Numerical Calculation Based On Arbitrary Mesh Generation

There is an urgent need for the integration of Computer Aided Design(CAD)and Computer Aided Engineering(CAE)in the field of engineering simulation.However,the traditional Finite Element Method has many limitations on the shape,connection mode and density transition of the mesh,which greatly increase the workload of the preprocessing of numerical calculation.Moreover,the actual curve boundary is usually discretized into a broken line form,which is hard to realize the CAE modeling based on the precise geometry of CAD and has brought a lot of troubles to CAE analysts.Consequently,a numerical method based on arbitrary mesh generation is proposed by using the manifold method based on independent covers.This method makes full use of the three arbitrariness characteristics of the cover mesh(arbitrary shape,arbitrary connection,arbitrary mesh refinement),breaks through the restrictions of the Finite Element Method on the mesh,realizes the arbitrary mesh generation,and can accurately simulate the curve boundary,including accurately imposing the boundary conditions on the curve.In computation,simplex analytical integration and numerical integration can be used,as long as the solution domain is divided into block meshes of arbitrary shape which can contain curve edges.Only the narrow strips(including curved strips)for overlapping between blocks need to be considered in the integration process,and these strips need not be generated in the calculation model.These methods greatly simplify the workload of preprocessing,open up a new path for the numerical calculation based on accurate geometric modeling and its fully automatic pre-processing,and lay a foundation for the automatic calculation of CAE and the integration of CAD and CAE.The main research work is as follows:(1)A method for calculating cover meshs with arbitrary shape is proposed.Firstly,the solution domain is divided into block meshes without considering the strip connection between the covers.Aiming at these block meshes with arbitrary shape,both of analytical integration and numerical integration methods are adopted,in particular,the integral formulas including curve edges are given.Then the strip connection between the covers is automatically generated.The expression of partition of unity function and integral method,and the strict application method of essential boundary conditions for precise geometric curve boundary are proposed.Through the cantilever beam and semi-circular plate examples,it is proved that manifold method based on independent covers can still obtain high accuracy in the case of arbitrary shape and connection of meshes.(2)An arbitrary mesh generation algorithm,Concave-Short Perpendicular method,is proposed for the two-dimensional solution domain.This method focuses on the subdivision algorithm of a single block,and subdivides each block of the current block meshes by the same subdivision operation.Then the solution domain is recursively subdivided step by step.The principle is simple,the algorithm is easy to be implemented,and it is convenient for adaptive analysis along with error control.(3)In the adaptive analysis technique of manifold method based on independent cover,the arbitrary meshing algorithm is introduced,and the automatic calculation of linear elastic static analysis of two-dimensional structures is preliminarily realized by combining error control.On this basis,the integration of CAD and CAE is attempted: defining structure shape in CAD,inputting computation parameters and boundary conditions to complete all necessary manual operations;inputting to CAE through DXF file,automatic modeling based on precise geometry,automatic computing under error control,and automatic output of stress graph.Finally,two examples,a plate with a circular hole and a gravity dam,are used to verify the feasibility of the above automatic calculation based on arbitrary meshing.