CN105260526A - Image based adaptive finite element mesh division method - Google Patents
Image based adaptive finite element mesh division method Download PDFInfo
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Abstract
An image based adaptive finite element mesh division method belongs to a mesh division method for finite element analysis of a material structure. The method comprises: 1, distinguishing different phases or components in an image with an image analysis method; 2, reading position information of all pixels into a computer memory by utilizing a computer language program; 3, according to the fineness of a spatial structure, reducing an image resolution of a region thick and big in structure and single in component; 4, directly constructing a finite element unit by the pixels, wherein different resolutions cause different mesh densities; and 5, transiting meshes different in density by mesh mapping. According to the method, nodes and units are directly constructed by utilizing images, and solid modeling is skipped, so that system resources can be saved; moreover, a mesh structure can be optimized on the premise of ensuring calculation precision, so that the number of nodes is remarkably reduced, the calculation time is shortened, and the memory consumption is reduced; and the whole process is automatically completed, so that the method is very practical for a model with a huge amount of nodes.
Description
Technical field
The present invention relates to a kind of Meshing Method of material structure finite element analysis, particularly a kind of self-adapting finite element grid division methods based on image.
Background technology
The performance of material has conclusive effect for its effective utilization, and therefore the performance of test material is a homework that must do before using it.But for structured material design, the structure of material usually to be changed frequently to the performance wanted can be obtained, this makes to need a large amount of test jobs.By the performance of material structure prediction material, the cycle of design of material can greatly be shortened, therefore widely apply in fields such as composite Materials Design.Traditional Forecasting Methodology generally all uses two kinds of methods: 1) based on the theory calculate and 2 of ideal hypothesis) based on the experimental formula of testing, or both are combined.For first method, actual conditions are often more complicated than perfect condition many, and therefore the result of theory calculate and virtual condition may have relatively large deviation.And for second method, due to the difference of experiment condition, the value calculated by experimental formula also may have larger difference with legitimate reading.This makes to be which kind of method above is all difficult to be applicable to general occasion.
In recent years along with the development of computer technology, people can utilize computer program to carry out virtual structure for simple material structure, then the numerical modelings such as finite element are carried out, rational boundary condition is set again and starting condition calculates, can analyze the performance of material, this method is computer aided design cad (ComputerAidedDesign).Because the method utilizes the real structure of material to carry out modeling, therefore result of calculation has good accuracy rate.At present, this method is widely used in composite structure design field.But, periodic structure, heterogeneous compound substance be there is no for some, such as hot spraying WC-Co coating, because its structure is too complicated, is difficult to build, therefore the method also difficulty have place to show one's prowess.
Digital photography method is that continuous print image information is stored as discrete pixel, is stacked up and approaches original image.Continuous print spatial spreading becomes the thinking of unit very close with in FEM (finite element) calculation by this, the numerical modeling method be therefore just born based on image.Numerical modeling based on image refers to the two dimension or the three-dimensional digital photo that utilize and can represent material structure, sets up a kind of method of numerical model.The method, directly using the image of material as its structure, is often unit with pixel, builds the mathematical calculation model of material, therefore, it is possible to be applicable to the material structure of various complexity.Nearly ten years, scholar is had to utilize the method to carry out modeling to mineral material, building materials and coating material, the success prediction performances such as the mechanics of these materials, calorifics.When material fine structure and complicated irregular time, need the structure carrying out display material compared with the resolution of hi-vision.But when zoning size one timing, resolution is higher, and pixel count is more, is that the model of unit is larger with pixel, calculates consuming time and the consumption of system resource will be risen by index.Time particularly to 3-D view modeling, because node and cell cube quantity are the 1.5 powers doubly left and right of same length of side two dimensional model, analysis time and required computer resource are extremely increased, and this may lose the simple and efficient advantage of numerical simulation.
Therefore, keep high cell density at the tissue regions of elaborate, reduce cell density at simply thick tissue regions, set up the adaptive mesh for fine structure degree, while guarantee computational accuracy, counting yield can be improved.Thus and be not suitable for image finite element modeling method current FEA Meshing Method, all needs first to set up solid model.Therefore the present invention proposes a kind of adaptive meshing algorithm method based on image pixel.
Summary of the invention
In order to take into account computational accuracy and improve counting yield, keep the advantage of numerical simulation on the Optimization of Material Property cycle, the invention provides a kind of according to material structure, the fineness of automatic control mesh, based on the adaptive meshing algorithm method of image pixel, the method is especially applicable for the three-dimensional problem that node amount is large.
The technical solution adopted for the present invention to solve the technical problems is: this division methods: first with the numerical imaging of suitable resolution picked-up material, the region meticulous in institutional framework keeps high density unit, reduce the density of node and unit in the region that institutional framework is thick, connected the unit of above-mentioned two kinds of yardsticks by rational transition element.
Specifically comprise the following steps:
A () obtains two dimension or the 3-D view that can represent material structure;
B () is with phases different in image analytical method differentiate between images or component;
C the positional information of all pixels is read in calculator memory by (), mark out them and belong to which phase or component;
D () reduces the image resolution ratio in uniform component, the simple region of structure;
E (), except the zone of transition between different resolution, directly builds up a unit each for all the other regions pixel;
F () sets up the unit of transitional region between different resolution;
(g) construction unit model.
In described step (d), uniform component, the simple region of structure in correspondent entity structure, as long as ensure the material unicity that pixel is corresponding, then the image resolution ratio in this region that constantly cyclically reduces by half.
Described step (e), with in (f), is directly sorted out according to the material of pixel and positional information structure finite element unit, the summit of the position respective pixel of node.
In described step (f), between the region of different resolution, two-dimensional grid adopts the polygon transition of mapping type to connect, and 3D grid adopts the polyhedron of mapping type to carry out transition;
The fine structure degree different according to material each several part region, selects different node grid density, and meticulousr Area Node density is higher, otherwise node density is lower.
Beneficial effect, owing to have employed such scheme, the present invention is a kind of finite element modeling method utilizing images of materials, it act as the image finite element modeling method improving and become finite element unit with image pixel direct construction, idea about modeling is based on adjustable image resolution ratio principle, single or organize thick region for composition, reduce the image resolution ratio in this region, also just can reduce the mesh-density in this region.Adopt multi-level images resolution, effectively can reduce the number of nodes of finite element model, save system resource and computing time.
Advantage is: based on image pixel direct construction finite element unit, avoids building solid model, reduces system resources consumption, improves arithmetic speed.When being applied to the comparatively complicated material of institutional framework, the modeling pattern that to compare with each pixel be unit, obviously can reduce number of nodes, reduce system resources consumption, under the prerequisite ensureing computational accuracy, improve arithmetic speed.Stress and strain model adopts computer program automatically to complete, simple to operation.
Accompanying drawing explanation
Fig. 1 is the schematic flow sheet of the self-adapting finite element grid division methods that the present invention is based on image.
Fig. 2 is the two-dimensional cross-section image (1024 × 768 pixel) of the composite material of magnesium alloy that cold spraying SiC of the present invention strengthens.
Fig. 3 is the photo of Fig. 2 after image procossing, and wherein black is hole, and white is SiC, and all the other are magnesium alloy.
Fig. 4 take Fig. 2 as the two-dimensional adaptive ELEMENT MESH GRAPH of modeling object.
Fig. 5 is the three-dimensional reconstruction image (80 × 80 × 50 pixel) of plasma spraying yttria-stabilized zirconia coating of the present invention.
Fig. 6 take Fig. 4 as the three-dimensional self-adapting finite element grid figure of modeling object.
Embodiment
This division methods: first with the numerical imaging of suitable resolution picked-up material, the region meticulous in institutional framework keeps high density unit, reduce the density of node and unit in the region that institutional framework is thick, connected the unit of above-mentioned two kinds of yardsticks by rational transition element.
Concrete operation step is as follows:
The first step, obtains two dimension or the 3-D view that can represent material structure;
Second step, with phases different in image analytical method differentiate between images or component;
3rd step, utilizes computer language procedure, reads in calculator memory by the positional information of all pixels, marks out them and belongs to which phase or component;
4th step, reduces the image resolution ratio in the simple region of composition homogeneous structural;
5th step, except the zone of transition between different resolution, directly builds up a unit each for all the other regions pixel;
6th step, sets up the unit of transitional region between different resolution;
7th step, builds finite element model.
The described first step, pickup image will select suitable resolution and territory, face or body territory size; The resolution of image is selected will can know that the structure of showing material is as the criterion, unsuitable too high or too low; The territory, face of pickup image or body territory size want the real structure that can represent material, for the material of periodic arrangement, can a cell element be picked-up region; For random material, picked-up region is unsuitable too small.
Described second step, in differentiate between images, homophase or component rely on its different form or different colors to realize.Image by analysis, represents different phases or component with color; Concrete step is as follows:
(1) use of waveforms method: if a certain phase or component have homogeneous specific form, such as spherical, and other phases or component do not have this form, then can identify this phase or component by waveforms method;
(2) use of colouring: if different phases or component have between different chromatic zoneses, then can set suitable threshold values and be separated various phase or component completely.
In described 3rd step, the categorizing information of available matrix storage pixel, the footmark respective pixel position in the picture of matrix.
In described 4th step, according to pixel arrangement position, individual element scans whole image, whether identical with surrounding pixel said material according to pixel, the image resolution ratio in the uniform component that constantly reduces by half region, at every turn complete scanning is the image resolution ratio in a circulation, continuous cycle down low target region; In each circulation, the region reducing resolution needs to leave the transitional region be connected with original resolution, can not reduce resolution again in transitional region.
In described 5th step, for the pixel of all non-transitional regions, directly according to classification and the positional information structure finite element unit of pixel, the position of the vertex correspondence node of pixel; The cell type of two-dimensional grid adopts square shaped cells, and the cell type of 3D grid adopts square unit; When giving material properties to cell cube, determine the material properties of this unit according to the color of this unit in the photo after image analysis processing, think that same phase or component have identical character.
In described 6th step, the transitional region stayed in the 4th step, for connecting the unit of two kinds of different sizes, must adopt the polygon polyhedral elements of mapping type to connect the unit of above-mentioned two kinds of yardsticks.For two-dimensional grid, the general mode adopting triangle and the collocation of trapezoidal grid; For 3D grid, the general mode adopting tetrahedron and hexahedron collocation.
In described 7th step, according to actual conditions, initial and boundary condition is loaded to finite element unit and node and calculates.
Following present the present invention for the rationality of the two and three dimensions FEA Meshing Method of polycomponent, phase material and superiority.
Embodiment 1: to cold spraying SiC strengthen composite material of magnesium alloy carry out two-dimensional finite Meta Model.
Compound substance comprises two or more components usually, the modeling of the present invention for the compound substance of three kinds of components of this examples show, triangular mesh and the quadrilateral mesh of multi-level yardstick is have employed in model, single for composition, thick region generates macrolattice automatically, and complicated component, structure careful Area generation fine grid blocks.This example can verify that the present invention divides ability for the two-dimensional grid of multi-component material.
Adopt the present invention to carry out two-dimensional finite Meta Model to the composite material of magnesium alloy that cold spraying SiC strengthens, comprise the following steps:
(1) the two-dimentional polishing cross-section image that can represent the composite material of magnesium alloy structure that SiC strengthens is obtained, as shown in Figure 2;
(2) with phases (or component) different in color analysis combining form analytic approach differentiate between images, give the color that different components is different, as shown in Figure 3, in figure, black represents hole, and white is SiC, and grey is magnesium alloy;
(3) utilize program of the present invention, export finite element order line statement, perform these statements with finite element software, export finite element model, as shown in Figure 4.
By the model that the present invention builds, through procedure judges, have employed the unit rank of 7 yardsticks, during out to out unit smallest dimension element length 2
7doubly.This model node quantity is 89503, and element number is 94135.If directly with each pixel for cell formation model, number of nodes is 788225, and element number is 786432.Under contrast, the present invention can reduce the number of nodes of 88.6%, the element number of 88.0%.
Calculated the elastic modulus of the composite material of magnesium alloy that cold spraying SiC strengthens by Fig. 2, the mechanical property parameters of each component is as shown in table 1.
The each component mechanical property parameters of composite material of magnesium alloy that table 1SiC strengthens
Table 2 illustrates the Comparative result that model by taking pixel as unit and adaptive mesh model calculate.Can find from table, adaptive mesh and pixel are that the grid computing result of unit is almost identical, and this illustrates that adaptive mesh can not affect computational accuracy.Be that to calculate consuming time be 139s for the model of unit with pixel, and the calculating of the adaptive mesh 11s that is only consuming time, saves the used time of 92.1%.With pixel be unit model consumption in save as 3978MB, and the calculating of the adaptive mesh 505MB that is only consuming time, save the memory consumption of 87.3%.
Table 2 take pixel as the model of unit and the Comparative result of adaptive mesh model calculating
Embodiment 2: microstructure of plasma sprayed yttria-stabilized zirconia (YSZ) coating carry out Three-dimensional finite element modeling.
Coating material comprises hole usually, and hole can think a kind of component, and character is identical with the gas that it is captured.The present invention of this examples show is for the modeling of plasma spraying yttria-stabilized zirconia coating comprising hole.Because the even structure degree of this coating and fine degree are higher than precedent, therefore only have employed hexahedral mesh and the tetrahedral grid of secondary yardstick in this model, single for composition, thick region makes the density of grid reduce half.This example can verify that the present invention divides ability for the 3D grid of multi-component material.
What adopt microstructure of plasma sprayed yttria-stabilized zirconia coating of the present invention carries out Three-dimensional finite element modeling, comprises following two steps:
(1) reconstruct the 3-D view of the YSZ coating of plasma spraying, as shown in Figure 5, in figure, black represents hole, and white is YSZ;
(2) utilize program of the present invention, export finite element order line statement, perform these statements with finite element software, export finite element model, as shown in Figure 5.
By the model that the present invention builds, have employed the unit rank of two yardsticks, 2 times of smallest dimension element length during out to out unit.This model node quantity is 196039, and element number is 331531.If directly with each pixel for cell formation model, number of nodes is 334611, and element number is 320000.Under contrast, the present invention can reduce the number of nodes of 41.4%, adds the element number of 3.6%.Although element number slightly increases, the system resources consumption of FEM (finite element) calculation mainly judges according to number of nodes, and therefore the present invention still can obviously reduce its system resources consumption for three-dimensional modeling, improves operation efficiency.
Calculated the thermal conductivity of plasma spraying YSZ coating by Fig. 5, the thermal property parameter of each component is as shown in table 3.
Table 3 plasma spraying YSZ coating each component thermal property parameter
Table 4 illustrates the Comparative result that model by taking pixel as unit and adaptive mesh model calculate.Can find from table, adaptive mesh and pixel are that the grid computing result of unit is almost identical, and this illustrates that adaptive mesh can not affect computational accuracy.Be that to calculate consuming time be 300s for the model of unit with pixel, and the calculating of the adaptive mesh 132s that is only consuming time, saves the used time of 60.3%.With pixel be unit model consumption in save as 860MB, and the calculating of the adaptive mesh 525MB that is only consuming time, save the memory consumption of 38.9%.
Table 4 take pixel as the model of unit and the Comparative result of adaptive mesh model calculating
Claims (5)
1. the finite element adaptive grid division methods based on image, it is characterized in that: this division methods: first with the numerical imaging of suitable resolution picked-up material, the region meticulous in institutional framework keeps high density unit, reduce the density of node and unit in the region that institutional framework is thick, connected the unit of above-mentioned two kinds of yardsticks by rational transition element; Concrete steps are as follows:
A () obtains two dimension or the 3-D view that can represent material structure;
B () is with phases different in image analytical method differentiate between images or component;
C the positional information of all pixels is read in calculator memory by (), mark out them and belong to which phase or component;
D () reduces the image resolution ratio in uniform component, the simple region of structure;
E (), except the zone of transition between different resolution, directly builds up a unit each for all the other regions pixel;
F () sets up the unit of transitional region between different resolution;
(g) construction unit model.
2. the finite element adaptive grid division methods based on image according to claim 1, be characterised in that: in described step (d), uniform component, the simple region of structure in correspondent entity structure, as long as ensure the material unicity that pixel is corresponding, then the image resolution ratio in this region that constantly cyclically reduces by half.
3. the finite element adaptive grid division methods based on image according to claim 1, be characterised in that: described step (e) is with in (f), directly sort out according to the material of pixel and positional information structure finite element unit, the summit of the position respective pixel of node.
4. the finite element adaptive grid division methods based on image according to claim 1, be characterised in that: in step (f), between the region of different resolution, two-dimensional grid adopts the polygon transition of mapping type to connect, and 3D grid adopts the polyhedron of mapping type to carry out transition.
5. the finite element adaptive grid division methods based on image according to claim 1, be characterised in that: the fine structure degree different according to material each several part region, select different node grid density, meticulousr Area Node density is higher, otherwise node density is lower.
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