CN107577894B - Real-time binary encryption-decryption method for quadrilateral unit - Google Patents
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Abstract
The invention belongs to the field of finite element simulation, and particularly relates to a quadrilateral unit real-time encryption-decryption method oriented to a calculation process, which is used for improving the calculation efficiency of sheet stamping finite element simulation based on quadrilateral units. The invention comprises a quadrilateral unit binary encryption method and a quadrilateral unit encryption method, wherein the quadrilateral unit binary encryption method comprises the following steps of (1): judging initial encryption; step (2): judging supplementary encryption; and (3): judging the unit dividing direction; and (4): and (4) dividing the unit. The quadrilateral unit encryption method comprises the following steps of (1): carrying out decryption judgment; step (2): and merging the units. The method is applied to the finite element simulation of sheet stamping, the grid density in the finite element calculation process can be adjusted in real time, the grids are automatically encrypted when the material flows through the edge folding area of the die, and the grids are automatically encrypted when the material flows through the gentle area of the die, so that the number of units in the calculation process is reduced, and the calculation efficiency is improved.
Description
Technical Field
The invention belongs to the field of finite element simulation, and particularly relates to a real-time dichotomous encryption-decryption method for quadrilateral units, which can be used for carrying out real-time adjustment based on quadrilateral mesh density in the sheet stamping simulation process.
Background
With the development of finite element theory and computer technology, Computer Aided Engineering (CAE) technology and software have gradually become a powerful tool for engineering designers to engage in product research and development. The quadrilateral unit is taken as a mainstream sheet unit and is widely applied to the field of simulation of stamping and forming of plates. Finite element models of actual engineering are more and more complex, and meshing is an important link for accurately reflecting the finite element models. The grid size and number directly affect the calculation accuracy and calculation scale, generally speaking, the smaller the cell grid size, the more the finite element model accuracy and calculation accuracy increase, and the more the cell number increases, the more the calculation time and calculation cost increase.
Patent CN105373672A discloses a method for real-time encryption-decryption of quadrilateral cells, which divides the cells to be divided into four small cells, and adjusts the grid density of the quadrilateral cells, and the method can adjust the grid density in real time, and because of the four-division type addition-subtraction-decryption method, the method has high calculation accuracy, and the calculation efficiency is greatly improved compared with the conventional method. However, further research shows that the calculation amount of the real-time encryption-decryption method for the quadrilateral unit in the patent is still large, so that the calculation cost is high, and in the stamping simulation process of large plates, because the calculation time and the calculation accuracy are high, the calculation time and the calculation cost required by the method are still large, and the actual requirements cannot be met.
Aiming at the technical problems, a set of time-saving, efficient and high-precision grid density real-time adjustment method is not found at present, and how to solve the technical difficulties is the problem to be solved by the invention.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides a real-time binary encryption-decryption method for a quadrilateral unit, which is designed based on the characteristic that the size of a grid is in direct proportion to both the simulation precision and the calculated amount in the field of the current finite element simulation, particularly the method for carrying out binary encryption-decryption on the quadrilateral unit is researched and designed aiming at the judgment aspect of the encryption direction in the method, and the aspects of grid division, the calculation process and the like in the whole method are also researched and designed, so that the problems of insufficient grid precision and large calculated amount in the finite element simulation can be effectively solved, and meanwhile, the method has the advantages of simple calculation method, low calculation cost and the like, and is particularly suitable for the field of the finite element simulation of plate stamping.
In order to achieve the purpose, the invention provides a quadrilateral unit real-time encryption-decryption method oriented to a calculation process, which is used for improving the calculation efficiency of sheet stamping finite element simulation based on quadrilateral units.
The technical scheme adopted by the invention is as follows: setting the highest encryption level of a unit as N, and setting the encryption level i of an initial unit as 0; adopting quadrilateral unit grids with larger sizes at the initial stage of calculation; with the calculation, the real-time encryption of the quadrilateral grids is carried out during severe deformation; when the encrypted area is not in the grid requiring high density, the encrypted cells are decrypted in real time.
According to one aspect of the invention, a real-time binary encryption method for a quadrilateral unit is provided, which is characterized by comprising the following steps:
step (1) initial encryption judgment:
step (1-1): taking a plate model as an analysis object, recording that the current plate comprises m quadrilateral units which are respectively a 1 st unit, a 2 nd unit, … and an m th unit, and setting a set U as a { 1 st unit, a 2 nd unit, … and an m th unit }; establishing a unit set to be encrypted, wherein the unit set to be encrypted is an empty set; setting j to 1; setting the highest encryption level as N;
step (1-2): if the encryption level of the j unit is N-1 and the j unit does not belong to the unit set to be encrypted, executing the step (1-3), otherwise, executing the step (1-5);
step (1-3): if the included angle between the jth unit and any one of the adjacent units is larger than the included angle critical value, and the encryption level of the adjacent unit is equal to that of the jth unit, adding the jth unit and the adjacent unit to the unit set to be encrypted, and executing the step (1-5); if the included angle between the jth unit and any adjacent unit is larger than the included angle critical value, and the encryption level of the adjacent unit is equal to the highest encryption level N, adding the jth unit to the unit set to be encrypted, and executing the step (1-5); otherwise, executing the step (1-4);
step (1-4): if the warping angle of the jth unit is larger than the critical value of the warping angle, adding the jth unit to the unit set to be encrypted;
step (1-5): if j < m, let j equal j +1, execute step (1-2); otherwise, adding 1 to the encryption levels of all units belonging to the unit set to be encrypted, recording the number of elements of the unit set to be encrypted as s, and executing the step (2);
and (2) supplementary encryption judgment:
step (2-1): marking the supplemental encryption flag as false; defining a supplementary encryption candidate set, wherein the supplementary encryption candidate set is a complement of the unit set to be encrypted in the set U, and the supplementary encryption candidate set comprises (m-s) elements which are a 1 st candidate unit, a 2 nd candidate unit, … and an (m-s) th candidate unit respectively; for the kth candidate unit, setting k to 1;
step (2-2): if the encryption level of the kth alternative unit is N-1 and other nodes except the two end points of the edge exist on any 2 non-adjacent edges, adding the kth alternative unit to the unit set to be encrypted, adding 1 to the encryption level of the kth alternative unit, and marking the supplementary encryption mark as true;
step (2-3): if k < (m-s), making k equal to k +1, and executing the step (2-2); otherwise, executing the step (2-4);
step (2-4): adding the alternative unit marked as true by the supplementary encryption into the unit set to be encrypted, updating the element number s of the unit set to be encrypted, and executing the step (3);
and (3): judging the unit dividing direction:
step (3-1): the s elements in the unit set to be encrypted are respectively marked as a 1 st unit to be encrypted, a 2 nd unit to be encrypted, … and an s th unit to be encrypted; setting i to 1 for the ith unit to be encrypted;
step (3-2): if no other nodes exist on the 4 edges of the ith cell to be encrypted except the two edge end points, executing the step (3-3); otherwise, executing the step (4);
step (3-3): respectively recording included angles of an ith unit to be encrypted and 4 units adjacent to the ith unit, and recording the included angles as < 1 >, < 2 >, < 3 > and < 4 > in a clockwise direction; if the angle is (& lt 1 & plus & lt 3) & gt (& lt 2 & plus & lt 4), dividing the shared edges of two adjacent units with the included angles of & lt 2 & gt and & lt 4 & gt respectively with the ith unit to be encrypted into two parts; otherwise, dividing the common edge of two adjacent units which respectively have included angles of & lt 1 & gt and & lt 3 & gt with the ith unit to be encrypted into two parts;
step (3-4): if i < s, let i become i +1, and execute step (3-2); otherwise, executing the step (4);
and (4): and partitioning units in the aggregation unit to be encrypted.
Specifically, the unit needing encryption is preliminarily determined through initial encryption judgment, the encryption units which do not meet the encryption condition are further subjected to supplementary encryption judgment, and the units which meet the encryption condition are selected, so that the final accurate encryption unit is obtained. The invention creatively provides that binary encryption is adopted, the judgment of the encryption direction is crucial, and the units are divided after the judgment of the encryption direction is carried out on each encryption unit. The method of the invention can accurately divide the meshes in the finite element simulation model according to the shape characteristics of the model, greatly reduces the calculated amount, improves the efficiency of the finite element simulation and reduces the cost.
Further preferably, in the step (1-3) and the step (3-3), the included angle between the units is the included angle between the normal vectors of the two quadrilateral units.
Preferably, in the step (1-4), the warping angle is calculated as follows: dividing a quadrilateral unit into two triangular units by taking one diagonal line of the quadrilateral unit as a boundary, and recording an included angle of normal vectors of the two triangular units as ^ 1; the quadrilateral unit is divided into two triangular units again by the other diagonal line of the quadrilateral unit, and the included angle of the normal vectors of the two triangular units is marked as < 2; the larger value of the angle 1 and the angle 2 is the warping angle of the quadrilateral unit.
Preferably, the step (4) is to divide the units in the unit to be encrypted, and take the quadrilateral units in the unit set to be encrypted as quadrilateral mother units; if no other node exists on any edge of the quadrilateral mother unit except the two end points of the edge, adding a middle node at the middle point of the two edges of the mother unit which need to be equally divided according to the step (3-3); if a middle node exists on one edge in the quadrilateral mother unit, adding the middle node at the midpoint position of the non-adjacent edge of the edge; if some two non-adjacent edges in the quadrilateral mother unit respectively have intermediate nodes; connecting the two intermediate nodes, and dividing the quadrilateral mother unit into two quadrilateral child units; the coordinate, the speed and the displacement of the middle node are the average values of two end point nodes of the edge where the quadrilateral mother unit is located; the stress, strain, thickness and material parameters of the quadrilateral sub-unit are the same as those of the quadrilateral mother unit.
According to another aspect of the present invention, there is provided a real-time binary reduction method for quadrilateral elements, comprising the following steps:
step (1): and (3) judging the encryption condition:
step (1-1): taking a plate model as an analysis object, recording that a current plate comprises p unit clusters, namely a 1 st unit cluster, a 2 nd unit cluster, … and a p th unit cluster, wherein any one unit cluster comprises 2 quadrilateral units; establishing a unit set to be subjected to density reduction, wherein the unit set to be subjected to density reduction is an empty set; setting n to 1;
step (1-2): if each quadrilateral unit in the nth unit cluster has the encryption level more than or equal to the encryption level of all units adjacent to the quadrilateral unit; and the included angle between each quadrilateral unit in the nth unit cluster and all adjacent units thereof is less than the included angle critical value; and the relative difference value of the main strains of the two quadrilateral units in the nth unit cluster is smaller than the critical value of the relative difference value of the main strains, adding the two quadrilateral units in the nth unit cluster to the unit set to be encrypted;
step (1-3): if n < p, let n be n +1, perform step (1-2); otherwise, executing the step (2);
step (2): and subtracting 1 from the encryption level of the unit in the unit set to be encrypted, and performing unit combination.
Specifically, in the binary reduction method of the invention, when the encrypted grids flow through an area with a simpler shape and a smoother deformation, the unit grids meeting the conditions are reduced according to the judgment of the size of the included angle between adjacent quadrilateral units, and the number of the grids is reduced to improve the calculation efficiency.
Preferably, the unit cluster is composed of 2 quadrilateral units with the same encryption level, the encryption level of the two quadrilateral units is the highest encryption level N, and the two quadrilateral units are obtained by encrypting the same quadrilateral mother unit with the encryption level N-1.
Preferably, in the step (1-2), the included angle between the units is the included angle between the normal vectors of the two quadrilateral units; the critical value of the included angle is preset.
Preferably, in the step (1-2), the relative difference of the principal strains of the two quadrilateral units is the absolute value of the difference of the principal strains of the two quadrilateral units divided by the smaller value of the principal strains of the two quadrilateral units; and presetting the relative difference critical value of the main strain.
Preferably, in the step (2), the unit merging is to take two quadrilateral units in the unit cluster as sub-units; the nodes in the unit cluster comprise 2 edge nodes and 4 corner nodes, wherein the edge nodes are nodes common to the two subunits, and the corner nodes are nodes unique to each of the two subunits; when the units are combined, if the edge nodes are the nodes of other adjacent units, the edge nodes are converted into unconventional nodes, and if not, the edge nodes are deleted; the four corner nodes form a new quadrilateral mother unit; and the stress, strain, thickness and material parameters of the quadrilateral mother unit are the average values of the stress, strain, thickness and material parameters of the two quadrilateral child units.
Generally, compared with the prior art, the technical scheme of the invention has the following advantages and beneficial effects:
(1) the invention provides a real-time dichotomous encryption-decryption method for quadrilateral elements, which is based on the characteristic that the size of a grid is in direct proportion to both simulation precision and calculated amount in the field of finite element simulation at present, and correspondingly designs a dichotomous encryption-decryption method for quadrilateral elements, particularly researches and designs on the judgment aspect of encryption direction in the method, and researches and designs on the aspects of grid division, calculation process and the like of the whole method.
(2) In the finite element calculation process, quadrilateral unit grids are segmented and combined in real time; when the blank flows through an area with a complex shape and severe deformation, the unit grids are subjected to dichotomy encryption, and the initial grids with larger size are divided into sufficiently fine grids to improve the calculation accuracy; when the encrypted grids flow through the area with simpler shape and smoother deformation, the unit grids are encrypted, and the number of the grids is reduced to improve the calculation efficiency. The real-time encryption and decryption of the grids in the same area are continuously carried out along with the finite element calculation, so that the calculation accuracy is ensured, the calculation efficiency is improved, and the calculation time and the calculation cost are reduced.
(3) The quadrilateral unit real-time binary encryption method preliminarily determines the units needing encryption through initial encryption judgment, further performs supplementary encryption judgment on the encryption units which do not meet encryption conditions, and selects the units meeting the encryption conditions, thereby obtaining the final accurate encryption units. The invention creatively provides that binary encryption is adopted, the judgment of the encryption direction is crucial, and the units are divided after the judgment of the encryption direction is carried out on each encryption unit. The method of the invention can accurately divide the meshes in the finite element simulation model according to the shape characteristics of the model, greatly reduces the calculated amount, improves the efficiency of the finite element simulation and reduces the cost.
(4) In the real-time dichotomy type encryption method for the quadrilateral units, when the encrypted grids flow through the area with simpler shape and more gentle deformation, the unit grids meeting the conditions are encrypted according to the judgment of the size of the included angle between the adjacent quadrilateral units, and the number of the grids is reduced so as to improve the calculation efficiency.
Drawings
FIG. 1 is a schematic diagram of encryption levels and non-regular nodes;
FIG. 2(a) shows the initial encryption determination based on the angle between adjacent units when the encryption level of the adjacent units is (N-1); FIG. 2(b) shows the initial encryption determination based on the angle between adjacent units when the encryption level of the adjacent units is N;
FIG. 3 is a block diagram of a unit with encryption level (N-1) determining encryption based on a warp angle;
FIG. 4 is a block supplemental encryption of two non-adjacent edges with non-regular nodes;
FIGS. 5(a) and (b) are diagrams illustrating the judgment of the encryption direction based on the angle between the units when the encryption level of the adjacent unit is (N-1);
FIGS. 6(a) and (b) are schematic diagrams of quadrilateral element binary encryption-decryption at an adjacent element encryption level of (N-1); FIG. 6(c) is a schematic diagram of quad cell binary encryption-decryption at an adjacent cell encryption level of N;
FIGS. 7(a) and (b) are initial and final sheet units of a U-piece drawing model using a quarter cell encryption-decryption method; FIGS. 7(c) and (d) are initial and final sheet units of a U-shaped drawing model using a quadrilateral unit real-time binary encryption-decryption method;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Examples
FIG. 1 is a schematic diagram of an encryption level and an irregular node, as shown in FIG. 1, with a "O" at the intersection indicating an irregular node and an N-level encryption unit being the highest encryption level unit; the (N-1) level encryption unit is a binary pre-encryption unit or a binary post-encryption unit; if a certain node is the node of all the adjacent units, the node is a regular node, otherwise, the node is called a non-regular node; in the finite element simulation calculation process, the coordinates of all the unconventional nodes are the average value of the coordinates of the conventional nodes on two sides.
The following is a detailed description of the process and significance of encryption-decryption in connection with drawing simulations of a simple U-shaped piece. During the drawing process of the U-shaped piece, the fillet area of the U-shaped piece requires mesh refinement, and the mesh refinement requirement in other areas is relatively low. In order to highlight the advantages of the binary real-time encryption-decryption method of the invention, the embodiment adopts two schemes for comparison: scheme 1 adopts the existing quadripartion grid encryption-decryption method, and scheme 2 adopts the dichotomy real-time encryption-decryption method. In the present embodiment 1 and 2, the highest encryption level N is set to 2, and the angle threshold θ is set0＝5°，θ1＝1.5θ0Critical value of the warp angle α0＝4°，α1＝1.1α0Relative difference of principal strain Δ1＝6％，Δ2＝1.25Δ1. The encryption mode of the scheme 1 is the same as that of the scheme 2 when the encryption level is 1, and the unit grid four-division encryption is adopted.
The 2-level encryption and quadrilateral unit real-time dichotomous encryption method in the scheme 2 comprises the following steps:
step (1) initial encryption judgment:
step (1-1): taking a plate model as an analysis object, recording that the current plate comprises m quadrilateral units which are respectively a 1 st unit, a 2 nd unit, … and an m th unit, and setting a set U as a { 1 st unit, a 2 nd unit, … and an m th unit }; establishing a unit set to be encrypted, wherein the unit set to be encrypted comprises s elements, and setting s as 0, and setting the unit set to be encrypted as an empty set; traversing the units in the set U from the j-th to 1-th unit;
step (1-2): if the encryption level of the j unit is 1 and the j unit does not belong to the unit set to be encrypted, executing the step (1-3), otherwise, executing the step (1-5);
step (1-3): if the included angle between the jth unit and any one of the adjacent units is larger than the included angle critical value theta1And the encryption level of the adjacent unit is equal to the encryption level 1 of the j unit, the j unit and the adjacent unit are added to the unit to be encryptedGathering, and executing the step (1-5); if the included angle between the jth unit and any adjacent unit is larger than the included angle critical value theta1And the encryption level of the adjacent unit is equal to the highest encryption level 2, adding the j unit to the unit set to be encrypted, and executing the step (1-5); otherwise, executing the step (1-4); as shown in FIG. 2(a), the encryption levels of the cells E1 and E2 are both 1, and when the initial encryption judgment is performed on the cell E1, if the included angle between the cells E1 and E2 is greater than the included angle threshold value θ1Then add both units E1, E2 to the set of units to be encrypted; as shown in FIG. 2(b), the encryption level of the cell E3 is 1, the encryption levels of the cells E4 and E5 are 2, and if the initial encryption judgment is made for the cell E3, the angle between the cells E3 and E4 (or E5) is larger than the angle threshold value θ1Then only element E3 is added to the set of elements to be encrypted.
Step (1-4): if the warpage angle of the jth cell is larger than the warpage angle threshold value alpha1Adding the j unit to the unit set to be encrypted; as shown in FIG. 3, a quad cell with encryption level 1 has two diagonals, and is divided into two triangle cells with one diagonal as a boundary, and the normal vectors of the two triangle cells
And
the included angle is marked as < 1; subdividing the quadrilateral unit into two triangular units with the other diagonal of the quadrilateral unit, wherein the normal vectors of the two triangular units
And
the included angle is marked as < 2; the larger value of the angle 1 and the angle 2 is the warping angle of the quadrilateral unit, and if the warping angle of the quadrilateral unit is larger than alpha1If the quadrilateral unit meets the encryption condition, adding the quadrilateral unit to be encryptedAnd (5) collecting the units.
Step (1-5): if j < m, let j equal j +1, execute step (1-2); otherwise, adding 1 to the encryption levels of all units belonging to the unit set to be encrypted, recording the number of elements of the unit set to be encrypted as s, and executing the step (2);
and (2) supplementary encryption judgment:
step (2-1): marking the supplemental encryption flag as false; defining a supplementary encryption candidate set, wherein the supplementary encryption candidate set is a complement of the unit set to be encrypted in the set U, and the supplementary encryption candidate set comprises (m-s) elements which are a 1 st candidate unit, a 2 nd candidate unit, … and an (m-s) th candidate unit respectively; traversing units in the supplementary encryption candidate set from the k-1 candidate unit;
step (2-2): if the encryption level of the kth alternative unit is 1 and other nodes except the two end points of the edge exist on any 2 non-adjacent edges, adding the kth alternative unit to the unit set to be encrypted, adding 1 to the encryption level of the kth alternative unit, and marking the supplementary encryption mark as true; as shown in fig. 4, the element E6 is subjected to the complementary encryption judgment, and the element E6 has irregular nodes on only two non-adjacent edges, so the element E6 is added to the set of elements to be encrypted;
step (2-3): if k < (m-s), making k equal to k +1, and executing the step (2-2); otherwise, executing the step (2-4);
step (2-4): adding the alternative unit marked as true by the supplementary encryption into the unit set to be encrypted, updating the element number s of the unit set to be encrypted, and executing the step (3);
and (3): judging the unit dividing direction:
step (3-1): the s elements in the unit set to be encrypted are respectively marked as a 1 st unit to be encrypted, a 2 nd unit to be encrypted, … and an s th unit to be encrypted; traversing units in the unit set to be encrypted from the unit to be encrypted with the ith-1;
step (3-2): if no other nodes exist on the 4 edges of the ith cell to be encrypted except the two edge end points, executing the step (3-3); otherwise, executing the step (4);
step (3-3): respectively recording included angles of an ith unit to be encrypted and 4 units adjacent to the ith unit, and recording the included angles as < 1 >, < 2 >, < 3 > and < 4 > in a clockwise direction; if (. sub.1 +. sub.3)>(less than 2 plus less than 4), dividing the shared edges of two adjacent units which respectively have included angles of less than 2 and less than 4 with the ith unit to be encrypted into two parts; otherwise, dividing the common edge of two adjacent units which respectively have included angles of & lt 1 & gt and & lt 3 & gt with the ith unit to be encrypted into two parts; as shown in fig. 5(a) and (b), the cell E7 is a cell to be encrypted, the encryption level of the cells E7, E8, E9, E10, E11 is 1, the angle between the cell E7 and the adjacent cell is the angle between the normal vectors of the cells,
and
the included angle of (c) is marked as < 1,
and
the included angle of (c) is marked as < 2,
and
the included angle of (c) is marked as < 3,
and
the included angle is marked as < 4, if (< 1 plus < 3)>(. 2+ less 4), the division direction of cell E7 is as shown in fig. 5(a) and (b);
step (3-4): if i < s, let i become i +1, and execute step (3-2); otherwise, executing the step (4);
and (4): and partitioning the units in the aggregation unit to be encrypted, wherein the unit partitioning mainly processes topological change and physical quantity information distribution in the encryption process of the units. As shown in FIGS. 6(a) and (b), a quadrilateral element E7 belongs to an element in the set of elements to be encrypted and is composed of nodes N1-N4; when the unit is divided, a quadrilateral unit E7 is used as a mother unit, a node N5 is newly added to the edge where the nodes N1 and N2 are located, the coordinate, the speed and the displacement of the node N5 are the average values of N1 and N2, and the coordinate, the speed and the displacement of a node N6 and N6 are newly added to the edge where the nodes N3 and N4 are located are the average values of N3 and N4 according to the dividing direction; the nodes N1-N6 form two sub-units E12 and E13 which are arranged in a structure like a Chinese character 'ri', and the stress, strain, thickness and material parameters of the two sub-units are the same as those of the mother unit E7. As shown in FIG. 6(c), the unit E14 is a unit to be encrypted and is composed of nodes N7-N10, wherein an edge has an unconventional node N11; when the cell is divided, the cell E14 is used as a mother cell, a node N12 is newly added at the middle point of the opposite side of the node N11, and the coordinate, the speed and the displacement of the node N12 are the average values of the node N8 and the node N9; the nodes N7-N12 form two sub-units E15 and E16 which are arranged in a structure like a Chinese character 'ri', and the stress, strain, thickness and material parameters of the two sub-units are the same as those of the mother unit E14. As shown in FIG. 4, the element E6 is an element to be encrypted, one side of the element has unconventional nodes, when the element is divided, the element E6 is used as a mother element, one side is added between the unconventional nodes, the element E6 is divided into two sub-elements arranged in a structure like a Chinese character 'ri', and the stress, strain, thickness and material parameters of the sub-elements are the same as those of the mother element E6.
In the scheme 2, the binary reduction method is adopted when the first-stage reduction is performed on the quadrilateral unit, and the method specifically comprises the following steps:
step (1): and (3) judging the encryption condition:
step (1-1): taking a plate model as an analysis object, recording that a current plate comprises p unit clusters, namely a 1 st unit cluster, a 2 nd unit cluster, … and a p th unit cluster, wherein any one unit cluster comprises 2 quadrilateral units; establishing a unit set to be subjected to density reduction, wherein the unit set to be subjected to density reduction is an empty set; starting from the n-1 unit cluster; as shown in fig. 6(a) and (b), the encryption levels of the cells E12 and E13 are 2, and the cells E12 and E13 constitute a cell cluster, which is obtained from a mother cell E7 having an encryption level of 1;
step (1-2): if each quadrilateral unit in the nth unit cluster has the encryption level more than or equal to the encryption level of all units adjacent to the quadrilateral unit; and the included angle between each quadrilateral unit in the nth unit cluster and all adjacent units thereof is less than the included angle critical value theta1(ii) a And the relative difference value of the main strains of the two quadrilateral units in the nth unit cluster is smaller than the critical value delta of the relative difference value of the main strains2Adding two quadrilateral units in the nth unit cluster to the unit set to be encrypted; as shown in fig. 6(a) and (b), the encryption levels of the quadrilateral elements E12 and E13 are 2, and are equal to or greater than the encryption level 1 of the adjacent elements E8 to E11; if the included angles between the unit E12 and the units E8, E9 and E10, the included angles between the unit E13 and the units E8, E10 and E11, and the included angles between the units E12 and E13 are all smaller than the threshold value theta1And the relative difference in principal strain between the cells E12 and E13 is less than the critical value Δ2Then the two quadrilateral cells E12 and E13 in the cell cluster are added to the set of cells to be reduced.
Step (1-3): if n < p, let n be n +1, perform step (1-2); otherwise, executing the step (2);
step (2): and subtracting 1 from the encryption level of the unit in the unit set to be encrypted, merging the units, and processing unit topology change and physical quantity information distribution in the encryption process of the main processing unit by merging the units. As shown in fig. 6(c), two quadrilateral elements E15 and E16 in the unit cluster are regarded as sub-units; the nodes in the unit cluster comprise edge nodes N11 and N12 and corner nodes N7-N10; when the units are combined, the edge node N12 is deleted, the edge node N11 is the node of other adjacent units, the edge node N11 is converted into an unconventional node, and the corner nodes N7-N10 form a new quadrilateral mother unit E14; the stress, strain, thickness and material parameters of the quadrangular mother cell E14 are the average values of the stress, strain, thickness and material parameters of the two quadrangular child cells E15 and E16.
The two-stage reduction process of the scheme 1 and the second-stage reduction process of the scheme 2 both adopt a four-section grid reduction method.
The initial grid and the final grid for the U-shaped drawing simulation of the two schemes are respectively shown in fig. 7(a) - (b) and fig. 7(c) - (d), and the initial unit number of the plate, the maximum unit number in the whole drawing simulation analysis and calculation process and the total calculation time length are compared as follows:
| | Scheme | 1 | Scheme 2 |
| Initial number of units | 1681 | 1681 | |
| Maximum number of cells | 10462 | 6077 | |
| Calculating time length | 1095.9s | 434.2s |
As shown in fig. 7(a) - (d) and the above table, the number of units can be effectively reduced and the time of simulation calculation can be shortened by using the real-time binary encryption-decryption method for quadrilateral units according to the present invention.
The invention is applied to the finite element simulation of sheet stamping, the size and the density of the quadrilateral unit can be adjusted in real time in the simulation calculation process, and when the material flows through complicated areas such as edge folding and transferring of a die, grids are automatically encrypted so as to improve the simulation accuracy; when the material flows through the gentle region of the mold, the grids are automatically densified, so that the number of units in calculation is reduced, the calculation efficiency is improved, and the calculation time is effectively reduced.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (9)
1. A real-time dichotomy encryption method for quadrilateral units is characterized by comprising the following steps:
step (1) initial encryption judgment:
step (1-1): taking a plate model as an analysis object, recording that the current plate comprises m quadrilateral units which are respectively a 1 st unit, a 2 nd unit, … and an m th unit, and setting a set U as a { 1 st unit, a 2 nd unit, … and an m th unit }; establishing a unit set to be encrypted, wherein the unit set to be encrypted is an empty set; setting j to 1; setting the highest encryption level as N;
step (1-2): if the encryption level of the j unit is N-1 and the j unit does not belong to the unit set to be encrypted, executing the step (1-3), otherwise, executing the step (1-5);
step (1-3): if the included angle between the jth unit and any one of the adjacent units is larger than the included angle critical value, and the encryption level of the adjacent unit is equal to that of the jth unit, adding the jth unit and the adjacent unit to the unit set to be encrypted, and executing the step (1-5); if the included angle between the jth unit and any adjacent unit is larger than the included angle critical value, and the encryption level of the adjacent unit is equal to the highest encryption level N, adding the jth unit to the unit set to be encrypted, and executing the step (1-5); otherwise, executing the step (1-4);
step (1-4): if the warping angle of the jth unit is larger than the critical value of the warping angle, adding the jth unit to the unit set to be encrypted;
step (1-5): if j < m, let j equal j +1, execute step (1-2); otherwise, adding 1 to the encryption levels of all units belonging to the unit set to be encrypted, recording the number of elements of the unit set to be encrypted as s, and executing the step (2);
and (2) supplementary encryption judgment:
step (2-1): marking the supplemental encryption flag as false; defining a supplementary encryption candidate set, wherein the supplementary encryption candidate set is a complement of the unit set to be encrypted in the set U, and the supplementary encryption candidate set comprises (m-s) elements which are a 1 st candidate unit, a 2 nd candidate unit, … and an (m-s) th candidate unit respectively; for the kth candidate unit, firstly setting k to 1;
step (2-2): if the encryption level of the kth alternative unit is N-1 and other nodes except the two end points of the edge exist on any 2 non-adjacent edges, adding the kth alternative unit to the unit set to be encrypted, adding 1 to the encryption level of the kth alternative unit, and marking the supplementary encryption mark as true;
step (2-3): if k < (m-s), making k equal to k +1, and executing the step (2-2); otherwise, executing the step (2-4);
step (2-4): adding the alternative unit marked as true by the supplementary encryption into the unit set to be encrypted, updating the element number s of the unit set to be encrypted, and executing the step (3);
and (3): judging the unit dividing direction:
step (3-1): the s elements in the unit set to be encrypted are respectively marked as a 1 st unit to be encrypted, a 2 nd unit to be encrypted, … and an s th unit to be encrypted; for the ith unit to be encrypted, firstly setting i to 1;
step (3-2): if no other nodes exist on the 4 edges of the ith cell to be encrypted except the two edge end points, executing the step (3-3); otherwise, executing the step (4);
step (3-3): respectively recording included angles of an ith unit to be encrypted and 4 units adjacent to the ith unit, and recording the included angles as < 1 >, < 2 >, < 3 > and < 4 > in a clockwise direction; if the angle is (& lt 1 & plus & lt 3) & gt (& lt 2 & plus & lt 4), dividing the shared edges of two adjacent units with the included angles of & lt 2 & gt and & lt 4 & gt respectively with the ith unit to be encrypted into two parts; otherwise, dividing the common edge of two adjacent units which respectively have included angles of & lt 1 & gt and & lt 3 & gt with the ith unit to be encrypted into two parts;
step (3-4): if i < s, let i become i +1, and execute step (3-2); otherwise, executing the step (4);
and (4): partitioning units in the set unit to be encrypted;
the real-time dichotomy type encryption method for the quadrilateral units is applied to sheet stamping finite element simulation, the size and the density of the quadrilateral units can be adjusted in real time in the simulation calculation process, and when a material flows through a die flanging area or a transfer area, grids are automatically encrypted so as to improve the simulation precision; the real-time quadrilateral unit binary encryption method divides meshes in the finite element model according to the shape characteristics of the model.
2. A real-time binary encryption method for quadrilateral elements according to claim 1, wherein in the steps (1-3) and (3-3), the included angle between the element to be encrypted and its adjacent element is the included angle between the normal vectors of the two quadrilateral elements.
3. The real-time binary encryption method for quadrilateral elements according to claim 1, wherein in the steps (1-4), the warping angle is calculated as follows: dividing a quadrilateral unit into two triangular units by taking one diagonal line of the quadrilateral unit as a boundary, and recording an included angle of normal vectors of the two triangular units as ^ 1; the quadrilateral unit is divided into two triangular units again by the other diagonal line of the quadrilateral unit, and the included angle of the normal vectors of the two triangular units is marked as < 2; the larger value of the angle 1 and the angle 2 is the warping angle of the quadrilateral unit.
4. The real-time binary encryption method for quadrilateral elements according to claim 1, wherein said step (4) divides the elements in the set of elements to be encrypted, taking quadrilateral elements in the set of elements to be encrypted as quadrilateral parent elements; if no other node exists on any edge of the quadrilateral mother unit except the two end points of the edge, adding a middle node at the middle point of the two edges of the mother unit which need to be equally divided according to the step (3-3); if a middle node exists on one edge in the quadrilateral mother unit, adding the middle node at the midpoint position of the non-adjacent edge of the edge; if some two non-adjacent edges in the quadrilateral mother unit respectively have intermediate nodes; connecting the two intermediate nodes, and dividing the quadrilateral mother unit into two quadrilateral child units; the coordinate, the speed and the displacement of the middle node are the average values of two end point nodes of the edge where the quadrilateral mother unit is located; the stress, strain, thickness and material parameters of the quadrilateral sub-unit are the same as those of the quadrilateral mother unit.
5. A real-time dichotomous type encryption method for quadrilateral units is characterized by comprising the following steps:
step (1): and (3) judging the encryption condition:
step (1-1): taking a plate model as an analysis object, recording that a current plate comprises p unit clusters, namely a 1 st unit cluster, a 2 nd unit cluster, … and a p th unit cluster, wherein any one unit cluster comprises 2 quadrilateral units; establishing a unit set to be subjected to density reduction, wherein the unit set to be subjected to density reduction is an empty set; for the nth unit cluster, firstly setting n to 1;
step (1-2): if each quadrilateral unit in the nth unit cluster has the encryption level more than or equal to the encryption level of all units adjacent to the quadrilateral unit; and the included angle between each quadrilateral unit in the nth unit cluster and all adjacent units thereof is less than the included angle critical value; and the relative difference value of the main strains of the two quadrilateral units in the nth unit cluster is smaller than the critical value of the relative difference value of the main strains, adding the two quadrilateral units in the nth unit cluster to the unit set to be encrypted;
step (1-3): if n < p, let n be n +1, perform step (1-2); otherwise, executing the step (2);
step (2): subtracting 1 from the encryption level of the unit in the unit set to be encrypted, and merging the units;
the real-time binary encryption method for the quadrilateral units is applied to finite element simulation of sheet stamping, the size and the density of the quadrilateral units can be adjusted in real time in the simulation calculation process, and when the quadrilateral units encrypted according to the real-time binary encryption method for the quadrilateral units disclosed by any one of claims 1-4 on the material flow through a gentle area of a die, the encryption is automatically reduced, so that the number of units in calculation is reduced, the calculation efficiency is improved, and the calculation time is effectively reduced; the real-time quadrilateral unit binary encryption method divides meshes in the finite element model according to the shape characteristics of the model.
6. The real-time binary decryption method for quadrilateral elements according to claim 5, wherein the encryption level of the two quadrilateral elements is the highest encryption level N, and the two quadrilateral elements are obtained by encrypting the same quadrilateral mother element with the encryption level N-1.
7. The real-time binary reduction method for quadrilateral elements according to claim 5, wherein in step (1-2), the angle between the elements is the angle between the normal vectors of the two quadrilateral elements.
8. The real-time binary reduction method for quadrilateral elements according to claim 5, wherein in step (1-2), the relative difference between the principal strains of two quadrilateral elements is the absolute value of the difference between the principal strains of the two quadrilateral elements divided by the smaller of the principal strains of the two quadrilateral elements.
9. The real-time binary reduction method for quadrilateral elements according to claim 5, wherein in the step (2), the element merging is to take two quadrilateral elements in an element cluster as sub-elements; the nodes in the unit cluster comprise 2 edge nodes and 4 corner nodes, wherein the edge nodes are nodes common to the two subunits, and the corner nodes are nodes unique to each of the two subunits; when the units are combined, if the edge nodes are the nodes of other adjacent units, the edge nodes are converted into unconventional nodes, and if not, the edge nodes are deleted; the four corner nodes form a new quadrilateral mother unit; and the stress, strain, thickness and material parameters of the quadrilateral mother unit are the average values of the stress, strain, thickness and material parameters of the two quadrilateral child units.
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