CN111859763A - Finite element simulation method, system and medium - Google Patents
Finite element simulation method, system and medium Download PDFInfo
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Abstract
The invention provides a finite element simulation method, a finite element simulation system and a finite element simulation medium, wherein the finite element simulation method comprises the following steps: step 1: discretizing each boundary of the product contact area to generate an initial grid; step 2: refining the deformation area of the product based on the initial grid to obtain a reconstructed grid; and step 3: assigning a new physical field to each cell in the reconstructed mesh based on the physical field of each cell in the initial mesh; and 4, step 4: performing analog simulation on the product according to the new physical field of each unit, and improving the geometric dimension of the product; the physical fields include displacement, temperature, damage, stress and strain. The invention adaptively controls the size of the grid according to the physical understanding or the geometric shape, optimizes the finite element grid and solves the contradiction between the calculation cost and the simulation precision.
Description
Technical Field
The invention relates to the technical field of finite element simulation, in particular to a finite element simulation method, a finite element simulation system and a finite element simulation medium. And more particularly, to a finite element simulation method based on adaptive mesh reconstruction.
Background
The dies, workpieces or end products often have complex geometries during metal forming and machining, which greatly increases the contradiction between discretization accuracy and computational cost. Meanwhile, metal forming and processing are dynamic deformation processes, and the geometric shape and the physical field of a workpiece are continuously changed along with plastic deformation or damage fracture. In the large plastic deformation or damage fracture area, serious unit distortion phenomena generally exist, so that the original finite element mesh loses the capability of accurately describing the material characteristics. Therefore, the geometry of discrete complex workpieces is a challenge in the finite element simulation process. In order to accommodate the changing physical fields and geometries, it is necessary to develop an advanced method with the capability of controlling the size of the finite element mesh and optimizing the quality of the finite element mesh.
Patent document CN106960070A (201611232930.5) discloses a seepage simulation method for reconstructing a coal body based on finite element-discrete element CT, which obtains a three-dimensional data volume of the coal body through industrial CT scanning, then performs three-dimensional reconstruction and removes an "island block" to obtain a general three-dimensional geometric model that can be called by simulation software.
Disclosure of Invention
In view of the defects in the prior art, the present invention provides a finite element simulation method, system and medium.
The finite element simulation method provided by the invention comprises the following steps:
step 1: discretizing each boundary of the product contact area to generate an initial grid;
step 2: refining the deformation area of the product based on the initial grid to obtain a reconstructed grid;
and step 3: assigning a new physical field to each cell in the reconstructed mesh based on the physical field of each cell in the initial mesh;
and 4, step 4: performing analog simulation on the product according to the new physical field of each unit, and improving the geometric dimension of the product;
the physical fields include displacement, temperature, damage, stress and strain.
Preferably, the damage judgment is performed on the deformation area of the product: if the damage of the unit is larger than a preset threshold value, deleting the unit and defining a new boundary; if the damage of the unit is smaller than a preset threshold value, the grids in the deformation area are subdivided and refined;
and (3) estimating the geometric deviation of the deformation area of the product: calculating the deviation between the new geometric boundary and the current discretization boundary, and defining a geometric dimension map to perform re-discretization on the boundary according to the deviation;
and (3) estimating the physical deviation of the deformation area of the product: and calculating the deviation between the object understanding of the deformation area and the ideal solution, and defining a physical dimension map to control the reconstruction grid in the deformation area.
Preferably, the new geometric boundary includes:
free deformation: the new geometry of the deformation zone is defined only by the boundary nodes and their new positions of connection, caused by mechanical constraints;
bounded deformation: the deformed region is related to the geometry of the contacted domain.
Preferably, the nodes of free and bounded deformation are classified using the Hausdorff distance if the node belongs to the associated region R(s) then define it as a bounded, associated domain R(s) is defined as:
R(s)＝{X∈R3,d(X,s)≤}…………(1)
wherein d (X, s) represents the distance from the point X to the surface s, represents the maximum displacement of the deformation zone omega, R3Representing the interaction domain.
Preferably, if the boundary node belongs to free deformation, the size of the boundary node is in direct proportion to the curvature radius of the new region boundary or the new geometric shape; if the boundary node belongs to a bounded deformation, the size of the boundary node is proportional to the radius of curvature of the contact area of the associated region.
Preferably, the grid reconstruction is carried out in the deformation region through a map with known size, the boundaries of the reconstructed grid are uniformly controlled by utilizing a Riemann matrix M, and the measurement standard of the point P in the deformation region is determined through a 3 multiplied by 3 symmetrical positive definite matrix map MPThe definition is as follows:
wherein h is a defined dimension map, and I is a unit matrix which converts the dimension map h into a unit matrix which keeps consistent in all directions; p is a vertex in the cell mesh,
is an edge with point P as an end point, and the length of edge e is:
wherein lM(e) Is the length of the edge (e), the size map h is a matrix map MPA grid that conforms to this metric is called a cell grid; t represents time.
Preferably, the shape quality q (K) of the grid cell K is measured in the reconstruction grid, and the formula is:
wherein V (K) and e (K) respectively represent the volume and the side length of the unit K, c is a scaling coefficient, and l is the Riemann length; the value range of q (K) is 0-1, the value of the regular unit tends to 1, and the value of the irregular unit tends to 0; in Riemann space, the cell K shape quality is defined as:
q(K)＝min[qi(K)]…………(5)
in the formula, qi(K) Represents and MPThe associated cell grid quality.
Preferably, the reconstructed grid edge is processed: removing small edges, segmenting large edges, and modifying topological relation related to shape quality;
optimizing the grid cells: repositioning the vertex and modifying the topological relation according to the shape quality;
if the length of the small side is less than
Removing is carried out; if the length of one edge is greater than
It is segmented.
According to the present invention, there is provided a finite element simulation system comprising:
module M1: discretizing each boundary of the product contact area to generate an initial grid;
module M2: refining the deformation area of the product based on the initial grid to obtain a reconstructed grid;
module M3: assigning a new physical field to each cell in the reconstructed mesh based on the physical field of each cell in the initial mesh;
module M4: performing analog simulation on the product according to the new physical field of each unit, and improving the geometric dimension of the product;
the physical fields include displacement, temperature, damage, stress and strain.
According to the present invention, a computer-readable storage medium is provided, in which a computer program is stored, which, when being executed by a processor, carries out the steps of the method as described above.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention adaptively controls the size of the grid according to the physical understanding or the geometric shape, optimizes the finite element grid, and solves the contradiction between the calculation cost and the simulation precision; the method can determine how accurate the grid needs to be or how coarse the grid needs to be without unacceptable influence on the accuracy of the solution result;
2. the invention facilitates the generation of a sufficiently fine grid, e.g. plastic regions, lesion regions, in the region of interest or in the vicinity of the location of interest;
3. the invention reduces the calculation cost, enables the finite element grid to adapt to local characteristics, optimizes the grid quality and obviously improves the convergence speed and the calculation precision of the finite element analysis;
4. the invention reproduces the meaningful geometrical features: the completely destroyed cells are deleted and the new boundary is divided with the optimized mesh.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a diagram of a general simulation grid size;
FIG. 2 is a schematic diagram of an adaptive simulation grid;
FIG. 3 is a flow chart of adaptive mesh reconstruction;
FIG. 4 is a schematic diagram of an initial mesh generation method;
FIG. 5 is a mesh reconstruction flow chart;
FIG. 6 is a schematic diagram of gradient construction;
FIG. 7 is a schematic diagram of a mesh reconstruction process;
fig. 8 is a grid reconstruction contrast diagram.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
Example 1:
the invention is based on initial grid data T0(Ω) (i.e., the input amount is the initial mesh), the region of interest is refined and the other regions are roughly treated by the following steps to obtain a reconstructed mesh (i.e., the output amount is the reconstructed mesh), as shown in fig. 8 below. At the same time, a new physical field (output) will also be given to each cell in the reconstructed mesh based on the physical field (displacement, temperature, damage, stress, strain, etc.) (input) of each cell in the initial mesh. The reconstructed grid is used for simulation, so that a real result can be reflected more accurately, and the calculation cost can be reduced.
The invention provides a self-adaptive grid reconstruction scheme for simulating metal forming and processing processes. Finite element discretization resulting from sub-optimal meshing of the model can limit the ability to obtain adequate analysis results at reasonable CPU cost. Fig. 1 shows two cases of simulation without adaptive mesh reconstruction: FIG. 1(a) uses coarse grids, which is less in calculation amount and high in simulation efficiency, but low in simulation precision; in the simulation of fig. 1(b) using a fine mesh, the simulation accuracy is high, but the calculation amount is large and the efficiency is low. FIG. 2 is a simulation result of using adaptive mesh reconstruction, where the initial mesh is set to be thicker, but as the simulation proceeds, the mesh refinement is automatically performed on the regions concerned by us, and unimportant regions still use the initial mesh, which can ensure the simulation accuracy, reduce the calculation amount, and improve the efficiency.
The basic flow of simulation to mesh reconstruction is shown in fig. 3. And refining and optimizing the finite element grid according to the geometric error prediction and the physical field error prediction. The mesh is refined and coarsened using a specific Delaunay algorithm, and the final mesh quality is improved using an optimizer.
Simulation problems in this process can be abstracted as R3The interaction domain of (2): one is a deformable body (workpiece) and the other two are rigid bodies (tools). We define the deformation region to be analyzed as Ω and its boundary as G0() It is numerically defined. Suppose ΩkFor the rigid body portion, we define the region of contact with the rigid body portion within the deformation region Ω as Ωj,k. To construct an initial grid T of deformation zones omega0(Ω), each boundary is first discretized, and then a mesh of deformation zones Ω is generated based on this discretization. Discretization of boundaries based on the numerical definition of boundaries G0() And initial geometric discretization T0() And (4) finishing.
In the invention, in order to adapt to the changing physical field and geometric shape, the grid self-adaptive reconstruction is realized in one step, namely, the whole deformation process is dispersed into a plurality of small analysis steps. The final simulation result is obtained by iterating each micro-deformation. After each deformation increment step j, the deformation zone is only slightly deformed, the deformation zone omegajThe mesh reconstruction scheme of (1) is as follows:
1. defining a new geometric boundary G after a small deformationj() And solving for loaded material understanding Sj-1(Ω) (displacement, temperature, mechanical field, etc.);
2. and (4) damage judgment: if the damage D of the unit is larger than the defined maximum damage threshold DmaxThen the cell is deleted and a new boundary is defined; if the damage D is less than DmaxDefining a damage refinement criterion Hd,j(omega) carrying out repartitioning and thinning on grids in a deformation region omega; at Hd,j(Ω) if the damage is greater than a critical value Dc, adjusting the grid size in the range to a minimum size;
3. and (3) estimating geometric deviation: new geometric boundary Gj() And the current discretization boundary Tj-1() Deviation between them, defining a geometric map Hg,j() Re-discretizing the boundary;
4. and (3) estimating the physical deviation: defining a physical dimension map of deviations between the object understanding and the ideal solution in the deformation zone
To control the reconstruction of the mesh within the deformation zone omega.
After deformation, the new geometry G of the boundaryj() There are two forms of definition, one is to retain the geometry before deformation and the other is to define a new smooth geometry. In the first approach, the new geometry is simply defined by the current discretized boundary, the new mesh Tj() Is placed in this discretized cell. In the second way, at the current discretization boundary Tj-1() By interpolating nodes or other geometric features, the new geometry G being defined by a smooth curvej() New nodes are placed within this curve. The advantage of the second approach is that the geometry of the deformation zone Ω remains smooth throughout the deformation process.
New geometric boundary Gj() Two types of variations are included:
free deformation: due to deformation caused by mechanical constraints (e.g., equilibrium conditions), the new geometry of the deformed region is defined only by the new locations of the boundary nodes and their connections;
bounded deformation: such deformation is limited by contact with another domain (e.g., a tool domain), and the deformation region Ω is limited by the domain Ω in contact with himkThe influence of the geometry.
Nodes that are free and bounded can be classified using the Hausdorff distance (). If the node under consideration belongs to a region R associated with another domain(s), then it is defined as bounded, and vice versa. Associated field R(s) can be defined as follows:
R(s)＝{X∈R3,d(X,s)≤}…………(1)
in the formula, d (X, s) represents the distance from the point X to the surface s, and represents the maximum displacement of the deformation region Ω.
Based on the definition of the nodes, defining a new grid size for the boundary nodes: if the node belongs to free deformation, its size and new region boundary or new geometry Gj() Is proportional to the radius of curvature of the lens; if it belongs to a bounded deformation, its size is associated with the region ΩkThe radius of curvature of the contact portion is proportional. This dimension specification defines the sum Tj-1() Is connected to the boundary node ofg,j() And can be determined by considering Tj-1() Maximum size H of internal node ofmaxThe size map is extended to the entire deformation region Ω.
Understanding Sj-1(Ω) is a subset of the physical field that controls the computation for a given accuracy. Se,j-1(Ω) represents the exact (ideal) value of the physical field. Solution S obtained by finite element calculationj-1(Ω) is not interpolated, i.e. at Tj-1Solution S found at a node in (omega)j-1(omega) and the exact value Se,j-1(Ω) is not completely uniform. The finite element error is assumed to be bounded by the interpolation error, so that the calculated material understanding S is limitedj-1(omega) and exact solution Se,j-1The error between (Ω) may be limited only by the interpolation error.
By considering Hd,j(Ω),Hg,j(omega) and
define a sum Tj-1(omega) node-dependent dimension map Hj(omega). To smooth out these dimensional changes, a dimension map Hj(Ω) is adjusted according to a given grid gradient. The obtained dimension map is used for controlling the self-adaptive grid reconstruction processThe process comprises two stages: the re-discretization of the boundary surface and the reconstruction of the mesh based on this re-discretized area. The re-dispersion of the boundary is to generate a size-fitting map H of the boundaryj(Ωj|) new discretization Tj(). Then, the entire deformation region is mesh-reconstructed based on this boundary discretization.
Applying a cell grid construction method to map H in a deformation region omega through a known dimensionj(Ω) generating a regular grid. In the method, edges of the grid after the self-adaptive grid is reconstructed are uniformly controlled by using a Riemann matrix M. The measurement of a point P in the deformation zone is defined by a 3 x 3 symmetric positive definite matrix MPThe definition is as follows:
in which H is represented by the formulaj(Ω) size map defined, I is a unit matrix that transforms the size map h to be consistent in all directions. If P is a vertex in the cell mesh,
is an edge with point P as an end point, the length of the edge e is
In the formula IM(e) Is the length of the edge (e), the size map h is considered as a matrix map MPA grid that conforms to this metric is called a cell grid.
Defining a grid more closely to a given size map is not only consistent with potential Riemann metrics, but also the Riemann volume of all cells must be consistent with a unit cell. This means that the cell mesh must be adapted to the finite elements, in particular in terms of convergence. To this end, another defining criterion relating to the shape of the cells, which is suitable for calculation, is added to the grid. In the classical euclidean space, one commonly used method for measuring the quality of the shape of a grid cell K is as follows:
where V (K) and e (K) represent the volume and side length, respectively, of unit K, and c is a scaling factor. The value range of q (K) is 0-1, the value of the regular unit is close to 1, and the value of the irregular unit is close to 0. In Riemann space, the cell K shape quality can be defined as follows:
q(K)＝min[qi(K)]…………(5)
in the formula, qi(K) Represents and MPThe associated cell grid quality.
By definition of unit grid and cell quality, grid generation and optimization can be divided into:
processing grid edges: removing small edges, segmenting large edges, and modifying topological relation related to shape quality;
grid cell optimization: repositioning the vertex and modifying the topological relation as the shape quality is improved.
If the length of one small side is less than
It is removed (shrinking the edge to its midpoint or end); if the length of one edge is greater than
It is divided (the cell is divided into two parts from the midpoint of the edge). The edge removal and segmentation operations do not require any control over the shape quality of the resulting cells, and therefore, the mesh quality needs to be improved by modifying the topological relation. The modification of the topological relation includes the reverse inversion of the edge or the face, and the inversion of the face is to simply convert two units into three units. The flipping of the edge is removed by triangularizing the edge again.
Example 2:
the invention provides a self-adaptive mesh reconstruction scheme, which is explained by combining with the self-adaptive reconstruction of finite element simulation software Abaqus based on tetrahedral mesh units.
As shown in FIG. 4, first, the deformation region to be analyzed is defined as Ω, and its boundary is defined as G0(). Then, discretizing each boundary to obtain an initial geometric discretization T0(). Finally, based on the boundary G0() And discretizing T0() Generating an initial grid T of deformation zones omega0(Ω)。
In the invention, in order to adapt to the changing physical field and geometric shape, the grid self-adaptive reconstruction is realized in one step, namely, the whole deformation process is dispersed into a plurality of small analysis steps. The final simulation result is obtained by iterating each micro-deformation. Assuming that the total load in the analysis is u and the number of analysis steps is n, the load Δ u per small analysis step is u/n. After each deformation increment step j, the deformation zone is only slightly deformed, the deformation zone omegajThe mesh reconstruction scheme of (1) is as follows:
1. defining a new geometric boundary G after a small deformationj() And solving the loaded understanding S using Abaqus/Exploxit and subroutine Vumatj-1(Ω) (displacement, temperature, damage, stress, strain, etc.);
2. in this example, the reconstruction is defined for the mesh by the impairment parameters. If the damage D of the unit is larger than the defined maximum damage threshold Dmax(in the present embodiment, Dmax0.6), the unit is deleted and a new boundary is defined; if the damage D is less than DmaxDefining a damage refinement criterion Hd,jAnd (omega) carrying out subdivision and refinement on grids in the deformation region omega. At Hd,j(Ω) if the damage is greater than the critical value Dc(in this example Dc0.2), the mesh size in this range is adjusted to the minimum size (in this embodiment, the minimum size is 0.1 mm). Refining all units with damage of more than 0.2 and less than 0.5, and deleting the units with damage of more than 0.5;
3. defining a geometric dimension map H based on geometric deviation estimationg,j() To re-discretize the boundary. Geometric deviation estimation methodGeometric boundary Gj() And the current discretization boundary Tj-1() The deviation therebetween;
4. defining a physical dimension map based on physical deviation estimation
To control the reconstruction of the mesh within the deformation zone omega. Physical deviation estimation refers to the deviation between the physical understanding and the ideal solution within the deformation zone.
New geometry G of the boundary after each small analysis step loading deformationj() The definition can be made in two forms, one is to retain the geometry before deformation, and the other is to define a new smooth geometry. In the first approach, the new geometry is simply defined by the current discretized boundary, the new mesh Tj() Is placed in this discretized cell. In the second way, at the current discretization boundary Tj-1() By interpolating nodes or other geometric features, the new geometry G being defined by a smooth curvej() New nodes are placed within this curve. The advantage of the second approach is that the geometry of the deformation zone Ω remains smooth throughout the deformation process.
In this embodiment, since there is no influence of other domains, all nodes in the deformation region Ω belong to free deformation (due to deformation caused by mechanical constraints, the new geometry of the deformed region is defined only by the boundary nodes and their new positions of connection). Thus, the new grid size of the boundary node and the new region boundary Gj() Is proportional to the radius of curvature of the lens. If the deformation area to be analyzed has the influence of other domains, the type of the node needs to be judged first. The judgment method uses the Hausdorff distance () for classification. If the node under consideration belongs to a region R associated with another domain(s) is defined as a bounded deformation (such deformation is limited by the contact area with another domain, the deformation zone Ω is limited by the domain Ω in contact with himkThe influence of geometry) and otherwise is free to deform. If a node is bounded, its new mesh size is associated with the region of association ΩkRadius of curvature of contact portionIs in direct proportion. Associated field R(s) can be defined as follows:
R(s)＝{X∈R3,d(X,s)≤}…………(1)
in the formula, d (X, s) represents the distance from the point X to the surface s, and represents the maximum displacement of the deformation region Ω.
The above-described dimensioning of the free-form and bounded-form boundary meshes defines and the current discretized boundary Tj-1() Is connected to the boundary node ofg,j() And can be determined by considering Tj-1() Maximum size H of internal node ofmaxThe size map is extended to the entire deformation region Ω.
During the reconstruction of the grid, H is taken into accountd,j(Ω),Hg,j(omega) and
define a sum Tj-1(omega) node-dependent dimension map Hj(omega). To smooth out these dimensional changes, a grid gradient versus dimension map H needs to be givenj(Ω) was adjusted. As shown in fig. 6, when the gradient finite element mesh and the gradient finite element mesh are not compared, it is obvious from fig. 6(a) that the size and shape of the boundary mesh are suddenly changed, which does not meet the calculation requirement. The adjusted size map is used to control an adaptive mesh reconstruction process, which includes two stages: the re-discretization of the boundary surface and the reconstruction of the mesh based on this re-discretized area. The re-dispersion of the boundary is to generate a size-fitting map H of the boundaryj(Ωj|) new discretization Tj(). Then, the entire deformation region is mesh-reconstructed based on this boundary discretization.
Understanding Sj-1(Ω) is a subset of the physical field that controls the computation for a given accuracy. Se,j-1(Ω) represents the exact (ideal) value of the physical field. Solution S obtained by finite element calculationj-1(Ω) is not interpolated, i.e. at Tj-1Solution S found at a node in (omega)j-1(omega) and the exact value Se,j-1(Ω) is not completely uniform. Assume limitedThe element error is bounded by the interpolation error, so that the calculated object understanding S is limitedj-1(omega) and exact solution Se,j-1The error between (Ω) may be limited only by the interpolation error.
Applying a cell grid construction method to map H in a deformation region omega through a known dimensionj(Ω) generating a regular grid. In the method, edges of the grid after the self-adaptive grid is reconstructed are uniformly controlled by using a Riemann matrix M. The measurement of a point P in the deformation zone is defined by a 3 x 3 symmetric positive definite matrix MPThe definition is as follows:
in which H is represented by the formulaj(Ω) size map defined, I is a unit matrix that transforms the size map h to be consistent in all directions. If P is a vertex in the cell mesh,
is an edge with point P as an end point, the length of the edge e is
In the formula IM(e) Is the length of the edge (e), the size map h is considered as a matrix map MPA grid that conforms to this metric is called a cell grid.
Defining a grid more closely to a given size map is not only consistent with potential Riemann metrics, but also the Riemann volume of all cells must be consistent with a unit cell. This means that the cell mesh must be adapted to the finite elements, in particular in terms of convergence. To this end, another defining criterion relating to the shape of the cells, which is suitable for calculation, is added to the grid. In the classical euclidean space, one commonly used method for measuring the quality of the shape of a grid cell K is as follows:
where V (K) and e (K) represent the volume and side length, respectively, of unit K, and c is a scaling factor. The value range of q (K) is 0-1, the value of the regular unit is close to 1, and the value of the irregular unit is close to 0. In Riemann space, the cell K shape quality can be defined as follows:
q(K)＝min[qi(K)]…………(5)
in the formula, qi(K) Represents and MPThe associated cell grid quality.
By definition of unit grid and cell quality, grid generation and optimization can be divided into two cases: if the length of an edge is less than
It is accumulated into the next edge (i.e., edge removal); if the length of one edge is greater than
It is divided (the cell is divided into two parts from the midpoint of the edge). Finally the Riemann length l of each edge satisfies
Neither the edge removal nor the segmentation operation needs any control over the shape quality of the resulting cells, and therefore the mesh quality needs to be improved by repositioning vertices and modifying topological relations. The modification of the topological relation includes the reverse turning of the edge or the face, the turning of the face is to simply convert two units into three units, and the turning of the edge is to remove the three units through triangularization again on the edge.
By iterating the computational analysis of each small analysis step, the simulation of the whole loading process is finally completed, and the process can be simply represented as fig. 7.
Those skilled in the art will appreciate that, in addition to implementing the systems, apparatus, and various modules thereof provided by the present invention in purely computer readable program code, the same procedures can be implemented entirely by logically programming method steps such that the systems, apparatus, and various modules thereof are provided in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system, the device and the modules thereof provided by the present invention can be considered as a hardware component, and the modules included in the system, the device and the modules thereof for implementing various programs can also be considered as structures in the hardware component; modules for performing various functions may also be considered to be both software programs for performing the methods and structures within hardware components.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.
Claims (10)
1. A finite element simulation method, comprising:
step 1: discretizing each boundary of the product contact area to generate an initial grid;
step 2: refining the deformation area of the product based on the initial grid to obtain a reconstructed grid;
and step 3: assigning a new physical field to each cell in the reconstructed mesh based on the physical field of each cell in the initial mesh;
and 4, step 4: performing analog simulation on the product according to the new physical field of each unit, and improving the geometric dimension of the product;
the physical fields include displacement, temperature, damage, stress and strain.
2. A finite element simulation method according to claim 1, wherein the damage judgment is performed on the deformed region of the product: if the damage of the unit is larger than a preset threshold value, deleting the unit and defining a new boundary; if the damage of the unit is smaller than a preset threshold value, the grids in the deformation area are subdivided and refined;
and (3) estimating the geometric deviation of the deformation area of the product: calculating the deviation between the new geometric boundary and the current discretization boundary, and defining a geometric dimension map to perform re-discretization on the boundary according to the deviation;
and (3) estimating the physical deviation of the deformation area of the product: and calculating the deviation between the object understanding of the deformation area and the ideal solution, and defining a physical dimension map to control the reconstruction grid in the deformation area.
3. A finite element simulation method as set forth in claim 2, wherein the new geometric boundary comprises:
free deformation: the new geometry of the deformation zone is defined only by the boundary nodes and their new positions of connection, caused by mechanical constraints;
bounded deformation: the deformed region is related to the geometry of the contacted domain.
4. A finite element simulation method according to claim 3, wherein the nodes of free and bounded deformation are classified using the Hausdorff distance if the node belongs to the associated region R(s) then define it as a bounded, associated domain R(s) is defined as:
R(s)＝{X∈R3,d(X,s)≤}…………(1)
wherein d (X, s) represents the distance from the point X to the surface s, represents the maximum displacement of the deformation zone omega, R3Representing the interaction domain.
5. A finite element simulation method according to claim 4, wherein if the boundary node belongs to free deformation, the size of the boundary node is proportional to the radius of curvature of the new region boundary or the new geometry; if the boundary node belongs to a bounded deformation, the size of the boundary node is proportional to the radius of curvature of the contact area of the associated region.
6. A finite element simulation method according to claim 1, wherein the finite element simulation method is characterized byThen, reconstructing grids in the deformation area through a map with known dimensions, uniformly controlling the boundaries of the reconstructed grids by using a Riemann matrix M, and determining the measurement standard of a point P in the deformation area through a 3 multiplied by 3 symmetrical positive definite matrix map MPThe definition is as follows:
wherein h is a defined dimension map, and I is a unit matrix which converts the dimension map h into a unit matrix which keeps consistent in all directions; p is a vertex in the cell mesh,
is an edge with point P as an end point, and the length of edge e is:
wherein lM(e) Is the length of the edge (e), the size map h is a matrix map MPA grid that conforms to this metric is called a cell grid; t represents time.
7. A finite element simulation method according to claim 6, wherein the grid cell K shape quality q (K) is measured in the reconstruction grid, and the formula is:
wherein V (K) and e (K) respectively represent the volume and the side length of the unit K, c is a scaling coefficient, and l is the Riemann length; the value range of q (K) is 0-1, the value of the regular unit tends to 1, and the value of the irregular unit tends to 0; in Riemann space, the cell K shape quality is defined as:
q(K)＝min[qi(K)]…………(5)
in the formula, qi(K) Represents and MPThe associated cell grid quality.
8. A finite element simulation method according to claim 7, wherein the reconstructed mesh edges are processed: removing small edges, segmenting large edges, and modifying topological relation related to shape quality;
optimizing the grid cells: repositioning the vertex and modifying the topological relation according to the shape quality;
if the length of the small side is less than
Removing is carried out; if the length of one edge is greater than
It is segmented.
9. A finite element simulation system, comprising:
module M1: discretizing each boundary of the product contact area to generate an initial grid;
module M2: refining the deformation area of the product based on the initial grid to obtain a reconstructed grid;
module M3: assigning a new physical field to each cell in the reconstructed mesh based on the physical field of each cell in the initial mesh;
module M4: performing analog simulation on the product according to the new physical field of each unit, and improving the geometric dimension of the product;
the physical fields include displacement, temperature, damage, stress and strain.
10. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 8.
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