sub-plane, the one with the second line inside the arc and the third line inside the arc as its sides is the third sub-plane, the one with the in-plane arc and the second line outside the arc as its sides is the fourth sub-plane, the one with the first line outside the arc and the second line outside the arc as its sides is the fifth sub-plane, and the one with the in-plane arc and the first line outside the arc as its sides is the sixth sub-plane.

[0173] The hexahedron with a specific shape that coincides with the first sub-plane along the reference direction is the first hexahedron, and the first sub-plane is the front face of the first hexahedron. The hexahedron with a specific shape that coincides with the second sub-plane along the reference direction is the second hexahedron, and the second sub-plane is the front face of the second hexahedron. The hexahedron with a specific shape that coincides with the third sub-plane along the reference direction is the third hexahedron, and the third sub-plane is the front face of the third hexahedron. The hexahedron with a specific shape that coincides with the fourth sub-plane along the reference direction is the fourth hexahedron, and the fourth sub-plane is the front face of the fourth hexahedron. The hexahedron with a specific shape that coincides with the fifth sub-plane along the reference direction is the fifth hexahedron, and the fifth sub-plane is the front face of the fifth hexahedron. The hexahedron with a specific shape that coincides with the sixth sub-plane along the reference direction is the sixth hexahedron, and the sixth sub-plane is the front face of the sixth hexahedron.

[0174] Step S2: Set the edge node ratio matrix G(m, q), where m represents the number of grids set on the edge of the hexahedron with a specific shape, q represents the ratio of the distance between two adjacent nodes, and q is a positive number. i represents the node number, and the value of the i-th element G(m, q) i is:

[0175]

[0176] In the first sub-plane, the length of the opposite side of the first line inside the arc is equal to L1, the number of grids is determined to be n1, and the coordinates of the upper edge nodes of the opposite side of the first line inside the arc are composed of the node abscissa matrix x1 and the node ordinate matrix y1, respectively, as follows:

[0177]

[0178] The coordinates of the upper edge nodes of the first line inside the arc are composed of the node abscissa matrix x2 and the node ordinate matrix y2, respectively, as follows:

[0179]

[0180] where represents a 1*(n1 + 1) all-1 matrix.

[0181] In the second sub-face, the upper edge node coordinates in the face are composed of the node abscissa matrix x3 and the node ordinate matrix y3, which are respectively:

[0182]

[0183] In the third sub-face, the length of the opposite side of the two lines inside the arc is equal to L1, the number of grids is determined to be n2, and the upper edge node coordinates of the opposite side of the two lines inside the arc are composed of the node abscissa matrix x4 and the node ordinate matrix y4, which are respectively:

[0184]

[0185] Among them, represents a 1*(n2 + 1) all-1 matrix.

[0186] The upper edge node coordinates of the two arcs in the face are composed of the node abscissa matrix x5 and the node ordinate matrix y5, which are respectively:

[0187]

[0188] In the fourth sub-face, the upper edge node coordinates of the opposite side of the two arcs in the face are composed of the node abscissa matrix x6 and the node ordinate matrix y6, which are respectively:

[0189]

[0190] In the fifth sub-face, the number of grids on the first line outside the arc is determined to be n3, and the upper edge node coordinates of the first line outside the arc are composed of the node abscissa matrix x7 and the node ordinate matrix y7, which are respectively:

[0191]

[0192] Among them, represents a 1*(n3 + 1) all-1 matrix.

[0193] The upper edge node coordinates of the opposite side of the first line outside the arc are composed of the node abscissa matrix x8 and the node ordinate matrix y8, which are respectively:

[0194]

[0195] In the sixth sub-face, the upper edge node coordinates of the opposite side of the first arc in the face are composed of the node abscissa matrix x9 and the node ordinate matrix y9, which are respectively:

[0196]

[0197] The number of grids on the edges of each hexahedron with a specific shape and the corresponding edge node coordinates have been determined.

[0198] Step S3: A set of opposite sides on each sub - surface is assigned a node abscissa matrix and a node ordinate matrix. Among any set of opposite sides: for any one side, the node abscissa matrix is the first - order abscissa matrix \(x\) s , and the node ordinate matrix is the first - order ordinate matrix \(y\) s . For the other side, the node abscissa matrix is the second - order abscissa matrix \(x\) t , and the node ordinate matrix is the second - order ordinate matrix \(y\) t .

[0199] The first - order abscissa matrix, the first - order ordinate matrix, the second - order abscissa matrix, and the second - order ordinate matrix are spliced in order from top to bottom into a first - order node matrix \(coor\) with 4 rows and the number of nodes on the side as the number of columns (1) :

[0200] \(coor\) (1) = [ \(x\) s T \(y\) s T \(x\) t T \(y\) t T ] T (11)

[0201] where the superscript \(T\) is the matrix transpose symbol.

[0202] Mirror - supplement the edge - node coordinates of the 6 sub - surfaces to obtain the mirror - supplemented node coordinates of each sub - surface. Take the edge - node coordinates of the 6 sub - surfaces with the first - order middle - surface as the symmetry plane, and mirror the first - order node matrix to obtain the second - order node matrix \(coor\) (2) . In the first - order node matrix \(coor\) (1) , exchange the positions of \(x\) s and \(x\) t , and exchange the positions of \(y\) s and \(y\) t to obtain a new first - order node matrix \(coor\) (1.5) . Take the edge - node coordinates of the 6 sub - surfaces with the intersection line of the first - order middle - surface and the second - order middle - surface as the symmetry axis, and mirror the new first - order node matrix to obtain the third - order node matrix \(coor\) (3) . Take the edge - node coordinates of the 6 sub - surfaces with the second - order middle - surface as the symmetry plane, and mirror the new first - order node matrix to obtain the fourth - order node matrix \(coor\) (4) . Thus, the edge - node coordinates of the front surface of the parallelepiped target plate have all been obtained.

[0203] Step S4: Expand the edge - node coordinates of the front surface of the target plate to the face - node coordinates of the front surface of the target plate, and supplement the edge - node coordinates of the parallelepiped target plate along the reference direction, specifically as follows:

[0204] Step S4-1: The abscissa matrix X′ and the ordinate matrix Y′ of the face node coordinates on the front of the parallelepiped target plate are calculated from the first-order node matrix of each sub-face, its mirror-supplemented node coordinates, and the boundary point ratio matrix as follows:

[0205]

[0206] For the first sub-face, the subscript s of the horizontal matrix is 1, the subscript t of the vertical matrix is 2, and the first grid variable n = n2.

[0207] For the second sub-face, the subscript s of the horizontal matrix is 2, the subscript t of the vertical matrix is 3, n = n4, and n4 is the number of grids determined on the three lines inside the arc.

[0208] For the third sub-face, the subscript s of the horizontal matrix is 4, the subscript t of the vertical matrix is 5, and n = n4.

[0209] For the fourth sub-face, the subscript s of the horizontal matrix is 5, the subscript t of the vertical matrix is 6, and n = n5, where n5 is the number of grids determined on the two lines outside the arc.

[0210] For the fifth sub-face, the subscript s of the horizontal matrix is 7, the subscript t of the vertical matrix is 8, and n = n5.

[0211] For the sixth sub-face, the subscript s of the horizontal matrix is 3, the subscript t of the vertical matrix is 9, and n = n3. Proceed to step S4-2.

[0212] Step S4-2: Determine the number of grids on the side of the planar parallelepiped target plate along the reference direction as n6. Then, the node value matrix Z′ of the node coordinates along the reference direction is:

[0213]

[0214] Among them, represents a 1*(n6 + 1) all-1 matrix.

[0215] Step S5: By setting a matrix arrangement function, based on the face node coordinates on the front of the parallelepiped target plate and the edge node coordinates of the planar parallelepiped target plate along the reference direction, and according to the orientation of the parallelepiped target plate, obtain the body node coordinates of the structured grid of the parallelepiped target plate, and then obtain the structured finite element grid of the parallelepiped target plate, specifically as follows:

[0216] Step S5-1: Set three matrix arrangement functions:

[0217] The first matrix arrangement function Re(A) means arranging the elements with column numbers greater than 1 in matrix A in ascending order of column numbers and splicing them below the elements in the first column to form a matrix with 1 column.

[0218] The second matrix rearrangement function De(A, p) represents a matrix formed by repeating each element in matrix A p times and placing them successively below the element.

[0219] The third matrix rearrangement function Dm(A, p) represents a matrix formed by repeating matrix A as a whole p times and placing them successively below matrix A. Go to step 5-2.

[0220] Step S5-2: In the X-Y-Z coordinate system, if the orientation of the parallelepiped target plate is the positive X-axis direction, then:

[0221] The matrix of all volume node coordinates (X″, Y″, Z″) of the first hexahedron, the second hexahedron, and the sixth hexahedron is:

[0222]

[0223] For the first hexahedron, the second grid variable b1 = n2.

[0224] For the second hexahedron, b1 = n4.

[0225] For the sixth hexahedron, b1 = n3.

[0226] The matrix of all volume node coordinates of the third hexahedron, the fourth hexahedron, and the fifth hexahedron is:

[0227]

[0228] For the third hexahedron, the third grid variable b2 = n2, and the fourth grid variable b3 = n4.

[0229] For the fourth hexahedron, b2 = n2, b3 = n5.

[0230] For the fifth hexahedron, b2 = n3, b3 = n5. Go to step S5-3.

[0231] Step S5-3: Obtain the structured grid node coordinate distribution matrix S:

[0232] S = [X″ Y″ Z″] (20)

[0233] Go to step S5-4.

[0234] Step S5-4: According to the quadratic node matrix, the cubic node matrix, and the quartic node matrix, repeat step S5-2 once respectively, and correspondingly obtain the quadratic structured grid node coordinate distribution matrix, the cubic structured grid node coordinate distribution matrix, and the quartic structured grid node coordinate distribution matrix, and then go to step S5-5.

[0235] Step S5-5: Concatenate the obtained structured grid node coordinate distribution matrices, quadratic structured grid node coordinate distribution matrices, cubic structured grid node coordinate distribution matrices, and quartic structured grid node coordinate distribution matrices in sequence from top to bottom to obtain the structured finite element grid of the parallelepiped target plate.

[0236] Step S6: Obtain the unstructured grid matrix by setting a three-dimensional serial number matrix. Sort and organize the body node coordinates of the structured finite element grid of the parallelepiped target plate to obtain the unstructured finite element grid of the parallelepiped target plate, as follows:

[0237] Step S6-1: The structured grid node coordinate distribution matrix, quadratic structured grid node coordinate distribution matrix, cubic structured grid node coordinate distribution matrix, and quartic structured grid node coordinate distribution matrix contain the body node coordinates of all the structured finite element grids of the parallelepiped target plate. The above four matrices have the same number of rows, which is the number of rows of the structured grid matrix.

[0238] Establish a three-dimensional serial number matrix B0, and use B0(u, v, w) to represent the element in the u-th row, v-th column, and w-th layer of the three-dimensional serial number matrix B0.

[0239] If the orientation of the parallelepiped target plate is the positive X-axis direction, then:

[0240] B0(u, v, w) = u + f2(v - 1) + f2f1(w - 1) + h, u ∈ [1, f2], v ∈ [1, f1], w ∈ [1, f3] (21)

[0241] Subsequently, exchange the first and second dimensions of the three-dimensional serial number matrix.

[0242] Among them, the value of h is 0. For the first hexahedron, the first-order quantity f1 = n2, the second-order quantity f2 = n1, and the third-order quantity f3 = n6.

[0243] For the second hexahedron, f1 = n4, f2 = n1, f3 = n6. For the third hexahedron, f1 = n2, f2 = n4, f3 = n6.

[0244] For the fourth hexahedron, f1 = n2, f2 = n5, f3 = n6. For the fifth hexahedron, f1 = n3, f2 = n5, f3 = n6.

[0245] For the sixth hexahedron, f1 = n3, f2 = n1, f3 = n6. Proceed to Step S6-2.

[0246] Step S6-2: Obtain the three-dimensional serial number processing matrix B1. Proceed to Step S6-3.

[0247] Step S6-3: Remove all elements corresponding to the maximum number of rows, columns, and layers from the three-dimensional serial number processing matrix B1 to obtain a three-dimensional serial number unstructured matrix B'. Arrange the three-dimensional serial number unstructured matrix B' in ascending order according to the order of row serial numbers first, then column serial numbers, and finally layer serial numbers to form a single-row matrix, obtaining an unstructured row matrix C. Proceed to Step S6-4.

[0248] Step S6-4: Obtain an unstructured grid information matrix D through the unstructured row matrix C. Each piece of unstructured finite element grid information formed by structured finite element grid nodes is represented in the unstructured grid information matrix D. If the orientation of the parallelepiped target plate is the positive X-axis direction, then:

[0249]

[0250] Proceed to Step S6-5.

[0251] Step S6-5: Construct a column of elements on the left side of the unstructured grid information matrix D. The value of each element is the row serial number of the row where it is located, forming a new matrix as the unstructured finite element grid node coordinate distribution matrix E2. Proceed to Step S6-6.

[0252] Step S6-6: Supplement a column of elements on the left side of the structured grid node coordinate distribution matrix, which is the row serial number of the element in the matrix where it is located, to obtain the unstructured finite element grid node coordinate distribution matrix E1. Arrange the unstructured finite element grid distribution matrix E2 below the unstructured finite element grid node coordinate distribution matrix E1 to obtain the unstructured finite element grid.

[0253] Change the value of h to the number of rows of the structured grid matrix, repeat Steps S6-1 to S6-4 once to obtain the quadratic unstructured finite element grid node coordinate distribution matrix E4. Supplement a column of elements on the left side of the quadratic structured grid node coordinate distribution matrix, which is the row serial number of the element in the matrix where it is located plus the number of rows of the structured grid matrix, to obtain the quadratic unstructured finite element grid node coordinate distribution matrix E3. Arrange the quadratic unstructured finite element grid distribution matrix E4 below the quadratic unstructured finite element grid node coordinate distribution matrix E3 to obtain the quadratic unstructured finite element grid.

[0254] Change the value of h to twice the number of rows of the structured grid matrix, repeat Steps S6-1 to S6-4 once to obtain the cubic unstructured finite element grid node coordinate distribution matrix E6. Supplement a column of elements on the left side of the cubic structured grid node coordinate distribution matrix, which is the row serial number of the element in the matrix where it is located plus the number of rows of the structured grid matrix, to obtain the cubic unstructured finite element grid node coordinate distribution matrix E5. Arrange the cubic unstructured finite element grid distribution matrix E6 below the cubic unstructured finite element grid node coordinate distribution matrix E5 to obtain the cubic unstructured finite element grid.

[0255] Change the value of h to three times the number of rows of the structured grid matrix, and repeat steps S6-1 to S6-4 once. Obtain the four-time unstructured finite element grid node coordinate distribution matrix E8. Supplement a column of elements on the left side of the four-time structured grid node coordinate distribution matrix, where the element is the row number in the matrix plus the number of rows of the structured grid matrix, to obtain the four-time unstructured finite element grid node coordinate distribution matrix E7. Arrange the four-time unstructured finite element grid distribution matrix E8 below the four-time unstructured finite element grid node coordinate distribution matrix E7 to obtain the four-time unstructured finite element grid, and then go to step S6-7.

[0256] Step S6-7: Place the unstructured finite element grid, the quadratic unstructured finite element grid, the cubic unstructured finite element grid, and the four-time unstructured finite element grid in a text file in sequence to obtain the unstructured finite element grid of the parallelepiped target plate.

[0257] So far, the structured finite element grid and the unstructured finite element grid of the parallelepiped target plate are completed. When facing a large number of working conditions, modify according to the actual geometric parameters and required grid parameters of the working conditions, and repeat steps S1 to S6 to quickly and automatically generate the finite element grids of the parallelepiped target plate under each working condition.

Claims

1. A method for quickly and automatically generating a finite element mesh of a parallelepiped target plate, characterized in that, The specific steps are as follows: Step S1: Determine the geometric parameters of the parallelepiped target plate, including thickness, height, width, orientation, offset distance, and inclination angle. Divide the parallelepiped target plate into 4 sub-target plates along the reference direction, namely the first sub-target plate, the second sub-target plate, the third sub-target plate, and the fourth sub-target plate. Divide the first sub-target plate into 6 hexahedrons with specific shapes along the reference direction, and then go to step S2; Step S2: Determine the number of grids of a set of opposite sides on the front surface of the 6 hexahedrons with specific shapes and determine the corresponding edge node coordinates, and then go to step S3; Step S3: Mirror and supplement the edge node coordinates of a set of opposite sides on the front surface of the 6 hexahedrons with specific shapes to obtain the edge node coordinates of the front surface of the parallelepiped target plate, and then go to step S4; Step S4: Expand the edge node coordinates of the front surface of the target plate to the face node coordinates of the front surface of the target plate, and supplement the edge node coordinates of the plane parallelepiped target plate along the reference direction, and then go to step S5; Step S5: By setting a matrix sorting function, obtain the volume node coordinates of the structured grid of the parallelepiped target plate from the face node coordinates of the front surface of the parallelepiped target plate and the edge node coordinates of the plane parallelepiped target plate along the reference direction according to the orientation of the parallelepiped target plate, and then obtain the structured finite element grid of the parallelepiped target plate, and then go to step S6; Step S6: By setting a three-dimensional serial number matrix, obtain an unstructured grid matrix, sort and arrange the volume node coordinates of the structured finite element grid of the parallelepiped target plate to obtain the unstructured finite element grid of the parallelepiped target plate.

2. The rapid automatic generation method of the finite element mesh of a parallelepiped target plate according to claim 1, wherein: In step S1, determine the geometric parameters of the parallelepiped target plate, including thickness, height, width, orientation, offset distance, and inclination angle. Divide the parallelepiped target plate into 4 sub-target plates along the reference direction, namely the first sub-target plate, the second sub-target plate, the third sub-target plate, and the fourth sub-target plate. Divide the first sub-target plate into 6 hexahedrons with specific shapes along the reference direction, specifically as follows: Taking the directions of the projectile, shock wave, and other incoming objects as the reference direction, the surface of the parallelepiped target plate that bears the projectile, shock wave, and other incoming objects is the front surface of the target plate, and its opposite surface is the back surface of the target plate. The other four surfaces are the top surface of the target plate, the bottom surface of the target plate, the left side surface of the target plate, and the right side surface of the target plate respectively; The distance between the front surface and the back surface of the target plate is the thickness L4 of the parallelepiped target plate; the distance between the top surface and the bottom surface of the target plate is 2*L2, where L2 is half of the height of the parallelepiped target plate; the distance between the left side surface and the right side surface of the target plate is 2*L3, where L3 is half of the width of the parallelepiped target plate; the ratio of the height to the width of the target plate is not less than 0.5 and not greater than 2; the opposite direction of the reference direction is the orientation of the parallelepiped target plate; the translation length of the parallelepiped target plate along the reference direction is the offset distance L5; the line-plane angle between the parallelepiped target plate and the reference direction is the inclination angle α of the parallelepiped target plate, and the inclination angle α is not less than 30 degrees and not greater than 90 degrees; All points equidistant from the top surface and the bottom surface of the target plate form the first mid-plane of the parallelepiped target plate; all points equidistant from the left side surface and the right side surface of the target plate form the second mid-plane of the parallelepiped target plate. The parallelepiped target plate is divided into four sub-target plates by the first middle plane and the second middle plane along the reference direction. The sub-target plate that synchronously contacts the top surface and the right side surface of the target plate is the first sub-target plate. Starting from the first sub-target plate along the equivalent thickness direction, the other sub-target plates are sequentially defined as the second sub-target plate, the third sub-target plate, and the fourth sub-target plate in a clockwise manner; The projection plane of the surface on the first sub-target plate that coincides with the front surface of the target plate along the reference direction is defined as the pre-partition plane, and the projection plane of the front surface of the target plate along the reference direction is the projected front surface of the target plate; Taking the intersection point of the pre-partition plane, the first middle plane, and the second middle plane as the center, a 1 / 4 arc with a radius of R is drawn within the pre-partition plane, which is called the in-plane arc, where 0.1L2 ≤ R ≤ 0.7L2 and 0.1L3 ≤ R ≤ 0.7L3; The in-plane arc divides the pre-partition plane into an inner-arc surface and an outer-arc surface. The midpoint of the in-plane arc divides the in-plane arc into two parts. The part intersecting with the first middle plane is the in-plane first arc, and the part intersecting with the second middle plane is the in-plane second arc. A face center point is determined within the inner-arc surface. The distance from the face center point to the first middle plane and the second middle plane is equal, and the distance from the face center point to the center of the circle is not less than 0.2 times the radius R and not greater than 0.75 times the radius R; Along the reference direction, on the inner-arc surface, a line segment is drawn from the face center point to the first middle plane by rotating the perpendicular line from the face center point to the first middle plane clockwise by the arc inner angle θ, which is the inner-arc first line, where 0° ≤ θ ≤ 32.5°. The distance from the intersection point of the inner-arc first line and the first middle plane to the center of the circle is L1, and 0.1L1 ≤ R ≤ 0.7L1; Along the reference direction, on the inner-arc surface, a line segment is drawn from the face center point to the second middle plane by rotating the perpendicular line from the face center point to the second middle plane counterclockwise by the arc inner angle, which is the inner-arc second line. The distance from the intersection point of the inner-arc second line and the second middle plane to the center of the circle is equal to the distance L1 from the intersection point of the inner-arc first line and the first middle plane to the center of the circle; along the reference direction, on the inner-arc surface, the counterclockwise rotation angle of the perpendicular line from the face center point to the second middle plane is equal to θ; A perpendicular line to the in-plane arc is drawn from the face center point, and the intersection point with the in-plane arc is the arc midpoint, and this perpendicular line is the inner-arc third line; Rotate the external arc angle clockwise along the reference direction on the outer surface of the arc with respect to the perpendicular line from the midpoint of the arc to the top surface of the parallelepiped target plate Draw a line segment connecting from the midpoint of the arc to the top surface of the parallelepiped target plate, which is a line outside the arc, where On the outer surface of the arc along the reference direction, a line segment is made by rotating the outer arc angle counterclockwise from the perpendicular line from the midpoint of the arc to the right side of the parallelepiped target plate, and it is connected from the midpoint of the arc to the right side of the parallelepiped target plate, which is the second line outside the arc. Along the reference direction, on the outer surface of the arc, the outer arc angle rotated counterclockwise from the perpendicular line from the midpoint of the arc to the right side of the parallelepiped target plate is equal to The first sub-target plate is divided into 6 hexahedrons with specific shapes by the in-plane arc, the inner-arc first line, the inner-arc second line, the inner-arc third line, the outer-arc first line, and the outer-arc second line along the reference direction; The pre-partition plane is divided into 6 sub-planes by the in-plane arc, the inner-arc first line, the inner-arc second line, the inner-arc third line, the outer-arc first line, and the outer-arc second line along the reference direction. Among these sub-planes, the one with the inner-arc first line and the inner-arc second line as sides is the first sub-plane, the one with the inner-arc first line and the inner-arc third line as sides is the second sub-plane, the one with the inner-arc second line and the inner-arc third line as sides is the third sub-plane, the one with the in-plane arc and the outer-arc second line as sides is the fourth sub-plane, the one with the outer-arc first line and the outer-arc second line as sides is the fifth sub-plane, and the one with the in-plane arc and the outer-arc first line as sides is the sixth sub-plane; The hexahedron with a specific shape that coincides with the first sub-face along the reference direction is the first hexahedron, and the first sub-face is the front face of the first hexahedron; the hexahedron with a specific shape that coincides with the second sub-face along the reference direction is the second hexahedron, and the second sub-face is the front face of the second hexahedron; the hexahedron with a specific shape that coincides with the third sub-face along the reference direction is the third hexahedron, and the third sub-face is the front face of the third hexahedron; the hexahedron with a specific shape that coincides with the fourth sub-face along the reference direction is the fourth hexahedron, and the fourth sub-face is the front face of the fourth hexahedron; the hexahedron with a specific shape that coincides with the fifth sub-face along the reference direction is the fifth hexahedron, and the fifth sub-face is the front face of the fifth hexahedron; the hexahedron with a specific shape that coincides with the sixth sub-face along the reference direction is the sixth hexahedron, and the sixth sub-face is the front face of the sixth hexahedron.

3. A method for rapidly and automatically generating a finite element mesh of a parallelepiped target plate according to claim 2, characterized in that: In step S2, determine the number of grids on a set of opposite sides on the front face of the 6 specific-shaped hexahedrons and determine the corresponding edge node coordinates, as follows: Set the edge node ratio matrix G(m,q), where m represents the number of meshes set on the edges of a hexahedron with a specific shape, q represents the ratio of the distances between two adjacent nodes, and q is a positive number. i represents the node number, and the value of the i-th element G(m,q) i is as follows: In the first sub-face, the length of the opposite side of the first line inside the arc is equal to L1, the number of grids is determined to be n1, and the upper edge node coordinates of the opposite side of the first line inside the arc are composed of the node abscissa matrix x1 and the node ordinate matrix y1, respectively, as follows: The upper edge node coordinates of the first line inside the arc are composed of the node abscissa matrix x2 and the node ordinate matrix y2, respectively, as follows: Among them, represents a 1*(n1 + 1) all-1 matrix; In the second sub-face, the upper edge node coordinates of the first arc inside the face are composed of the node abscissa matrix x3 and the node ordinate matrix y3, respectively, as follows: In the third sub-face, the length of the opposite side of the second line inside the arc is equal to L1, the number of grids is determined to be n2, and the upper edge node coordinates of the opposite side of the second line inside the arc are composed of the node abscissa matrix x4 and the node ordinate matrix y4, respectively, as follows: Among them, represents a all-ones matrix of 1*(n2+1); The upper edge node coordinates of the second arc inside the face are composed of the node abscissa matrix x5 and the node ordinate matrix y5, respectively, as follows: In the fourth sub-face, the upper edge node coordinates of the opposite side of the second arc inside the face are composed of the node abscissa matrix x6 and the node ordinate matrix y6, respectively, as follows: In the fifth sub-face, the number of grids on the first line outside the arc is determined to be n3, and the upper edge node coordinates of the first line outside the arc are composed of the node abscissa matrix x7 and the node ordinate matrix y7, respectively, as follows: Among them, represents a all-ones matrix of 1*(n3 + 1); The upper edge node coordinates of the opposite side of the first line outside the arc are composed of the node abscissa matrix x8 and the node ordinate matrix y8, respectively, as follows: In the sixth sub-face, the upper edge node coordinates of the opposite side of the first arc inside the face are composed of the node abscissa matrix x9 and the node ordinate matrix y9, respectively, as follows: The number of grids on the edges of each specific-shaped hexahedron and the corresponding edge node coordinates have been determined.

4. A method for rapidly and automatically generating a finite element mesh of a parallelepiped target plate according to claim 3, characterized in that: In step S3, mirror and supplement the edge node coordinates of a set of opposite sides on the front face of the 6 specific-shaped hexahedrons to obtain the edge node coordinates of the front face of the parallelepiped target plate, as follows: A set of opposite sides on each sub-surface is given a node abscissa matrix and a node ordinate matrix. Among any set of opposite sides: for any one side, the node abscissa matrix is the first-order abscissa matrix x s , and the node ordinate matrix is the first-order ordinate matrix y s ; for the other side, the node abscissa matrix is the second-order abscissa matrix x t , and the node ordinate matrix is the second-order ordinate matrix y t ; The primary horizontal matrix, primary vertical matrix, secondary horizontal matrix, and secondary vertical matrix are concatenated in sequence from top to bottom to form a primary node matrix coor with 4 rows and the number of nodes on the side as the number of columns (1) : coor (1) = [x s T y s T x t T y t T T (11)​ Among them, the superscript T is the matrix transpose symbol; Mirror supplement the edge node coordinates of the 6 sub-faces to obtain the mirror-supplemented node coordinates of each sub-face. Take the edge node coordinates of the 6 sub-faces with the primary mid-plane as the symmetry plane, and mirror the primary node matrix to obtain the secondary node matrix coor (2) ; In the primary node matrix coor (1) exchange the positions of x s and x t , and exchange the positions of y s and y t to obtain the new primary node matrix coor (1.5) . Take the edge node coordinates of the 6 sub-faces with the intersection line of the primary mid-plane and the secondary mid-plane as the axis of symmetry, and mirror the new primary node matrix to obtain the tertiary node matrix coor (3) ; Take the edge node coordinates of the 6 sub-faces with the secondary mid-plane as the symmetry plane, and mirror the new primary node matrix to obtain the quaternary node matrix coor (4) ; So far, the edge node coordinates of the front face of the parallelepiped target plate have been obtained.

5. A method for quickly and automatically generating a finite element mesh of a parallelepiped target plate according to claim 4, characterized in that: In step S4, expand the edge node coordinates of the front face of the parallelepiped target plate to the face node coordinates of the front face of the parallelepiped target plate, and supplement the node value matrix of the plane parallelepiped target plate along the reference direction, as follows: Step S4-1: The abscissa matrix X' and the ordinate matrix Y' of the face node coordinates on the front of the parallelepiped target plate are calculated from the first-order node matrix of each sub-face, its mirror-supplemented node coordinates, and the boundary point ratio matrix, as shown in the following formula: For the first sub-face, the subscript s of the horizontal matrix is 1, the subscript t of the vertical matrix is 2, and the first grid variable n = n2; For the second sub-face, the subscript s of the horizontal matrix is 2, the subscript t of the vertical matrix is 3, n = n4, where n4 is the number of grids determined on the three lines inside the arc; For the third sub-face, the subscript s of the horizontal matrix is 4, the subscript t of the vertical matrix is 5, n = n4; For the fourth sub-face, the subscript s of the horizontal matrix is 5, the subscript t of the vertical matrix is 6, n = n5, where n5 is the number of grids determined on the two lines outside the arc; For the fifth sub-face, the subscript s of the horizontal matrix is 7, the subscript t of the vertical matrix is 8, n = n5; For the sixth sub-face, the subscript s of the horizontal matrix is 3, the subscript t of the vertical matrix is 9, n = n3; Go to step S4-2; Step S4-2: Determine that the number of grids on the side of the plane parallelepiped target plate along the reference direction is n6, then the node value matrix Z' of the node coordinates along the reference direction is: Among them, represents a all-ones matrix of 1*(n6+1).

6. A method for rapidly and automatically generating a finite element mesh of a parallelepiped target plate according to claim 5, characterized in that: In step S5, by setting a matrix arrangement function, from the face node coordinates on the front of the parallelepiped target plate and the edge node coordinates of the plane parallelepiped target plate along the reference direction, according to the orientation of the parallelepiped target plate, the body node coordinates of the structured grid of the parallelepiped target plate are obtained, and then the structured finite element grid of the parallelepiped target plate is obtained, specifically as follows: Step S5-1: Set three matrix arrangement functions: The first matrix arrangement function Re(A) represents a matrix with a column number of 1 formed by splicing the elements with column numbers greater than 1 in matrix A below the first column element in ascending order of column numbers; The second matrix arrangement function De(A, p) represents a matrix formed by repeating each element in matrix A p times and placing them below the element in turn; The third matrix arrangement function Dm(A, p) represents a matrix formed by repeating matrix A as a whole p times and placing them below matrix A in turn; Go to step 5-2; Step S5-2: Determine the orientation of the parallelepiped target plate in the X-Y-Z coordinate system. If it is the positive X-axis direction, then: The matrix of all body node coordinates (X″, Y″, Z″) of the first hexahedron, the second hexahedron, and the sixth hexahedron is: For the first hexahedron, the second grid variable b1 = n2; For the second hexahedron, b1 = n4; For the sixth hexahedron, b1 = n3; The matrix of all body node coordinates of the third hexahedron, the fourth hexahedron, and the fifth hexahedron is: For the third hexahedron, the third grid variable b2 = n2, and the fourth grid variable b3 = n4; For the fourth hexahedron, b2 = n2, b3 = n5; For the fifth hexahedron, b2 = n3, b3 = n5; If it is the positive Y-axis direction, then: The matrix of all body node coordinates of the first hexahedron, the second hexahedron, and the sixth hexahedron is: For the first hexahedron, the fifth grid variable b4 = n2; For the second hexahedron, b4 = n4; For the sixth hexahedron, b4 = n3; The matrix of all body node coordinates of the third hexahedron, the fourth hexahedron, and the fifth hexahedron is: For the third hexahedron, the fifth grid variable b5 = n2, and the sixth grid variable b6 = n4; For the fourth hexahedron, b5 = n2, b6 = n5; For the fifth hexahedron, b5 = n3, b6 = n5; If it is in the positive Z-axis direction, then: The full body node coordinate matrices of the first, second, and sixth hexahedrons are: For the first hexahedron, the seventh grid variable b7 = n2; For the second hexahedron, b7 = n4; For the sixth hexahedron, b7 = n3; The full body node coordinate matrices of the third, fourth, and fifth hexahedrons are: For the third hexahedron, the eighth grid variable b8 = n2, and the ninth grid variable b9 = n4; For the fourth hexahedron, b8 = n2, b9 = n5; For the fifth hexahedron, b8 = n3, b9 = n5; Go to step S5-3; Step S5-3: Obtain the structured grid node coordinate distribution matrix S: S = [X″ Y″ Z″] (20) Go to step S5-4; Step S5-4: According to the quadratic node matrix, cubic node matrix, and quartic node matrix, repeat step S5-2 once respectively, and correspondingly obtain the quadratic structured grid node coordinate distribution matrix, cubic structured grid node coordinate distribution matrix, and quartic structured grid node coordinate distribution matrix, then go to step S5-5; Step S5-5: Stack the obtained structured grid node coordinate distribution matrix, quadratic structured grid node coordinate distribution matrix, cubic structured grid node coordinate distribution matrix, and quartic structured grid node coordinate distribution matrix together from top to bottom, and the structured finite element grid of the parallelepiped target plate can be obtained.

7. A method for quickly and automatically generating a finite element mesh of a parallelepiped target plate according to claim 6, characterized in that: In step S6, sort and organize the body node coordinates of the structured finite element grid of the parallelepiped target plate to obtain the unstructured grid of the parallelepiped target plate, specifically as follows: The structured grid node coordinate distribution matrix, quadratic structured grid node coordinate distribution matrix, cubic structured grid node coordinate distribution matrix, and quartic structured grid node coordinate distribution matrix contain the body node coordinates of all the structured finite element grids of the parallelepiped target plate. The above four matrices have the same number of rows, which is the number of rows of the structured grid matrix; Establish a three-dimensional serial number matrix B0, and use B0(u, v, w) to represent the element in the u-th row, v-th column, and w-th layer of the three-dimensional serial number matrix B0; Judge the orientation of the parallelepiped target plate. If it is in the positive X-axis direction, then: B0(u, v, w) = u + f2(v - 1) + f2f1(w - 1) + h, u ∈ [1, f2], v ∈ [1, f1], w ∈ [1, f3] (21) Subsequently, exchange the first and second dimensions of the three-dimensional serial number matrix; If it is in the positive Y-axis direction, then: B0(u, v, w) = u + f1(v - 1) + f1f3(w - 1) + h, u ∈ [1, f1], v ∈ [1, f3], w ∈ [1, f2] (22) Subsequently, exchange the second and third dimensions of the three-dimensional serial number matrix; If it is in the positive Z-axis direction, then: B0(u, v, w) = u + f3(v - 1) + f2f3(w - 1) + h, u ∈ [1, f3], v ∈ [1, f2], w ∈ [1, f1] (23) Subsequently, swap the first and third dimensions of the three-dimensional serial number matrix; where the value of h is 0; for the first hexahedron, the first-order quantity f1 = n2, the second-order quantity f2 = n1, and the third-order quantity f3 = n6; for the second hexahedron, f1 = n4, f2 = n1, f3 = n6; for the third hexahedron, f1 = n2, f2 = n4, f3 = n6; for the fourth hexahedron, f1 = n2, f2 = n5, f3 = n6; for the fifth hexahedron, f1 = n3, f2 = n5, f3 = n6; for the sixth hexahedron, f1 = n3, f2 = n1, f3 = n6; go to step S6-2; Step S6-2: Obtain the three-dimensional serial number processing matrix B1; go to step S6-3; Step S6-3: Remove all elements corresponding to the maximum number of rows, columns, and layers from the three-dimensional serial number processing matrix B1 to obtain the three-dimensional serial number unstructured matrix B'. Arrange the three-dimensional serial number unstructured matrix B' in ascending order as a single-row matrix according to the order of the row serial number first, then the column serial number, and finally the layer serial number to obtain the unstructured row matrix C; go to step S6-4; Step S6-4: Obtain the unstructured grid information matrix D through the unstructured row matrix C. Each unstructured finite element grid information formed by structured finite element grid nodes is represented in the unstructured grid information matrix D. Determine the orientation of the parallelepiped target plate. If it is the positive X-axis direction, then: If it is the positive Y-axis direction, then: If it is the positive Z-axis direction, then: Go to step S6-5; Step S6-5: Construct a column of elements on the left side of the unstructured grid information matrix D. The value of each element is the row serial number of the row where it is located. The new matrix formed is the unstructured finite element grid node coordinate distribution matrix E2. Go to step S6-6; Step S6-6: Supplement a column of elements on the left side of the structured grid node coordinate distribution matrix, which is the row serial number of the element in the matrix where it is located, to obtain the unstructured finite element grid node coordinate distribution matrix E1. Arrange the unstructured finite element grid distribution matrix E2 below the unstructured finite element grid node coordinate distribution matrix E1 to obtain the unstructured finite element grid; Change the value of h to the number of rows of the structured grid matrix. Repeat steps S6-1 to S6-4 once to obtain the secondary unstructured finite element grid node coordinate distribution matrix E4. Supplement a column of elements on the left side of the secondary structured grid node coordinate distribution matrix, which is the row serial number of the element in the matrix where it is located plus the number of rows of the structured grid matrix, to obtain the secondary unstructured finite element grid node coordinate distribution matrix E3. Arrange the secondary unstructured finite element grid distribution matrix E4 below the secondary unstructured finite element grid node coordinate distribution matrix E3 to obtain the secondary unstructured finite element grid; Change the value of h to twice the number of rows of the structured grid matrix, and repeat steps S6-1 to S6-4 once to obtain the non-structured finite element grid node coordinate distribution matrix E6 of the third order. Supplement a column of elements on the left side of the third-order structured grid node coordinate distribution matrix, where the element is the row number in the matrix plus the number of rows of the structured grid matrix, to obtain the non-structured finite element grid node coordinate distribution matrix E5 of the third order. Arrange the non-structured finite element grid distribution matrix E6 of the third order below the non-structured finite element grid node coordinate distribution matrix E5 of the third order to obtain the non-structured finite element grid of the third order. Change the value of h to three times the number of rows of the structured grid matrix, and repeat steps S6-1 to S6-4 once; obtain the non-structured finite element grid node coordinate distribution matrix E8 of the fourth order. Supplement a column of elements on the left side of the fourth-order structured grid node coordinate distribution matrix, where the element is the row number in the matrix plus the number of rows of the structured grid matrix, to obtain the non-structured finite element grid node coordinate distribution matrix E7 of the fourth order. Arrange the non-structured finite element grid distribution matrix E8 of the fourth order below the non-structured finite element grid node coordinate distribution matrix E7 of the fourth order to obtain the non-structured finite element grid of the fourth order, and then go to step S6-7. Step S6-7: Place the non-structured finite element grid, the second-order non-structured finite element grid, the third-order non-structured finite element grid, and the fourth-order non-structured finite element grid in a text file in sequence to obtain the non-structured finite element grid of the parallelepiped target plate.

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