CN115329635A

CN115329635A - Rapid and automatic generation method for finite element grid of parallelepiped target plate

Info

Publication number: CN115329635A
Application number: CN202210981136.XA
Authority: CN
Inventors: 郭锐; 陈佑明; 俞旸晖; 杨贵涛
Original assignee: Nanjing University of Science and Technology
Current assignee: Nanjing University of Science and Technology
Priority date: 2022-08-16
Filing date: 2022-08-16
Publication date: 2022-11-11

Abstract

The invention discloses a method for quickly and automatically generating finite element grids of a parallelepiped target plate, which comprises the steps of firstly determining geometric parameters of the parallelepiped target plate, including thickness, height, width, orientation, offset distance and inclination angle, dividing the parallelepiped target plate into hexahedrons with specific shapes, then determining the grid number of edges of each hexahedron with specific shapes and determining corresponding node coordinates, then carrying out mirror image supplement on the node coordinates, then expanding the node coordinates to the node coordinates of the parallelepiped target plate, outputting the node coordinates to structured finite element grids, finally sequencing and sorting the node coordinates of the structured grids, outputting the node coordinates to unstructured finite element grids, carrying out calculation and use such as penetration, loading, contact and the like, needing no existing finite element grid generation software, obviously reducing the workload of related technicians, and improving the calculation efficiency.

Description

Rapid and automatic generation method for finite element grid of parallelepiped target plate

Technical Field

The invention belongs to the technical field of finite element numerical simulation, and particularly relates to a method for quickly and automatically generating a finite element grid of a parallelepiped target plate.

Background

The parallelepiped target plate is a very common damage target for penetration, explosion and collision simulation calculation, and the finite element simulation calculation programs commonly used in the military industry are mainly AUTODYN and LS-DYNA, wherein the finite element simulation calculation programs are mainly calculated on the basis of a structured finite element grid, the finite element simulation calculation programs are calculated on the basis of an unstructured finite element grid, the node ordering of the structured finite element grid has a specific format, the connection between the nodes does not need to be additionally indicated, the node ordering of the unstructured finite element grid is random, and the nodes forming the grid and the sequence thereof need to be additionally indicated. For some academic research or engineering projects taking a parallelepiped target plate as a damaged target, working conditions based on calculating the parallelepiped target plate with different thicknesses, heights, widths, inclination angles, orientations and offset distances are often faced, under the conditions, finite element mesh generation software such as HYPERMESH, ICEM which draws meshes through a GUI needs to continuously draw different parallelepiped target plates, and through a series of steps such as modeling, importing, drawing, exporting and importing again, finite element mesh generation software such as truegarid which is a programmable modeling drawing mesh needs to continuously calculate a target plate normal vector generated due to the inclination angle, so that the working efficiency is low, time and labor are consumed, the workload of related technicians is increased, and in order to solve the problems, a method for quickly and automatically generating the finite element mesh of the parallelepiped target plate which can simultaneously generate a structured finite element mesh suitable for an AUTODYN program LS and an unstructured finite element mesh suitable for an DYNA program is provided.

Disclosure of Invention

The invention aims to solve the problems of repeated generation process, low calculation efficiency and large workload of the finite element grid of the parallelepiped target plate under the condition of numerous working conditions, and provides a rapid automatic generation method of the finite element grid of the parallelepiped target plate, which has simple and convenient flow and is easy to popularize to other structures.

The technical solution for realizing the purpose of the invention is as follows: a method for quickly and automatically generating a finite element grid of a parallelepiped target plate comprises the following steps:

step S1, determining geometric parameters of the parallelepiped target plate, including thickness, height, width, orientation, offset distance and inclination angle, dividing the parallelepiped target plate into 4 sub-target plates along a reference direction, sequentially including a first sub-target plate, a second sub-target plate, a third sub-target plate and a fourth sub-target plate, dividing the first sub-target plate into 6 hexahedrons with specific shapes along the reference direction, and turning to step S2.

And S2, determining the number of grids of a group of opposite sides on the front surfaces of the 6 hexahedrons with specific shapes, determining corresponding edge node coordinates, and turning to the step S3.

And S3, performing mirror image supplement on the edge node coordinates of a group of opposite sides on the front surfaces of the 6 hexahedrons with specific shapes to obtain the edge node coordinates of the front surface of the parallelepipedal target plate, and turning to the step S4.

And S4, expanding the edge node coordinates of the front surface of the target plate to the surface node coordinates of the front surface of the target plate, supplementing the edge node coordinates of the planar hexahedral target plate along the reference direction, and turning to the step S5.

And S5, setting a matrix sorting function, obtaining body node coordinates of the structured grid of the parallelepiped target plate according to the orientation of the parallelepiped target plate by using the face node coordinates of the front face of the parallelepiped target plate and the edge node coordinates of the planar hexahedron target plate along the reference direction, further obtaining the structured finite element grid of the parallelepiped target plate, and turning to the step S6.

And S6, obtaining an unstructured grid matrix by setting the three-dimensional sequence number matrix, and sequencing and sorting the body node coordinates of the structured finite element grids of the parallelepiped target plate to obtain the unstructured finite element grids of the parallelepiped target plate.

Compared with the prior art, the invention has the remarkable advantages that: the invention can generate the finite element mesh without using commercial modeling software and finite element mesh drawing software, and input the geometric parameters of the target plate, such as the height, the width, the thickness, the inclination angle, the orientation and the deviation position of the target plate, and determine the number of meshes of each side, and the internal mesh can be further adjusted by the geometric parameters of the hexahedron with a specific shape, thereby not only generating the structured finite element mesh suitable for the AUTODYN program, but also generating the unstructured finite element mesh suitable for the LS-DYNA program, and the nodes of the unstructured finite element mesh and the node combination source generating each mesh are directly based on the structured finite element mesh, thereby greatly improving the efficiency of simultaneously generating the two meshes, combining the advantages of matrix calculation, compared with the finite element mesh generating software of HYPERMESH, ICEM drawing meshes through GUI drawing meshes, the invention does not need to continuously draw different hexahedron target plates, and does not need to pass through a series of steps of modeling, drawing, exporting, reintroducing and the like, compared with the finite element mesh generating software of the programmable drawing meshes, the invention does not need to artificially calculate normal vector vectors of the target plate, and the time of generating millions of mesh, and only needs to be clear and the working efficiency is reduced, thereby the whole working difficulty of the personnel is reduced.

Drawings

FIG. 1 is a flow chart of the present invention.

FIG. 2 is a block diagram of a target plate of the present invention.

FIG. 3 is a schematic view of each line segment of the target plate of the present invention.

FIG. 4 is a schematic view of the geometric parameters of the target plate of the present invention.

FIG. 5 is a schematic diagram of the parameters of the target plate grid of the present invention.

FIG. 6 is a diagram illustrating an embodiment of the present invention.

Detailed Description

The present invention is described in further detail below with reference to the attached drawing figures.

With reference to fig. 1 to 6, a method for rapidly and automatically generating a finite element mesh of a parallelepiped target plate comprises the following steps:

step S1, determining geometric parameters of the parallelepiped target plate, including thickness, height, width, orientation, offset distance and inclination angle, dividing the parallelepiped target plate into 4 sub-target plates along a reference direction, sequentially including a first sub-target plate, a second sub-target plate, a third sub-target plate and a fourth sub-target plate, and dividing the first sub-target plate into 6 hexahedrons with specific shapes along the reference direction, wherein the specific parameters are as follows:

the direction of the projectile, the shock wave and other attacking objects is taken as a reference direction, the surface of the parallelepiped target plate, which bears the projectile, the shock wave and other attacking objects, is taken as the front surface of the target plate, the back surface of the parallelepiped target plate is taken as the back surface of the target plate, and the rest four surfaces are respectively 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.

The distance between the front surface and the back surface of the target plate is the thickness L of the parallelepipedic target plate ₄ . Distance 2*L between target plate top surface and target plate bottom surface ₂ ，L ₂ Half 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*L ₃ ，L ₃ Half 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 more 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 an offset distance L ₅ . The line surface angle between the parallelepiped target plate and the reference direction is the inclination angle alpha of the parallelepiped target plate, and the inclination angle alpha is not less than 30 degrees and not more than 90 degrees.

All points with equal distance between the top surface of the target plate and the bottom surface of the target plate form a primary middle surface of the parallelepipedal target plate. All points with equal distance to the left side surface of the target plate and the right side surface of the target plate form a secondary middle surface of the parallelepiped target plate.

Divide into four sub-target boards by the secondary well face in the reference direction with the parallelepiped target board once, the sub-target board of synchronous contact target board top surface and target board right flank is a sub-target board, begins to define other sub-target boards as second sub-target board, third sub-target board and fourth sub-target board according to clockwise from a sub-target board along equivalent thickness direction.

And defining a projection surface of a surface of the first target plate, which is coincident with the front surface of the target plate, along the reference direction as a pre-division surface, and defining a projection surface of the front surface of the target plate along the reference direction as a projection front surface of the target plate. The pre-dividing surface is just the part surrounded by the primary middle surface, the secondary middle surface, the top surface of the target plate and the right side surface of the target plate in the front surface of the target plate.

With a pre-divided surface,Drawing a 1/4 circular arc with radius R in the pre-divided plane, called inner arc of plane, 0.1L, with the intersection point of the primary middle plane and the secondary middle plane as the center of circle ₂ ≤R≤0.7L ₂ And 0.1L ₃ ≤R≤0.7L ₃ 。

The inner arc of the surface divides the pre-divided surface into an inner arc surface and an outer arc surface, the middle point of the inner arc of the surface divides the inner arc of the surface into two parts, the inner arc of the surface intersects with the primary middle surface to form an inner arc, the inner arc of the surface intersects with the secondary middle surface to form an inner arc, a center point of the surface is determined in the inner arc surface, the distance from the center point of the surface to the primary middle surface and the secondary middle surface is equal, and the distance from the center point of the surface to the center point of the circle is not less than 0.2 times of the radius R and not more than 0.75 times of the radius R.

Rotating an arc inner angle theta clockwise along a reference direction on the arc inner surface and a perpendicular line from the face center point to the primary middle surface to form a line segment, connecting the line segment from the face center point to the primary middle surface, wherein the angle segment is more than or equal to 0 degree and less than or equal to 32.5 degrees, and the distance L from the intersection point of the line segment and the primary middle surface to the center of the circle ₁ ，0.1L ₁ ≤R≤0.7L ₁ 。

Rotating an arc inner angle along a reference direction in a counterclockwise direction with a perpendicular line from a face center point to a secondary middle plane to form a line segment, connecting the line segment from the face center point to the secondary middle plane, namely two lines in the arc, wherein the distance from the intersection point of the two lines in the arc and the secondary middle plane to the circle center is equal to the distance L from the intersection point of the one line in the arc and the primary middle plane to the circle center ₁ . The arc inner face is rotated counterclockwise along the reference direction by an inner angle equal to theta from the center point of the face to the perpendicular line of the secondary midplane.

The vertical line of the inner arc of the surface is made from the center point of the surface and intersects with the inner arc of the surface at the middle point of the arc, and the vertical line is the three lines in the arc.

Rotating the outer corner of the arc clockwise along the reference direction from the arc outer face and the perpendicular from the arc midpoint to the top surface of the parallelepiped target plate

A line segment is connected from the middle point of the arc to the top surface of the parallelepiped target plate and is a line outside the arc, wherein,

making a line segment along the reference direction on the outer surface of the arc along the arc outer surface counterclockwise rotation arc outer angle from the arc center point to the right side surface of the parallelepiped target plate, connecting the line segment to the right side surface of the parallelepiped target plate from the arc center point, being an outer arc line, along the reference direction on the outer surface of the arc along the reference direction counterclockwise rotation arc outer angle from the arc center point to the right side surface of the parallelepiped target plate equal to

A first horn target plate is divided into 6 hexahedrons with specific shapes along the reference direction by an inner arc of a surface, an inner line of an arc, an inner two line of the arc, an inner three line of the arc, an outer line of the arc and an outer two line of the arc.

The pre-divided surface is divided into 6 sub-surfaces by an inner arc, an inner arc line, a third arc line, an outer arc line and an outer arc line along a reference direction, wherein the sub-surfaces comprise a first sub-surface with the inner arc line and the inner arc line as edges, a second sub-surface with the inner arc line and the inner arc line as edges, a third sub-surface with the inner arc line and the inner arc line as edges, a fourth sub-surface with the inner arc line and the outer arc line as edges, a fifth sub-surface with the outer arc line and the outer arc line as edges, and a sixth sub-surface with the inner arc line and the outer arc line as edges.

The specific-shaped hexahedron coinciding with a horn face in the reference direction is a horn, and a horn face is the front face of the horn. The hexahedron with the specific shape coinciding with the second hexahedron along the reference direction is the second hexahedron, and the second hexahedron is the front face of the second hexahedron. The hexahedron with the specific shape coinciding with the third hexahedron along the reference direction is the third hexahedron, and the third hexahedron is the front face of the third hexahedron. The hexahedron of the specific shape coinciding with the fourth sub-surface in the reference direction is a fourth hexahedron, and the fourth sub-surface is the front surface of the fourth hexahedron. The specific-shaped hexahedron coinciding with the five-sided surface in the reference direction is a five-sided hexahedron, and the five-sided surface is the front surface of the five-sided hexahedron. The hexahedron of the specific shape coinciding with the six-size surface in the reference direction is the six-size hexahedron, and the six-size surface is the front surface of the six-size hexahedron.

S2, determining the number of grids of a group of opposite sides on the front faces of the 6 hexahedrons with the specific shapes and determining corresponding edge node coordinates, wherein the specific steps are as follows:

setting an edge node proportion matrix G (m, q), wherein m represents the number of grids set on a hexahedron edge with a specific shape, q represents the ratio of the distance between two adjacent nodes, q is a positive number, i represents a node serial number, and the ith element value G (m, q) _i Comprises the following steps:

in the first plane, the length of the opposite side of a line in the arc is equal to L ₁ The number of grids is determined as n ₁ The coordinates of the upper edge nodes of the opposite edges of a line in the arc are represented by a node abscissa matrix x ₁ And a node ordinate matrix y ₁ The structure is as follows:

the coordinates of the upper nodes on the line in the arc are represented by a node abscissa matrix x ₂ And a node ordinate matrix y ₂ The structure is as follows:

wherein the content of the first and second substances,

denotes 1 (n) ₁ + 1) of all 1 matrices.

In the second sub-plane, the node coordinates on the upper edge of the first arc in the plane are represented by a node abscissa matrix x ₃ And a node ordinate matrix y ₃ The structure is as follows:

in the third sub-surface, the length of the opposite side of the two lines in the arc is equal to L ₁ The number of grids is determined as n ₂ The coordinates of the nodes on the opposite sides and the upper sides of two lines in the arc are represented by a node abscissa matrix x ₄ And a node ordinate matrix y ₄ The structure is as follows:

wherein the content of the first and second substances,

denotes 1 (n) ₂ + 1) of all 1 matrices.

The node coordinate on the two arcs in the plane is represented by a node abscissa matrix x ₅ And a node ordinate matrix y ₅ The structure is as follows:

in the fourth sub-surface, the node coordinates on the opposite sides and the upper sides of the two arcs in the surface are represented by a node abscissa matrix x ₆ And a node ordinate matrix y ₆ The structure is as follows:

in the fifth sub-plane, the number of grids on the first line outside the arc is determined as n ₃ The coordinates of the upper node on the outer line of the arc are represented by a node abscissa matrix x ₇ And a node ordinate matrix y ₇ The structure is as follows:

wherein the content of the first and second substances,

denotes 1 (n) ₃ + 1) of all 1 matrices.

The coordinates of the nodes on the opposite side and the upper side of one line outside the arc are represented by a node abscissa matrix x ₈ And a node ordinate matrix y ₈ The structure is as follows:

in the six sub-surfaces, the coordinates of the nodes on the opposite sides and the upper sides of an arc in the surface are represented by a node abscissa matrix x ₉ And a node ordinate matrix y ₉ The structure is as follows:

the grid number of each hexahedral edge with a specific shape and the corresponding edge node coordinates are determined.

S3, performing mirror image supplement on the edge node coordinates of a group of opposite sides on the front surfaces of the 6 hexahedrons with specific shapes to obtain the edge node coordinates of the front surface of the parallelepipedal target plate, wherein the mirror image supplement is specifically as follows:

each sub-surface has a set of opposite edges assigned with a node abscissa matrix and a node ordinate matrix, and any pair of opposite edges: the node abscissa matrix of any one edge is a primary abscissa matrix x _s The node ordinate matrix is a primary ordinate matrix y _s . The node abscissa matrix of the other edge is a quadratic abscissa matrix x _t The node ordinate matrix is a quadratic ordinate matrix y _t 。

The primary transverse matrix, the primary longitudinal matrix, the secondary transverse matrix and the secondary longitudinal matrix are spliced into a primary node matrix color with 4 rows and 4 columns as edge nodes from top to bottom in sequence ⁽¹⁾ ：

coor ⁽¹⁾ ＝[x _s ^T y _s ^T x _t ^T y _t ^T ] ^T (11)

Wherein, the superscript T is a matrix transposition symbol.

For the edge sections of 6 sub-surfacesPerforming mirror image supplement on the point coordinates to obtain mirror image supplement node coordinates of each sub-surface, taking the edge node coordinates of 6 sub-surfaces as a symmetrical surface by taking a primary middle surface as a symmetrical surface, and mirroring the primary node matrix to obtain a secondary node matrix color ⁽²⁾ . At a primary node matrix coor ⁽¹⁾ Middle exchange x _s And x _t Position, and exchange y _s And y _t Position to obtain a new primary node matrix coor ^(1.5) Taking the edge node coordinates of the 6 sub-surfaces as a symmetry axis by taking the intersection line of the primary middle surface and the secondary middle surface, and mirroring the new primary node matrix to obtain a tertiary node matrix coor ⁽³⁾ . Taking the edge node coordinates of 6 sub-surfaces as a symmetry plane by taking the secondary middle surface as a mirror image of the new primary node matrix to obtain a quartic node matrix cor ⁽⁴⁾ . So far, the edge node coordinates of the front surface of the parallelepiped target plate are obtained.

S4, expanding the edge node coordinates of the front surface of the target plate to the surface node coordinates of the front surface of the target plate, and supplementing the edge node coordinates of the planar hexahedral target plate along the reference direction, wherein the method specifically comprises the following steps:

s4-1, calculating an abscissa matrix X 'of a surface node coordinate of the front surface of the parallelepiped target plate and an ordinate matrix Y' of the surface node coordinate from primary node matrixes of each sub-surface, mirror image supplementary node coordinates of the primary node matrixes and boundary point proportional matrixes, and obtaining the following formula:

for a number one sub-surface, the horizontal matrix subscript s =1, the vertical matrix subscript t =2, and the first grid variable n = n ₂ 。

For the sub-surface two, the horizontal matrix subscript s =2, the vertical matrix subscript t =3,n = n ₄ ，n ₄ The number of grids determined on the three lines in the arc.

For the three sub-planes, the horizontal matrix subscript s =4, the vertical matrix subscript t =5,n = n ₄ 。

For the four sub-planes, the horizontal matrix subscript s =5, the vertical matrix subscript t =6,n = n ₅ ，n ₅ The number of grids determined on the two lines outside the arc.

For the five sub-planes, the horizontal matrix subscript s =7, the vertical matrix subscript t =8, n = n ₅ 。

For the six sub-planes, the horizontal matrix subscript s =3, the vertical matrix subscript t =9,n = n ₃ . Proceed to step S4-2.

S4-2, determining the number of grids to be n on the edge of the plane hexahedral target plate along the reference direction ₆ Then, the node value matrix Z' of each node coordinate along the reference direction is:

wherein, the first and the second end of the pipe are connected with each other,

denotes 1 (n) ₆ + 1) of all 1 matrices.

S5, by setting a matrix sorting function, obtaining body node coordinates of the structured grid of the parallelepiped target plate according to the orientation of the parallelepiped target plate by using the face node coordinates of the front face of the parallelepiped target plate and the edge node coordinates of the plane hexahedron target plate along the reference direction, and further obtaining the structured finite element grid of the parallelepiped target plate, wherein the matrix sorting function is specifically as follows:

s5-1, setting three matrix sorting functions:

the first matrix sorting function Re (a) represents a matrix with 1 column number formed by splicing elements with column ordinal numbers larger than 1 in the matrix a in an order from small to large in the column ordinal numbers below the elements in the first column.

The second matrix sorting function De (a, p) represents a matrix composed of repeating each element in the matrix a p times and sequentially placing under the elements.

The third matrix sorting function Dm (a, p) represents a matrix composed of the matrix a entirely repeated p times and sequentially disposed below the matrix a. And (5) transferring to a step 2.

S5-2, judging the orientation of the parallelepiped target plate in the X-Y-Z coordinate system, if the orientation is the positive direction of the X axis, then:

the overall body node coordinates (X ', Y ', Z ') of the first, second and sixth hexahedrons are in the matrix:

for a first hexahedron, the second grid variable b ₁ ＝n ₂ 。

For hexahedron II, b ₁ ＝n ₄ 。

For hexahedron of six size, b ₁ ＝n ₃ 。

The coordinate matrixes of all body nodes of the third hexahedron, the fourth hexahedron and the fifth hexahedron are as follows:

for a cube number three, the third grid variable b ₂ ＝n ₂ Fourth grid variable b ₃ ＝n ₄ . For hexahedron of four size, b ₂ ＝n ₂ ，b ₃ ＝n ₅ 。

For a hexahedron of five size, b ₂ ＝n ₃ ，b ₃ ＝n ₅ 。

If the positive direction of the Y axis is adopted, then:

the coordinate matrixes of all body nodes of the first hexahedron, the second hexahedron and the sixth hexahedron are as follows:

for a hexahedron of one, the fifth grid variable b ₄ ＝n ₂ 。

For hexahedron II, b ₄ ＝n ₄ 。

For hexahedron of six size, b ₄ ＝n ₃ 。

for a hexahedron of three, the fifth grid variable b ₅ ＝n ₂ Sixth grid variable b ₆ ＝n ₄ . For hexahedron of four size, b ₅ ＝n ₂ ，b ₆ ＝n ₅ 。

For a five-sided hexahedron, b ₅ ＝n ₃ ，b ₆ ＝n ₅ 。

If the positive direction of the Z axis is adopted, then:

for hexahedron I, seventh grid variable b ₇ ＝n ₂ 。

For hexahedron II, b ₇ ＝n ₄ 。

For hexahedron of six size, b ₇ ＝n ₃ 。

for hexahedron III, eighth grid variable b ₈ ＝n ₂ Ninth grid variable b ₉ ＝n ₄ 。

For a hexahedron of four, b ₈ ＝n ₂ ，b ₉ ＝n ₅ 。

For a five-sided hexahedron, b ₈ ＝n ₃ ，b ₉ ＝n ₅ . And (5) turning to step S5-3.

S5-3, obtaining a structural grid node coordinate distribution matrix S:

S＝[X″ Y″ Z″] (20)

and (5) turning to step S5-4.

And S5-4, respectively repeating the step S5-2 once according to the secondary node matrix, the tertiary node matrix and the quartic node matrix to correspondingly obtain a secondary structured grid node coordinate distribution matrix, a tertiary structured grid node coordinate distribution matrix and a quartic structured grid node coordinate distribution matrix, and turning to the step S5-5.

And S5-5, sequentially splicing the obtained structural grid node coordinate distribution matrix, the secondary structural grid node coordinate distribution matrix, the tertiary structural grid node coordinate distribution matrix and the quartic structural grid node coordinate distribution matrix from top to bottom to obtain the structural finite element grid of the parallelepiped target plate.

S6, obtaining an unstructured grid matrix by setting a three-dimensional sequence number matrix, and sorting the body node coordinates of the structured finite element grids of the parallelepiped target plate to obtain the unstructured finite element grids of the parallelepiped target plate, wherein the method specifically comprises the following steps:

and S6-1, the body node coordinates of all the structured finite element grids of the parallelepiped target plate are contained in the structured grid node coordinate distribution matrix, the secondary structured grid node coordinate distribution matrix, the tertiary structured grid node coordinate distribution matrix and the quartic structured grid node coordinate distribution matrix, and the four matrixes have the same row number and are the row number of the structured grid matrix.

Establishing a three-dimensional sequence number matrix B ₀ With B ₀ (u, v, w) represents a three-dimensional sequence number matrix B ₀ Row (u) th, column (v) th, layer (w) th elements.

Judging the orientation of the parallelepiped target plate, if the orientation is the positive direction of the X axis, then:

B ₀ (u,v,w)＝u+f ₂ (v-1)+f ₂ f ₁ (w-1)+h,u∈[1,f ₂ ],v∈[1,f ₁ ],w∈[1,f ₃ ] (21)

the first and second dimensions of the three-dimensional sequence number matrix are then swapped.

If the positive direction of the Y axis is adopted, then:

B ₀ (u,v,w)＝u+f ₁ (v-1)+f ₁ f ₃ (w-1)+h,u∈[1,f ₁ ],v∈[1,f ₃ ],w∈[1,f ₂ ] (22)

the second and third dimensions of the three-dimensional sequence number matrix are then swapped.

If the positive direction of the Z axis is adopted, then:

B ₀ (u,v,w)＝u+f ₃ (v-1)+f ₂ f ₃ (w-1)+h,u∈[1,f ₃ ],v∈[1,f ₂ ],w∈[1,f ₁ ] (23)

the first and third dimensions of the three-dimensional sequence number matrix are then swapped.

Wherein h has a value of 0. For a hexahedron I, the first order f ₁ ＝n ₂ Second step quantity f ₂ ＝n ₁ Third order quantity f ₃ ＝n ₆ 。

For hexahedron II, f ₁ ＝n ₄ ，f ₂ ＝n ₁ ，f ₃ ＝n ₆ . For hexahedron III, f ₁ ＝n ₂ ，f ₂ ＝n ₄ ，f ₃ ＝n ₆ 。

For a hexahedron of four, f ₁ ＝n ₂ ，f ₂ ＝n ₅ ，f ₃ ＝n ₆ . For a pentagon, f ₁ ＝n ₃ ，f ₂ ＝n ₅ ，f ₃ ＝n ₆ 。

For six hexahedron, f ₁ ＝n ₃ ，f ₂ ＝n ₁ ，f ₃ ＝n ₆ . Proceed to step S6-2.

S6-2, obtaining a three-dimensional sequence number processing matrix B ₁ . Proceed to step S6-3.

Step S6-3, processing the matrix B by the three-dimensional sequence number ₁ And removing all elements corresponding to the maximum row number, column number and layer number to obtain a three-dimensional serial number non-structural matrix B ', and arranging the three-dimensional serial number non-structural matrix B' into a single-row matrix from small to large according to the sequence of the serial numbers of the first row, the second row and the last layer to obtain a non-structural row matrix C. Go to stepAnd S6-4.

S6-4, obtaining an unstructured grid information matrix D through the unstructured row matrix C, wherein each piece of unstructured finite element grid information formed by structured finite element grid nodes is represented in the unstructured grid information matrix D, judging the orientation of the parallelepiped target plate, and if the orientation is the positive direction of the X axis, then:

if the positive direction of the Y axis is adopted, then:

if the positive direction of the Z axis is adopted, then:

proceed to step S6-5.

S6-5, constructing a row of elements on the left side of the unstructured grid information matrix D, wherein the numerical value of each element is the row sequence number of the row where the element is located, and the constructed new matrix is an unstructured finite element grid node coordinate distribution matrix E ₂ The process proceeds to step S6-6.

S6-6, supplementing a row of elements on the left side of the structured grid node coordinate distribution matrix, and obtaining an unstructured finite element grid node coordinate distribution matrix E for the row sequence numbers in the matrix where the elements are located ₁ Distributing matrix E of unstructured finite element grid ₂ A node coordinate distribution matrix E arranged in the unstructured finite element grid ₁ Next, an unstructured finite element mesh is obtained.

Changing the value of h into the number of rows of the structured grid matrix, repeating the step S6-1 to the step S6-4 once to obtain a secondary unstructured finite element grid node coordinate distribution matrix E ₄ Supplementing a row of elements on the left side of the secondary structured grid node coordinate distribution matrix, and obtaining the row sequence of the elements in the matrixAdding the number to the number of rows of the structured grid matrix to obtain a secondary unstructured finite element grid node coordinate distribution matrix E ₃ A quadratic unstructured finite element grid distribution matrix E ₄ A node coordinate distribution matrix E distributed in a secondary unstructured finite element grid ₃ Next, a quadratic unstructured finite element mesh is obtained.

The value of h is changed to be twice of the line number of the structured grid matrix, and the step S6-1 to the step S6-4 are repeated once to obtain a three-time unstructured finite element grid node coordinate distribution matrix E ₆ Supplementing a row of elements on the left side of the cubic structured grid node coordinate distribution matrix, adding the row sequence number of the structured grid matrix row number to the row sequence number of the element in the matrix to obtain a cubic unstructured finite element grid node coordinate distribution matrix E ₅ Distributing matrix E of cubic unstructured finite element grid ₆ A distribution matrix E arranged in a cubic unstructured finite element grid node coordinate ₅ Next, a cubic unstructured finite element mesh is obtained.

The value of h is changed to three times the number of rows of the structured grid matrix and steps S6-1 to S6-4 are repeated once. Obtaining a quartic unstructured finite element grid node coordinate distribution matrix E ₈ Supplementing a row of elements on the left side of the quartic structured grid node coordinate distribution matrix, adding the row sequence number of the structured grid matrix row number to the row sequence number of the element in the matrix to obtain a quartic unstructured finite element grid node coordinate distribution matrix E ₇ Distributing matrix E of quadruply unstructured finite element grids ₈ A distribution matrix E arranged in the node coordinates of the quadric unstructured finite element grid ₇ Next, the fourth unstructured finite element mesh is obtained, and the process goes to step S6-7.

And S6-7, sequentially placing the unstructured finite element grid, the secondary unstructured finite element grid, the tertiary unstructured finite element grid and the quartic unstructured finite element grid in a text file to obtain the unstructured finite element grid of the parallelepiped target plate.

According to the steps, the finite element meshes of the parallelepiped target plate can be rapidly and automatically generated.

Examples

first, an example was set, and a target plate having a thickness of 80mm, a height and a width of 800mm, an inclination angle of 45 °, a positive direction of the x-axis, and an offset distance of 300mm was drawn.

The target plate geometric parameter values are input as follows:

the target plate grid parameter values are input as follows:

n ₁	n ₂	n ₃	n ⁴	n ⁵	n ⁶	q
							20	20	40	30	40	30	1

step S1, taking the direction of the projectile, the shock wave and other incoming objects as a reference direction, taking the surface of the parallelepiped target plate, which bears the projectile, the shock wave and the other incoming objects, as the front surface of the target plate, taking the reverse surface of the parallelepiped target plate as the back surface of the target plate, and taking the other four surfaces as the top surface, the bottom surface, the left side surface 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 L of the parallelepipedic target plate ₄ . Distance 2*L between target plate top surface and target plate bottom surface ₂ ，L ₂ Half 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*L ₃ ，L ₃ Half the width of the parallelepiped target plate. 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 an offset distance L ₅ . The line surface angle between the parallelepiped target plate and the reference direction is the inclination angle α of the parallelepiped target plate.

All points with equal distance to the top surface of the target plate and the bottom surface of the target plate form a primary middle surface of the parallelepiped target plate. All points with equal distance between the left side surface of the target plate and the right side surface of the target plate form a secondary middle surface of the parallelepipedal target plate.

And drawing a 1/4 circular arc with the radius of R in the pre-dividing surface by taking the intersection point of the pre-dividing surface, the primary middle surface and the secondary middle surface as the center of a circle, wherein the circular arc is called an in-plane arc.

The inner arc divides the pre-divided surface into an inner arc surface and an outer arc surface, the middle point of the inner arc divides the inner arc into two parts, the inner arc intersects with the primary middle surface to form an inner arc, the inner arc intersects with the secondary middle surface to form an inner arc, a center point of a surface is determined in the inner arc surface, and the distances from the center point of the surface to the primary middle surface and the secondary middle surface are equal.

Rotating an arc inner angle theta clockwise along a reference direction on the arc inner surface along a perpendicular line from the surface center point to the primary middle surface to form a line segment, connecting the arc inner angle theta to the primary middle surface from the surface center point to form a line in the arc, wherein the distance from the intersection point of the line in the arc and the primary middle surface to the circle center is L ₁ 。

Rotating the outer corner of the arc clockwise on the outer face of the arc along the reference direction from the center point of the arc to the perpendicular to the top surface of the parallelepiped target plate

A line segment is connected from the middle point of the arc to the top surface of the parallelepiped target plate and is a line outside the arc.

Making a line segment along the reference direction on the outer surface of the arc along the arc outer angle rotating counterclockwise from the arc center point to the vertical line of the right side surface of the parallelepiped target plate, connecting the line segment from the arc center point to the right side surface of the parallelepiped target plate, and making the line segment be an outer line of the arc, wherein the reference direction on the outer surface of the arc along the reference direction along the arc outer angle rotating counterclockwise from the arc center point to the vertical line of the right side surface of the parallelepiped target plate is equal to

The first horn target plate is divided into 6 hexahedrons with specific shapes along the reference direction by an inner arc surface, an inner arc line, a third arc line, an outer arc line and an outer arc line.

The specific-shaped hexahedron coinciding with a horn face in the reference direction is a horn, and a horn face is the front face of the horn. The hexahedron with the specific shape coinciding with the second hexahedron along the reference direction is the second hexahedron, and the second hexahedron is the front face of the second hexahedron. The hexahedron with the specific shape coinciding with the third hexahedron along the reference direction is the third hexahedron, and the third hexahedron is the front face of the third hexahedron. The hexahedron with the specific shape coinciding with the fourth hexahedron along the reference direction is the fourth hexahedron, and the fourth hexahedron is the front face of the fourth hexahedron. The specific-shaped hexahedron coinciding with the five-sided surface in the reference direction is a five-sided hexahedron, and the five-sided surface is the front surface of the five-sided hexahedron. The hexahedron of the specific shape coinciding with the six-size surface in the reference direction is the six-size hexahedron, and the six-size surface is the front surface of the six-size hexahedron.

S2, setting an edge node proportion matrix G (m, q), wherein m represents the number of grids set on a hexahedron edge with a specific shape, q represents the ratio of the distance between two adjacent nodes, q is a positive number, i represents a node serial number, and the ith element value G (m, q) _i Comprises the following steps:

in the first plane, the length of the opposite side of a line in the arc is equal toL ₁ The number of grids is determined as n ₁ The node coordinates on the opposite sides and the upper sides of a line in the arc are defined by a node abscissa matrix x ₁ And a node ordinate matrix y ₁ The structure is as follows:

wherein the content of the first and second substances,

denotes 1 (n) ₁ + 1) of all 1 matrices.

In the second sub-surface, the node coordinates on the upper edge of the first arc in the surface are represented by a node abscissa matrix x ₃ And a node ordinate matrix y ₃ The structure is as follows:

wherein the content of the first and second substances,

denotes 1 (n) ₂ + 1) of all 1 matrices.

In-planeThe coordinates of upper nodes of the two arcs are represented by a node abscissa matrix x ₅ And a node ordinate matrix y ₅ The structure is as follows:

in the fifth sub-surface, the number of grids on the first line outside the arc is determined as n ₃ The coordinates of the upper nodes on the line outside the arc are represented by a node abscissa matrix x ₇ And a node ordinate matrix y ₇ The structure is as follows:

wherein the content of the first and second substances,

denotes 1 (n) ₃ + 1) of all 1 matrices.

The node coordinates on the opposite side and the upper side of one line outside the arc are represented by a node abscissa matrix x ₈ And a node ordinate matrix y ₈ The structure is as follows:

in the six-sub-surface, the node coordinates on the opposite side and the upper side of an arc in the surface are represented by a node abscissa matrix x ₉ And a node ordinate matrix y ₉ The structure is as follows:

the grid number of each hexahedron edge with a specific shape and the corresponding edge node coordinates are determined.

Step S3, a group of opposite sides are endowed with a node abscissa matrix and a node ordinate matrix on each sub-surface, and any pair of opposite sides: the node abscissa matrix of any one edge is a primary abscissa matrix x _s The node ordinate matrix is a primary ordinate matrix y _s . The node abscissa matrix of the other edge is a quadratic abscissa matrix x _t The node ordinate matrix is a quadratic ordinate matrix y _t 。

coor ⁽¹⁾ ＝[x _s ^T y _s ^T x _t ^T y _t ^T ] ^T (11)

Wherein, the superscript T is a matrix transposition symbol.

Mirror image supplement is carried out on the edge node coordinates of the 6 sub-surfaces to obtain mirror image supplement node coordinates of each sub-surface, the edge node coordinates of the 6 sub-surfaces take the primary middle surface as a symmetrical surface, and the primary node matrix is mirrored to obtain a secondary node matrix color ⁽²⁾ . At a primary node matrix coor ⁽¹⁾ Middle exchange x _s And x _t Position, and exchange y _s And y _t Position to obtain a new primary node matrix coor ^(1.5) Taking the edge node coordinates of 6 sub-surfaces and the intersection line of the primary middle surface and the secondary middle surface as a symmetry axis, and mirroring the new primary node matrix to obtain a tertiary node matrix color ⁽³⁾ . Taking the edge node coordinates of 6 sub-surfaces as a symmetry plane by taking the secondary middle surface as a mirror image of the new primary node matrix to obtain a quartic node matrix cor ⁽⁴⁾ . So far, the edge node coordinates of the front surface of the parallelepiped target plate are all obtained.

for a sub-surface number one, the horizontal matrix subscript s =1, the vertical matrix subscript t =2, and the first grid variable n = n ₂ 。

wherein the content of the first and second substances,

denotes 1 (n) ₆ + 1) of all 1 matrices.

s5-1, setting three matrix sorting functions:

The second matrix sorting function De (a, p) represents a matrix composed of repeating each element in the matrix a p times and sequentially placing the elements thereunder.

S5-2, in the X-Y-Z coordinate system, the orientation of the parallelepiped target plate is the positive direction of the X axis, then:

for a first hexahedron, the second grid variable b ₁ ＝n ₂ 。

For hexahedron II, b ₁ ＝n ₄ 。

For six hexahedron, b ₁ ＝n ₃ 。

for a cube three, the third grid becomesAmount b ₂ ＝n ₂ Fourth grid variable b ₃ ＝n ₄ 。

For hexahedron of four size, b ₂ ＝n ₂ ，b ₃ ＝n ₅ 。

For a five-sided hexahedron, b ₂ ＝n ₃ ，b ₃ ＝n ₅ . And (4) turning to step S5-3.

S5-3, obtaining a structural grid node coordinate distribution matrix S:

S＝[X″ Y″ Z″] (20)

and (5) turning to step S5-4.

And S5-4, respectively repeating the step S5-2 once according to the secondary node matrix, the tertiary node matrix and the quartic node matrix, correspondingly obtaining a secondary structured grid node coordinate distribution matrix, a tertiary structured grid node coordinate distribution matrix and a quartic structured grid node coordinate distribution matrix, and turning to the step S5-5.

Establishing a three-dimensional sequence number matrix B ₀ With B ₀ (u, v, w) represents a three-dimensional sequence number matrix B ₀ Row (u) th and column (v)Elements of the w-th layer.

The orientation of the parallelepiped target plate is the positive direction of the X-axis, then:

Wherein h has a value of 0. For a hexahedron of one size, the first order quantity f ₁ ＝n ₂ Second order quantity f ₂ ＝n ₁ Third order quantity f ₃ ＝n ₆ 。

For a hexahedron of four size, f ₁ ＝n ₂ ，f ₂ ＝n ₅ ，f ₃ ＝n ₆ . For a hexahedron of five size f ₁ ＝n ₃ ，f ₂ ＝n ₅ ，f ₃ ＝n ₆ 。

Step S6-3, processing the matrix B by the three-dimensional sequence number ₁ And removing all elements corresponding to the maximum row number, column number and layer number to obtain a three-dimensional serial number non-structural matrix B ', and arranging the three-dimensional serial number non-structural matrix B' into a single-row matrix from small to large according to the sequence of the serial numbers of the first row, the second row and the last layer to obtain a non-structural row matrix C. Proceed to step S6-4.

S6-4, obtaining an unstructured grid information matrix D through the unstructured row matrix C, wherein each unstructured finite element grid information formed by structured finite element grid nodes is represented in the unstructured grid information matrix D, and the orientation of the parallelepiped target plate is the positive direction of the X axis, then:

and (6) turning to step S6-5.

S6-6, supplementing a row of elements to the left side of the structured grid node coordinate distribution matrix, and obtaining an unstructured finite element grid node coordinate distribution matrix E for the row sequence number in the matrix where the elements are located ₁ Distributing matrix E of unstructured finite element grid ₂ A node coordinate distribution matrix E arranged in the unstructured finite element grid ₁ Next, an unstructured finite element mesh is obtained.

Changing the value of h into the number of rows of the structured grid matrix, repeating the step S6-1 to the step S6-4 once to obtain a secondary unstructured finite element grid node coordinate distribution matrix E ₄ Supplementing a row of elements on the left side of the secondary structured grid node coordinate distribution matrix, adding the row sequence number of the structured grid matrix row number to the row sequence number of the element in the matrix to obtain a secondary unstructured finite element grid node coordinate distribution matrix E ₃ A quadratic unstructured finite element grid distribution matrix E ₄ A distribution matrix E arranged on the node coordinates of the secondary unstructured finite element grid ₃ Next, a quadratic unstructured finite element mesh is obtained.

The value of h is changed to be twice of the number of rows of the structured grid matrix, and the step S6-1 to the step S6-4 are repeated once to obtain a cubic unstructured finite element grid node coordinate distribution matrix E ₆ Supplementing a row of elements on the left side of the three-time structured grid node coordinate distribution matrix, adding the row sequence number of the element in the matrix to the row number of the structured grid matrix to obtain a three-time unstructured finite element grid node coordinate distribution matrix E ₅ Distributing cubic unstructured finite element gridsMatrix E ₆ A distribution matrix E arranged in a cubic unstructured finite element grid node coordinate ₅ Next, a cubic unstructured finite element mesh is obtained.

The value of h is changed to three times the number of rows of the structured grid matrix and steps S6-1 to S6-4 are repeated once. Obtaining a quartic unstructured finite element grid node coordinate distribution matrix E ₈ Supplementing a row of elements on the left side of the quadric structured grid node coordinate distribution matrix, adding the row number of the structured grid matrix to the row sequence number of the element in the matrix to obtain a quadric unstructured finite element grid node coordinate distribution matrix E ₇ Distributing matrix E of quadric unstructured finite element mesh ₈ A distribution matrix E arranged in the node coordinates of the quadric unstructured finite element grid ₇ Next, the fourth unstructured finite element mesh is obtained, and the process proceeds to step S6-7.

And finishing the structured finite element grids and the unstructured finite element grids of the parallelepipedal target plate, when a large number of working conditions are faced, modifying according to actual geometrical parameters and required grid parameters of the working conditions, and repeating the steps S1-S6 to realize the rapid and automatic generation of the parallelepipedal target plate finite element grids under each working condition.

Claims

1. A method for quickly and automatically generating a finite element grid of a parallelepiped target plate is characterized by comprising the following specific steps:

step S1, determining geometric parameters of the parallelepiped target plate, including thickness, height, width, orientation, offset distance and inclination angle, dividing the parallelepiped target plate into 4 sub-target plates along a reference direction, sequentially including a first sub-target plate, a second sub-target plate, a third sub-target plate and a fourth sub-target plate, dividing the first sub-target plate into 6 hexahedrons with specific shapes along the reference direction, and turning to step S2;

s2, determining the number of grids of a group of opposite sides on the front surfaces of the 6 hexahedrons with the specific shapes, determining corresponding edge node coordinates, and turning to S3;

s3, mirror image supplement is carried out on edge node coordinates of a group of opposite sides on the front faces of the 6 hexahedrons with specific shapes, edge node coordinates of the front faces of the parallelepipedic target plates are obtained, and the step S4 is carried out;

s4, expanding the edge node coordinates of the front surface of the target plate to the surface node coordinates of the front surface of the target plate, supplementing the edge node coordinates of the planar hexahedral target plate along the reference direction, and turning to the step S5;

s5, setting a matrix sorting function, obtaining body node coordinates of the structured grid of the parallelepiped target plate according to the orientation of the parallelepiped target plate by using the face node coordinates of the front face of the parallelepiped target plate and the edge node coordinates of the planar hexahedron target plate along the reference direction, further obtaining the structured finite element grid of the parallelepiped target plate, and turning to the step S6;

2. The method of claim 1, wherein the method comprises the steps of: in step S1, determining geometric parameters of the parallelepiped target plate, including thickness, height, width, orientation, offset distance, and inclination angle, dividing the parallelepiped target plate into 4 sub-target plates along the reference direction, sequentially including a first sub-target plate, a second sub-target plate, a third sub-target plate, and a fourth sub-target plate, and dividing the first sub-target plate into 6 hexahedrons of specific shapes along the reference direction, specifically as follows:

taking the directions of the shot, the shock wave and other attacking objects as reference directions, taking the surface of the parallelepiped target plate, which bears the shot, the shock wave and other attacking objects, as the front surface of the target plate, taking the back surface of the parallelepiped target plate as the back surface of the target plate, and respectively taking the rest four surfaces as 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;

the distance between the front surface and the back surface of the target plate is the thickness L of the parallelepipedic target plate ₄ (ii) a Distance 2*L between target plate top surface and target plate bottom surface ₂ ，L ₂ 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*L ₃ ，L ₃ Is half of the width of the parallelepipedal 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 more than 2; the direction opposite to the reference direction is the orientation of the parallelepiped target plate; the translation length of the parallelepiped target plate along the reference direction is an offset distance L ₅ (ii) a The line surface angle between the parallelepiped target plate and the reference direction is the inclination angle alpha of the parallelepiped target plate, and the inclination angle alpha is not less than 30 degrees and not more than 90 degrees;

all points with equal distance to the top surface and the bottom surface of the target plate form a primary middle surface of the parallelepiped target plate; all points with equal distance between the left side surface of the target plate and the right side surface of the target plate form a secondary middle surface of the parallelepipedal target plate;

dividing the parallelepiped target plate into four sub-target plates by a primary middle surface and a secondary middle surface along a reference direction, wherein the sub-target plate synchronously contacting the top surface of the target plate and the right side surface of the target plate is a first sub-target plate, and the other sub-target plates are sequentially defined as a second sub-target plate, a third sub-target plate and a fourth sub-target plate from the first sub-target plate clockwise along the equivalent thickness direction;

defining a projection surface of a surface, which is superposed with the front surface of the target plate, of the first target plate along a reference direction as a pre-division surface, and defining a projection surface of the front surface of the target plate along the reference direction as a projection front surface of the target plate;

drawing a 1/4 circular arc with the radius of R in the pre-dividing surface by taking the intersection point of the pre-dividing surface, the primary middle surface and the secondary middle surface as the center of a circle, wherein the circular arc is called an in-plane arc and is 0.1L ₂ ≤R≤0.7L ₂ And 0.1L ₃ ≤R≤0.7L ₃ ；

The inner arc divides the pre-divided surface into an inner arc surface and an outer arc surface, the middle point of the inner arc divides the inner arc into two parts, the inner arc intersects with the primary middle surface to form an inner arc, the inner arc intersects with the secondary middle surface to form an inner arc, a center point of a surface is determined in the inner arc surface, the distances from the center point of the surface to the primary middle surface and the secondary middle surface are equal, and the distance from the center point of the surface to the center point of the circle is not less than 0.2 time of the radius R and not more than 0.75 time of the radius R;

rotating an arc inner angle theta clockwise along a reference direction with a perpendicular line from a face center point to a primary middle plane on an arc inner surface, connecting a line segment from the face center point to the primary middle plane, wherein the line segment is a line in the arc, the theta is more than or equal to 0 degree and less than or equal to 32.5 degrees, and the distance from the intersection point of the line in the arc and the primary middle plane to the circle center is L ₁ ，0.1L ₁ ≤R≤0.7L ₁ ；

Rotating an arc inner angle along a reference direction in a counterclockwise direction with a perpendicular line from a face center point to a secondary middle plane to form a line segment, connecting the line segment from the face center point to the secondary middle plane, namely two lines in the arc, wherein the distance from the intersection point of the two lines in the arc and the secondary middle plane to the circle center is equal to the distance L from the intersection point of the one line in the arc and the primary middle plane to the circle center ₁ (ii) a Rotating the arc inner surface along the reference direction counterclockwise with the perpendicular line from the center point of the surface to the secondary middle surface to form an arc inner angle equal to theta;

making a vertical line of the inner arc of the surface from the center point of the surface, and intersecting the inner arc of the surface with the middle point of the arc, wherein the vertical line is a three-line in the arc;

Dividing a first-size target plate into 6 hexahedrons with specific shapes along a reference direction by an inner arc of a surface, an inner first line of an arc, an inner second line of the arc, an inner third line of the arc, an outer first line of the arc and an outer second line of the arc;

the pre-divided surface is divided into 6 sub-surfaces by an inner arc of the surface, an inner arc line, an outer arc line and an outer arc line along a reference direction, wherein the sub-surfaces comprise a first sub-surface with the inner arc line and the inner arc line as edges, a second sub-surface with the inner arc line and the inner arc line as edges, a third sub-surface with the inner arc line and the inner arc line as edges, a fourth sub-surface with the inner arc line and the outer arc line as edges, a fifth sub-surface with the outer arc line and the outer arc line as edges, and a sixth sub-surface with the inner arc line and the outer arc line as edges;

the hexahedron with the specific shape coinciding with the first hexahedron along the reference direction is the first hexahedron, and the first hexahedron is the front surface of the first hexahedron; the hexahedron with the specific shape coinciding with the second hexahedron along the reference direction is the second hexahedron, and the second hexahedron is the front surface of the second hexahedron; the hexahedron with the specific shape coinciding with the third hexahedron along the reference direction is the third hexahedron, and the third hexahedron is the front face of the third hexahedron; the hexahedron with the specific shape coinciding with the fourth hexahedron along the reference direction is the fourth hexahedron, and the fourth hexahedron is the front surface of the fourth hexahedron; the hexahedron with the specific shape coinciding with the fifth hexahedron along the reference direction is a fifth hexahedron, and the fifth hexahedron is the front surface of the fifth hexahedron; the hexahedron of the specific shape coinciding with the six-size surface in the reference direction is the six-size hexahedron, and the six-size surface is the front surface of the six-size hexahedron.

3. The method of claim 2, wherein the method comprises the steps of: in step S2, the number of meshes of a group of opposite sides on the front surfaces of the 6 specially-shaped hexahedrons is determined, and corresponding edge node coordinates are determined as follows:

setting an edge node proportion matrix G (m, q), wherein m represents a net set on the edges of a hexahedron with a specific shapeThe number of grids, q represents the ratio of the distances between two adjacent nodes, q is a positive number, i represents the node number, the ith element value G (m, q) _i Comprises the following steps:

in the first plane, the length of the opposite side of a line in the arc is equal to L ₁ The number of grids is determined as n ₁ The node coordinates on the opposite sides and the upper sides of a line in the arc are defined by a node abscissa matrix x ₁ And a node ordinate matrix y ₁ The structure is as follows:

wherein the content of the first and second substances,

denotes 1 (n) ₁ + 1) full 1 matrix;

wherein the content of the first and second substances,

denotes 1 (n) ₂ + 1) full 1 matrix;

wherein the content of the first and second substances,

denotes 1 (n) ₃ + 1) full 1 matrix;

4. The method of claim 3, wherein the method comprises the steps of: in step S3, mirror image supplementation is performed on edge node coordinates of a group of opposite sides on the front surfaces of the 6 hexahedrons with specific shapes to obtain edge node coordinates of the front surface of the parallelepiped target plate, which are specifically as follows:

each sub-surface has a set of opposite edges assigned with a node abscissa matrix and a node ordinate matrix, and any pair of opposite edges: the node abscissa matrix of any one edge is a primary abscissa matrix x _s The node ordinate matrix is a primary ordinate matrix y _s (ii) a The node abscissa matrix of the other edge is a quadratic abscissa matrix x _t The node ordinate matrix is a quadratic ordinate matrix y _t ；

coor ⁽¹⁾ ＝[x _s ^T y _s ^T x _t ^T y _t ^T ] ^T (11)

Wherein, the superscript T is a matrix transposition symbol;

mirror image supplement is carried out on the edge node coordinates of the 6 sub-surfaces to obtain mirror image supplement node coordinates of each sub-surface, the edge node coordinates of the 6 sub-surfaces take the primary middle surface as a symmetrical surface, and the primary node matrix is mirrored to obtain a secondary node matrix color ⁽²⁾ (ii) a At a primary node matrix coor ⁽¹⁾ Middle exchange x _s And x _t Position, and exchange y _s And y _t Position to obtain a new primary node matrix coor ^(1.5) Taking the edge node coordinates of the 6 sub-surfaces as a symmetry axis by taking the intersection line of the primary middle surface and the secondary middle surface, and mirroring the new primary node matrix to obtain a tertiary node matrix coor ⁽³⁾ (ii) a Taking the edge node coordinates of 6 sub-surfaces as a symmetry plane by taking the secondary middle surface as a mirror image of the new primary node matrix to obtain a quartic node matrix cor ⁽⁴⁾ (ii) a So far, the edge node coordinates of the front surface of the parallelepiped target plate are obtained.

5. The method of claim 4, wherein the method comprises the steps of: in step S4, the edge node coordinates of the front surface of the parallelepiped target plate are expanded to the surface node coordinates of the front surface of the parallelepiped target plate, and a node value matrix of the planar hexahedral target plate along the reference direction is supplemented, specifically as follows:

for a sub-surface number one, the horizontal matrix subscript s =1, the vertical matrix subscript t =2, and the first grid variable n = n ₂ ；

For the sub-surface two, the horizontal matrix subscript s =2, the vertical matrix subscript t =3,n = n ₄ ，n ₄ The number of grids determined for three lines in the arc;

for the third sub-surface, under the horizontal matrixThe index s =4, the vertical matrix index t =5, n = n ₄ ；

For the four sub-planes, the horizontal matrix subscript s =5, the vertical matrix subscript t =6,n = n ₅ ，n ₅ The number of grids determined for the two lines outside the arc;

for the five sub-planes, the horizontal matrix subscript s =7, the vertical matrix subscript t =8, n = n ₅ ；

For the six sub-planes, the horizontal matrix subscript s =3, the vertical matrix subscript t =9,n = n ₃ (ii) a Step S4-2 is carried out;

denotes 1 (n) ₆ + 1) of all 1 matrices.

6. The method of claim 5, wherein the method comprises the steps of: in step S5, by setting a matrix sorting function, the body node coordinates of the structured grid of the parallelepiped target plate are obtained from the face node coordinates of the front face of the parallelepiped target plate and the edge node coordinates of the planar hexahedron target plate along the reference direction according to the orientation of the parallelepiped target plate, and then the structured finite element grid of the parallelepiped target plate is obtained, which is specifically as follows:

s5-1, setting three matrix sorting functions:

the first matrix sorting function Re (A) represents a matrix with the column number of 1 formed by splicing elements with the column ordinal number larger than 1 in the matrix A into a first column of elements in sequence from small to large;

the second matrix sorting function De (a, p) represents a matrix formed by repeating each element in the matrix a p times and sequentially placing the elements below the element;

a third matrix sorting function Dm (a, p) represents a matrix composed of a matrix a which is entirely repeated p times and sequentially disposed below the matrix a; turning to the step 5-2;

for a first hexahedron, the second grid variable b ₁ ＝n ₂ ；

For hexahedron II, b ₁ ＝n ₄ ；

For hexahedron of six size, b ₁ ＝n ₃ ；

for a cube three, the third grid variable b ₂ ＝n ₂ Fourth grid variable b ₃ ＝n ₄ ；

For a hexahedron of four, b ₂ ＝n ₂ ，b ₃ ＝n ₅ ；

For a five-sided hexahedron, b ₂ ＝n ₃ ，b ₃ ＝n ₅ ；

If the positive direction of the Y axis is adopted, then:

for a hexahedron of one, the fifth grid variable b ₄ ＝n ₂ ；

For hexahedron II, b ₄ ＝n ₄ ；

For six hexahedron, b ₄ ＝n ₃ ；

for a hexahedron III, the fifth grid variable b ₅ ＝n ₂ Sixth grid variable b ₆ ＝n ₄ ；

For hexahedron of four size, b ₅ ＝n ₂ ，b ₆ ＝n ₅ ；

For a hexahedron of five size, b ₅ ＝n ₃ ，b ₆ ＝n ₅ ；

If the positive direction of the Z axis is formed, the following steps are carried out:

for a hexahedron of one, the seventh grid variable b ₇ ＝n ₂ ；

For hexahedron II, b ₇ ＝n ₄ ；

For hexahedron of six size, b ₇ ＝n ₃ ；

for hexahedron III, eighth grid variable b ₈ ＝n ₂ Ninth grid variable b ₉ ＝n ₄ ；

For hexahedron of four size, b ₈ ＝n ₂ ，b ₉ ＝n ₅ ；

For a five-sided hexahedron, b ₈ ＝n ₃ ，b ₉ ＝n ₅ (ii) a Turning to step S5-3;

s5-3, obtaining a structural grid node coordinate distribution matrix S:

S＝[X″ Y″ Z″] (20)

turning to the step S5-4;

s5-4, respectively repeating the step S5-2 once according to the secondary node matrix, the tertiary node matrix and the quartic node matrix, correspondingly obtaining a secondary structured grid node coordinate distribution matrix, a tertiary structured grid node coordinate distribution matrix and a quartic structured grid node coordinate distribution matrix, and turning to the step S5-5;

7. The method of claim 6, wherein the method comprises the steps of: in step S6, the body node coordinates of the structured finite element mesh of the parallelepiped target plate are sorted and sorted to obtain the unstructured mesh of the parallelepiped target plate, which is specifically as follows:

s6-1, including body node coordinates of all structured finite element grids of the parallelepiped target plate in a structured grid node coordinate distribution matrix, a secondary structured grid node coordinate distribution matrix, a tertiary structured grid node coordinate distribution matrix and a quartic structured grid node coordinate distribution matrix, wherein the four matrixes have the same row number and are the row number of the structured grid matrix;

establishing a three-dimensional sequence number matrix B ₀ With B ₀ (u, v, w) represents a three-dimensional sequence number matrix B ₀ Element of w layer of w row and v column;

then exchanging the first dimension and the second dimension of the three-dimensional sequence number matrix;

if the positive direction of the Y axis is formed, then:

then exchanging the second dimension and the third dimension of the three-dimensional sequence number matrix;

if the positive direction of the Z axis is adopted, then:

then exchanging the first dimension and the third dimension of the three-dimensional sequence number matrix;

wherein h has a value of 0; for a hexahedron of one size, the first order quantity f ₁ ＝n ₂ Second step quantity f ₂ ＝n ₁ Third order quantity f ₃ ＝n ₆ ；

For hexahedron II, f ₁ ＝n ₄ ，f ₂ ＝n ₁ ，f ₃ ＝n ₆ (ii) a For a cube number three, f ₁ ＝n ₂ ，f ₂ ＝n ₄ ，f ₃ ＝n ₆ ；

For a hexahedron of four, f ₁ ＝n ₂ ，f ₂ ＝n ₅ ，f ₃ ＝n ₆ (ii) a For a pentagon, f ₁ ＝n ₃ ，f ₂ ＝n ₅ ，f ₃ ＝n ₆ ；

For six hexahedron, f ₁ ＝n ₃ ，f ₂ ＝n ₁ ，f ₃ ＝n ₆ (ii) a Step S6-2 is carried out;

s6-2, obtaining a three-dimensional sequence number processing matrix B ₁ (ii) a Step S6-3 is carried out;

step S6-3, processing the matrix B by the three-dimensional sequence number ₁ Removing all elements corresponding to the maximum row number, column number and layer number to obtain a three-dimensional serial number non-structural matrix B ', and arranging the three-dimensional serial number non-structural matrix B' into a single-row matrix from small to large according to the sequence of the serial numbers of the first serial number, the second serial number and the last layer to obtain a non-structural row matrix C; turning to step S6-4;

if the positive direction of the Y axis is adopted, then:

if the positive direction of the Z axis is adopted, then:

turning to the step S6-5;

s6-5, constructing a row of elements on the left side of the unstructured grid information matrix D, wherein the numerical value of each element is the row sequence number of the row where the element is located, and the constructed new matrix is an unstructured finite element grid node coordinate distribution matrix E ₂ Step S6-6 is carried out;

s6-6, supplementing a row of elements to the left side of the structured grid node coordinate distribution matrix, and obtaining an unstructured finite element grid node coordinate distribution matrix E for the row sequence number in the matrix where the elements are located ₁ Distributing matrix E of unstructured finite element grid ₂ A node coordinate distribution matrix E arranged in the unstructured finite element grid ₁ Then, obtaining an unstructured finite element mesh;

changing the value of h into the number of rows of the structured grid matrix, repeating the step S6-1 to the step S6-4 once to obtain a secondary unstructured finite element grid node coordinate distribution matrix E ₄ Supplementing a row of elements on the left side of the secondary structured grid node coordinate distribution matrix, adding the row sequence number of the structured grid matrix row number to the row sequence number of the element in the matrix to obtain a secondary unstructured finite element grid node coordinate distribution matrix E ₃ A quadratic unstructured finite element grid distribution matrix E ₄ A distribution matrix E arranged on the node coordinates of the secondary unstructured finite element grid ₃ Then, obtaining a secondary unstructured finite element grid;

the value of h is changed to be twice of the line number of the structured grid matrix, and the step S6-1 to the step S6-4 are repeated once to obtain a three-time unstructured finite element grid node coordinate distribution matrix E ₆ Supplementing a row of elements on the left side of the cubic structured grid node coordinate distribution matrix, adding the row sequence number of the structured grid matrix row number to the row sequence number of the element in the matrix to obtain a cubic unstructured finite element grid node coordinate distribution matrix E ₅ Distributing matrix E of cubic unstructured finite element grid ₆ Node coordinate distribution matrix E distributed in cubic unstructured finite element grid ₅ Then, obtaining a cubic unstructured finite element grid;

changing the value of h to be three times of the row number of the structured grid matrix, and repeating the step S6-1 to the step S6-4 once; obtaining a quartic unstructured finite element grid node coordinate distribution matrix E ₈ Supplementing a row of elements on the left side of the quadric structured grid node coordinate distribution matrix, adding the row number of the structured grid matrix to the row sequence number of the element in the matrix to obtain a quadric unstructured finite element grid node coordinate distribution matrix E ₇ Will not be structured four timesFinite element mesh distribution matrix E ₈ Node coordinate distribution matrix E distributed in four times of unstructured finite element grids ₇ Then, obtaining a quartic unstructured finite element grid, and turning to the step S6-7;