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Research On Topological Optimization Method Of Quadrilateral Mesh

Posted on:2020-02-28Degree:MasterType:Thesis
Country:ChinaCandidate:Z FangFull Text:PDF
GTID:2370330572990896Subject:Engineering
Abstract/Summary:PDF Full Text Request
Numerical analysis methods such as finite difference method,finite element method and finite volume method have been widely used in scientific calculation and various kinds of engineering analysis.One of the common features of these numerical methods is discreteness,that is,when applying numerical analysis,the analytical model needs to be discretized into a finite number of simple mesh elements.Quadrilateral element and triangular element are common mesh elements.Compared with triangular mesh,quadrilateral mesh has higher computational accuracy and iterative convergence rate.Therefore,quadrilateral mesh is the first choice for numerical analysis.The mesh quality has an important influence on the accuracy and efficiency of numerical analysis.The mesh with poor quality will reduce the accuracy of numerical solution,sometimes even make the iterative process not converge,and the analysis process will be interrupted.For quadrilateral mesh,an important metric of mesh quality is the inner angle of the element.The element with an inner angle close to 90 degree is an ideal element,corresponding to which the node with the number of surrounding elements of 4 is regular node.In a mesh,the more elements with an inner angle close to 90 degree,the better the quality of the mesh,or the more regular nodes in the mesh,the better the quality of the mesh.Structured mesh is ideal mesh,but only suitable for area with regular shape.For arbitrary geometric shape,unstructured mesh will be the only choice when structured mesh cannot be generated.There are many methods to generate unstructured quadrilateral mesh,each of which is likely to generate poor-quality mesh.Therefore,it is necessary to optimize the generated initial mesh to improve the quality of the mesh.In fact,after generating the initial mesh,all mesh generation software have a post-processing procedure to optimize the mesh.In this thesis,a topology optimization method for unstructured quadrilateral meshes is proposed,which is called patch remeshing method.The traditional Laplace smoothing algorithm only optimizes the node position.The method proposed in this thesis optimizes the mesh quality by changing the connectivity of element nodes.Compared with the local topology optimization method,the patch remeshing method is a global topology optimization method,which can significantly reduce the number of irregular nodes within the mesh and make the mesh shape closer to structured mesh.Therefore,the optimized mesh will have higher quality.For the planar quadrilateral mesh,two irregular nodes are first selected,and the shortest path of the two nodes is used as the skeleton to combine the elements around the skeleton into an initial blob,and according to certain criteria,the elements are continuously added to the blob,in which way the blob continues to expand.When the shape of a blob is a logical triangle,a quadrangle or a pentagonal patch,the regular mesh elements containing only one irregular node can be regenerated in the form of a template,and the original mesh of the region can be replaced.Therefore,as long as the number of irregular nodes in the patch is greater than 1,the quality of the regenerated mesh will be better than that of the initial mesh.When the number of irregular nodes in the patch is large,the quality of the mesh can be greatly improved by the remeshing operation.In this thesis,the methods,steps and algorithms of mesh topology optimization are given in detail.In this thesis,the conditions of remeshing in triangle,quadrilateral and pentagonal patches and the method of mesh generation are given in detail,and the steps and algorithms of patch expansion are also given.In order to ensure that the constraint conditions will not be changed in the process of patch expansion,a method is proposed to deal with the situation where there are characteristic constraints in the mesh.In this thesis,the topology optimization method of planar quadrilateral mesh is extended to 3D surface mesh optimization.The 3D surface quadrilateral mesh can be flattened to the plane by parametric mapping,and then the planar mesh topology optimization method is used to optimize the flattened quadrilateral mesh.Finally,the optimized quadrilateral mesh is mapped back to the original 3D surface,and the mesh node is projected onto the surface of the model,then the quadrilateral mesh optimization of the 3D surface can be realized.In this thesis,the realization steps of the 3D surface quadrilateral mesh topology optimization are given in detail,including the establishment of the background triangular mesh,the flattening of the 3D surface quadrilateral mesh,and the mapping of the optimized mesh back to the original 3D surface.On the basis of the 2D planar quadrilateral mesh topology optimization method and the 3D surface quadrilateral mesh topology optimization method proposed in this thesis,the corresponding mesh topology optimization program is programmed on the VS2010 platform with C++ language.2D and 3D quadrilateral meshes generated by different mesh generation algorithms and software are optimized.The optimization results show that the optimization algorithm proposed in this thesis is suitable for any mesh source and can effectively reduce the number of irregular nodes within the mesh and significantly improve the mesh quality,which also verifies the reliability of the mesh optimization method proposed in this thesis.
Keywords/Search Tags:mesh optimization, topology optimization, quadrilateral mesh, surface mesh
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