The Study Of Numerical Manifold Method Based On CAD Geometry

The iterative process of design-analysis-redesign implies urgent requests of the integration of Computer Aided Design(CAD) and Computer Aided Engineering(CAE).In this paper, Numerical Manifold Method(NMM) based on CAD geometry is presented.This method makes full use of the characteristics that mathematical mesh and physical mesh are separated from each other in NMM. And the mathematical meshes and the order of approximation functions are arranged according to the complex level of physical field distribution in CAE. When a CAD model enters into CAE procedures, direct modeling can be achieved without geometric modifications, by means of automatic and fast cutting operations. At the same time, it avoids the geometric error due to the linearization of curved boundaries of the geometric model in the traditional NMM. It can achieve automatic analysis from CAD to CAE by using self-adaptive technology based on the independent covers. The new idea presented lays the foundation for the integration of CAD and CAE. The main research works are list as follows:(1) To solve the problem that curves on geometric boundaries are required to be discretized into line segments in present NMM, algorithms for cutting the curved boundaries with the lines of mesh edges are given, which realizes shape preserving of the geometric model in the procedures of CAE modeling and mesh refinement.(2) As for the polynomial approximation functions usually used in NMM, analytic integral formula of “approximate” simplex with a curve edge is deduced, which is applied to obtain precise integral calculations of manifold elements with curved boundaries.(3) In order to realize the direct communication between CAD and CAE, CAD geometric model is directly output to CAE by using DXF graphic standard in AutoCAD.(4) Automatic analysis of CAE is preliminarily achieved by using self-adaptive technology based on the independent covers in NMM.(5)The feasibility of the method is verified through some examples, such as a plate containing a circular hole, crown cantilever of arch dam, and section of peripheral concrete of spiral case in two-dimensional problems. These exhibit the advantages of the method in the integration of CAD and CAE.