CN109948206B - Flat finite element grid parametric modeling method for processing diamond pattern by high energy beam - Google Patents
Flat finite element grid parametric modeling method for processing diamond pattern by high energy beam Download PDFInfo
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Abstract
The invention provides a parametric modeling method for a plate finite element grid of a high-energy beam processing rhombus pattern, which utilizes nodes to construct a rhombohedral grid and completes the division of the plate grid containing high-energy beam slot lines; then, four end faces around the flat grid are filled; determining the number of units in the defect area of the high-energy beam-trough line according to the proportional relation between the high-energy beam-trough line and the width and height directions of the flat plate; secondly, deleting the area grids of the high-energy beam slot line defect area along the width direction and the height direction of the flat plate respectively to complete modeling; and finally, outputting node and unit information of the grid according to the format requirement of the finite element software. The method can realize the modeling of the plate finite element mesh of the high-energy beam processing diamond pattern with different geometrical characteristics, is simple and convenient, has high efficiency, and is used for the bomb body to carry out strength analysis.
Description
Technical Field
The invention relates to the technical field of ammunition, in particular to a flat finite element grid parametric modeling method for processing diamond patterns by high energy beams.
Background
In order to improve the power of the warhead, a high-energy beam precontrol technology is adopted, so that the projectile body can obtain precontrol fragments with relatively consistent shapes and qualities under detonation loading, and the power of the warhead is improved. The high-energy beam pre-control technology is that high-energy beams such as electron beams, laser beams or ion beams are used for heating the local part of the material to a melting state quickly, the bullet body cools the melted metal quickly, and zone units are formed on the bullet body to control the breakage of the bullet body. The high-energy beam diamond-shaped groove means that the unit shape of the high-energy beam groove is diamond-shaped. When designing high-energy-beam diamond-shaped notches of a projectile body, the strength of the projectile body with the diamond-shaped notches needs to be analyzed, and a flat plate test piece can be generally taken on the projectile body for analysis. Through a high-energy beam grooving flat plate tensile test, the influence of different grooving parameters on the strength of the projectile body can be researched, and the influence rule of high-energy beam grooving on the strength of the projectile body can be obtained by combining numerical simulation analysis. However, since the geometry of the diamond-shaped grooves of the flat plate is complicated, the high-energy beam processing area has a complicated composition, including a melting area, a transition area and a defect area, as shown in fig. 1.
However, due to the complicated geometry of the slab diamond-shaped grooves, it is time consuming to build a finite element mesh using commercial modeling software. Firstly, establishing a three-dimensional model of a diamond-shaped grooved flat plate, then introducing finite element software to carry out meshing, generally adopting tetrahedral meshing, and having low precision; if a hexahedral mesh is adopted, one notch needs to be divided firstly, and then the mirror image is copied to other notches, but if the angle of each notch is different, the mirror image cannot be directly mirrored, and the step of dividing again is complex. In addition, if the characteristic size of the notch needs to be changed, the finite element mesh needs to be divided again, a large amount of repeated operations on modeling are complicated and prone to errors, and design efficiency is seriously influenced.
Disclosure of Invention
In view of the above, the invention provides a high-energy beam processing diamond pattern flat finite element mesh parametric modeling method, which can realize high-energy beam processing diamond pattern flat finite element mesh modeling with different geometric characteristics, is simple and convenient, has high efficiency, and is used for the elastomer to perform strength analysis.
The technical scheme adopted by the invention is as follows:
a flat finite element mesh parametric modeling method for processing diamond patterns by high energy beams comprises the following steps:
constructing a rhombohedral grid by using nodes to finish the division of a flat grid containing high-energy beam slot lines;
step two, four end faces around the flat grid are filled;
determining the number of units in the defect area of the high-energy beam slot line according to the proportional relation between the high-energy beam slot line and the width and height directions of the flat plate;
deleting the area grids of the high-energy beam slot line defect area along the width direction and the height direction of the flat plate respectively to complete modeling;
and step four, outputting node and unit information of the grid according to the format requirement of the finite element software.
Further, taking the length direction of the flat plate as the X direction, the specific method of the first step is as follows:
101, calculating X, Y subdivision numbers in a Z direction under a Cartesian coordinate system, and setting the subdivision number in the Z direction;
102, generating nodes according to the X, Y and the subdivision number in the Z direction;
103, moving the nodes along the positive X direction, so that the connecting line of the moving nodes and the original Y-direction nodes forms a half of the grooving angle with the X direction;
104, determining a grid area of the high-energy beam groove line in the Z direction according to the groove depth, the plate thickness and the Z direction section;
105, moving the node in the Z direction to enable the depth of the node at the bottom of the groove to be consistent with that of the notch groove; meanwhile, moving the node in the Z direction to enable the upper-layer node of the slot line defect area to be consistent with the height of the defect area;
and 106, constructing a diamond unit by using the nodes to obtain a diamond hexahedron grid containing the high-energy beam slot line.
Further, the specific method of the second step is as follows:
step 201, two end faces in the X direction: copying a starting end row and an ending end row of nodes in the X direction, and respectively moving along the positive direction and the negative direction of the X direction to obtain end surface nodes of two end surfaces; for the nodes which have moved along the X forward direction, the nodes which are copied and moved by the starting end column or the ending end column after copying and moving are collinear;
two end faces in the Y direction: copying two columns of nodes of a starting end and two columns of nodes of an ending end in the Y direction, and respectively moving along the positive direction and the negative direction of the Y direction to obtain end surface nodes of two end surfaces;
and 202, constructing end face units of four end faces by the nodes.
Further, the moving method in step 201 is:
in the X direction: taking L as the moving distance of the starting end column and the ending end columnc/2NxThe moving distance after copying the node which has moved in the X direction is taken as Lc/Nx，LcIs the length of the plate, NxIs the fraction in the X direction;
in the Y direction: the moving distance of the first column at the starting end and the last column at the ending end can be b/NyThe moving distance of the second row of the starting end and the second row of the ending end is 2b/NyB is the width of the plate, NyIs the fraction in the Y direction.
Further, the specific method of constructing the end face unit from the nodes in step 202 is as follows: 8 nodes construct a unit, and the nodes and the node index are stored according to the directions of z, y and xnodeiThe calculation is as follows, i, j, k are node indexes of X, Y, Z directions respectively, NxIs the fraction in the X direction, NyIs a fraction in the Y direction, NzIs the section in the Z direction, and is the section in the Z direction,
further, the specific method of the third step is as follows:
step 301, determining a transition area unit according to the number of the notching interval units in the Y direction and the number of the notching units in the Z direction;
step 302, determining a melting area unit according to the number of the interval units of the groove in the Y direction and the number of the groove units in the Z direction;
step 303, determining the defective area unit according to the number of the spacing units for notching in the Y direction and the number of the notching units in the Z direction.
Has the advantages that:
1. the invention can realize the modeling of the flat finite element mesh of the high-energy beam processing rhomboid pattern with different geometric characteristics, and because the processing pattern is rhomboid, the method directly constructs rhomboid hexahedral mesh for division, and is simple and easy to realize; if the characteristic size of the high-energy beam slot line needs to be changed, modeling can be performed only by changing the geometric characteristic parameters of the rhombohedral grid, the operations of re-establishing a three-dimensional model and dividing a finite element grid while changing the characteristic size of the high-energy beam slot line are avoided, a large amount of repeated labor is avoided being brought to analysts, the problems that the geometric shape of a high-energy beam processing rhombohedral pattern plate is complex and the establishing process of the finite element grid is complicated are solved, convenience is brought to the bomb body analysis of the high-energy beam processing rhombohedral pattern, and efficiency is high.
2. The invention constructs the rhombohedral hexahedral mesh by moving the nodes, accurately controls the size of the high-energy beam slot line by changing the geometric characteristics of the nodes and has high response speed.
3. The invention constructs a rectangular end face by moving and filling four end faces in a mode of copying end part nodes, has good end face consistency and is convenient to be butted with other models.
4. The invention limits the moving distance of the end node, so that the constructed rectangular end surface grid is not too large or too small, and the calculation time of the finite element step length is not influenced by the size of the grid.
Drawings
FIG. 1 is a schematic diagram of a model area distribution based on high energy beam processing;
FIG. 2 is a front view of the flat rhombohedral grid of the invention;
FIG. 3 is a partial cross-sectional view of a plate of the present invention;
FIG. 4 is a schematic diagram of the side length of a diamond according to the present invention;
FIG. 5 is a schematic diagram of the node of the present invention before moving in the X direction;
FIG. 6 is a schematic diagram of the node of the present invention after moving in the X direction;
FIG. 7 is a diagram illustrating an index sequence for constructing a unit from 8 nodes according to the present invention;
FIG. 8 is a schematic diagram of node movement on four end faces of the present invention;
FIG. 9 is a schematic diagram of the meshing of the end face units of the present invention;
FIG. 10 is a schematic diagram of the flat high energy beam rhombohedral meshing of the present invention;
FIG. 11 is a schematic diagram of rhombohedral meshing of the high energy beam-slot line of the present invention;
FIG. 12 is a left side view of the invention after slab meshing.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a parametric modeling method for a plate finite element grid with diamond patterns processed by high energy beams, which comprises the following steps of constructing a diamond hexahedral grid by using nodes to divide the plate grid containing high energy beam slot lines, filling up four end faces around the plate grid, determining the number of units in a high energy beam slot line defect area according to the proportional relation between the high energy beam slot lines and the width and height directions of a plate, and deleting area grids in the high energy beam slot line defect area along the width and height directions of the plate to complete modeling, as shown in fig. 10, 11 and 12, and specifically comprises the following steps:
plate thickness t is 10mm, plate width b is 20mm, and plate length Lc100mm, 1mm for the width w of the groove, 5mm for the depth h of the groove, 10mm for the distance a of the groove, 90 ° for the angle θ of the groove, 3 for the number of units N in the width direction of the groove of the diamond shape obtained by intersecting the groove lines, and 3 for the height h of the defect area01mm, the ratio S of the width of the melting area to the width of the notch 01/3. As shown in fig. 2, 3 and 4.
as shown in fig. 4, the side length of the rhombus obtained by intersecting the groove lines is represented by l, namely the side length of the rhombus hexahedron grid, the calculation of the side length of the rhombus l is 1mm calculated according to the formula (1),
the length direction of the flat plate is taken as the X direction, and the section number in the X direction is NxAnd the Y-direction section number is NyAnd the Z-direction section number is Nz。NzRoot of KegenGiven a constant value, the X-direction profile number NxAnd the fraction N in the Y directionyCan be calculated according to formula (2), Nx＝212，NyTaking the vertical section number N as 28z＝10。
the X-direction cross-section according to step 3 is NxAnd the Y-direction section number is NyAnd the Z-direction section number is NzAnd generating flat plate internal nodes, obtaining the nodes of the line from the end points of the line, obtaining the nodes of the surface from the nodes of the opposite side, and obtaining the nodes of the body from the nodes of the opposite side. The nodes are stored in the X direction, the Y direction and the Z direction, so that the diamond-shaped unit is constructed conveniently in the subsequent steps.
moving the node in the positive X direction, wherein under a Cartesian coordinate system, node indexes in X, Y, Z three directions are i, j and k respectively, wherein i is 1, 2, … …, and Nx；j＝1，2，……，Ny；k＝1，2，……，Nz. The moving distance Δ x of each node is calculated by equation (3) to obtain Δ x as 0.2358. As shown in fig. 5, a dotted frame I indicates the position of the node before movement, and as shown in fig. 6, a dotted frame I' indicates the position of the node after movement.
number N 'of mesh to be grooved in Z direction'rCalculating N from formula (4)r'＝5。
moving the node in Z direction to make the depth of the groove bottom node consistent with that of the groove, calculating the moving distance according to formula (5), and calculating to obtain
Δz＝0。
h for number of Z-direction cells in defect areazIs expressed by the formula (6) to calculate Hz＝1。
Step 9, moving the node in the Z direction to enable the upper layer node of the defect area to be consistent with the height of the defect area;
under the cylindrical coordinate system, r,
The node indexes in the three directions of z are i, j and k respectively, and the index i is equal to Nr-N'r+HrThe node(s) is moved radially, the node(s) is moved in the Z direction to make the upper node(s) of the defect area(s) and the defect area(s) have the same height, the movement distance is calculated according to the formula (7), and the delta Z is calculatedh＝0。
Step 10, constructing a diamond-shaped unit by nodes;
the eight nodes construct a unit, the index order is as shown in fig. 7, the origin of the cartesian coordinate system is node 1, the point in the y direction is node 2, the point on the xy plane is node 3, the point in the x direction is node 4, the point in the z direction is node 5, the point on the yz plane is node 6, the point in the xyz space is node 7, and the point on the xz plane is node 8. Node index of cell for all nodes stored in the z, then y, then x directionsnodeiCan be calculated according to equation (8). The constructed diamond-shaped units are stored in the directions of z, y and x, so that subsequent grooving is facilitated.
When the index j in the Y direction is an even number, the calculation is performed according to the formula (9)
Step 11, generating four end face nodes;
the X-axis negative direction is a rear end face, the X-axis positive direction is a front end face, the Y-axis negative direction is a left end face, and the Y-axis positive direction is a right end face. The nodes of the rear end face are obtained by copying the first row of nodes of the starting end in the X direction and then moving along the X direction, the moving direction is the negative direction of the X axis, and the moving distance can be Lc/2NxFor nodes that have moved in the forward direction of X, the post-copy movement distance can be taken as Lc/Nx. The node of the front end surface is obtained by copying a row of nodes of the X-direction end and moving, the moving direction is the positive direction of the X axis, and the moving distance can be Lc/2NxAnd Lc/Nx. The nodes of the left end face are obtained by copying the nodes of the first row and the second row at the starting end in the Y-axis direction and then moving along the Y direction, the moving direction is the negative direction of the Y axis, and the moving distance of the first row at the starting end can be b/NyThe moving distance of the second row of the starting end can be 2b/Ny. The node on the right end face is obtained by copying the last two rows of nodes at the end in the Y-axis direction and then moving along the Y direction, the moving direction is the positive direction of the Y axis, and the moving distance of the first row can be b/NyThe second row may have a moving distance of 2b/NyThe resulting four end nodes are shown in dashed boxes in fig. 8.
Step 12, constructing four end face units by the nodes;
a unit is constructed by 8 nodes, and for the nodes stored in the directions of Z, Y and X, the node index of the unitnodeiFour end faces, which can be calculated according to equation (10)The unit is shown in fig. 9.
Step 13, calculating the grid number of the notch intervals in the Y direction;
the grid number of the intervals of the notches in the Y direction is calculated by the width of the notches and the grid number of a single notch, and can be calculated according to the formula (11).
Step 14, setting a transition area;
and respectively determining the Y-direction index and the Z-direction index of the grooving area unit according to the number of the grooving interval units in the Y direction and the number of the grooving units in the Z direction, and setting all units meeting the Y-direction index and the Z-direction index in the units as transition areas.
Step 15, calculating the number of units in the Z direction of the melting area and the number of units in the width of the melting area;
the number H of units in the Z direction of the melting zone is calculated from the formula (12)m。
Hm＝Nz-Hz(12)
The number of cells N in the width of the melting zone is calculated from equation (13)m。
Nm＝NS0(13)
Step 16, setting a melting area;
and respectively determining the Y-direction index and the Z-direction index of the melting area unit according to the number of the Y-direction grooving interval units and the number of the Z-direction grooving units, and setting all units meeting the Y-direction index and the Z-direction index in the units as melting areas.
Step 17, deleting the defective area unit;
and respectively determining the Y-direction index and the Z-direction index of the defective area unit according to the number of the Y-direction grooving interval units and the number of the Z-direction grooving units, setting all units meeting the Y-direction index and the Z-direction index in the units as defective areas, and deleting the defective area units.
Step 18, output unit and node;
the node and unit information of the output grid can be formatted according to the format requirements of different resolvers.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A flat finite element mesh parametric modeling method for processing diamond patterns by high energy beams is characterized by comprising the following steps:
constructing a rhombohedral grid by using nodes to finish the division of a flat grid containing high-energy beam slot lines;
step two, four end faces around the flat grid are filled;
determining the number of units in the defect area of the high-energy beam slot line according to the proportional relation between the high-energy beam slot line and the width and height directions of the flat plate;
deleting the area grids of the high-energy beam slot line defect area along the width direction and the height direction of the flat plate respectively to complete modeling;
and step four, outputting node and unit information of the grid according to the format requirement of the finite element software.
2. The parametric modeling method for finite element meshes of a plate with a diamond-shaped pattern processed by high energy beams as claimed in claim 1, wherein the length direction of the plate is taken as the X direction, and the specific method of the step one comprises the following steps:
101, calculating X, Y subdivision numbers in a Z direction under a Cartesian coordinate system, and setting the subdivision number in the Z direction;
102, generating nodes according to the X, Y and the subdivision number in the Z direction;
103, moving the node along the positive X direction, so that the connecting line of the moving node and the adjacent node in the Y direction forms a half of the grooving angle with the X direction;
104, determining a grid area of the high-energy beam groove line in the Z direction according to the groove depth, the plate thickness and the Z direction section;
105, moving the node in the Z direction to enable the depth of the node at the bottom of the groove to be consistent with that of the notch groove; meanwhile, moving the node in the Z direction to enable the upper-layer node of the slot line defect area to be consistent with the height of the defect area;
and 106, constructing a diamond unit by using the nodes to obtain a diamond hexahedron grid containing the high-energy beam slot line.
3. The method for modeling a flat finite element mesh with a diamond pattern processed by high energy beams according to claim 2, wherein the specific method in the second step is as follows:
step 201, two end faces in the X direction: copying a starting end row and an ending end row of nodes in the X direction, and respectively moving along the positive direction and the negative direction of the X direction to obtain end surface nodes of two end surfaces; for the nodes which have moved along the X forward direction, the nodes which are copied and moved by the starting end column or the ending end column after copying and moving are collinear;
two end faces in the Y direction: copying two columns of nodes of a starting end and two columns of nodes of an ending end in the Y direction, and respectively moving along the positive direction and the negative direction of the Y direction to obtain end surface nodes of two end surfaces;
and 202, constructing end face units of four end faces by the nodes.
4. The method for parameterizing the finite element mesh of a slab with a diamond-shaped pattern processed by high energy beams of claim 3, wherein the moving method of the step 201 comprises the following steps:
in the X direction: taking L as the moving distance of the starting end column and the ending end columnc/2NxThe moving distance after copying the node which has moved in the X direction is taken as Lc/Nx，LcIs the length of the plate, NxIs the fraction in the X direction;
in the Y direction: the moving distance of the first column at the starting end and the last column at the ending end can be b/NyThe moving distance of the second row of the starting end and the second row of the ending end is 2b/NyB is the width of the plate, NyIs the fraction in the Y direction.
5. The method of parametric modeling of high energy beam machined diamond patterned flat finite element mesh as claimed in claim 3 wherein said step 202 of constructing end face elements from nodes is by: 8 nodes construct a unit, and the nodes and the node index are stored according to the directions of z, y and xnodeiThe calculation is as follows, i, j, k are node indexes of X, Y, Z directions respectively, NxIs the fraction in the X direction, NyIs a fraction in the Y direction, NzIs the section in the Z direction, and is the section in the Z direction,
6. the method for modeling a flat finite element mesh with a diamond pattern processed by high energy beams according to claim 1, wherein the specific method in the third step is as follows:
step 301, determining a transition area unit according to the number of the notching interval units in the Y direction and the number of the notching units in the Z direction;
step 302, determining a melting area unit according to the number of the interval units of the groove in the Y direction and the number of the groove units in the Z direction;
step 303, determining the defective area unit according to the number of the spacing units for notching in the Y direction and the number of the notching units in the Z direction.
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