A Review on Attempts towards CAD/CAE Integration Using Macroelements

摘要

In this paper we review several aspects of older and contemporary attempts to integrate computer-aided design (CAD: geometric model) and computer-aided engineering (CAE: finite elements, boundary elements, etc.). After a short review on formulas for the description of CAD surfaces, a systematic mechanism for creating several types of corresponding isoparametric macroelements is presented. Gordon-Coons is initially applied in conjunction with piecewise linear, Lagrange polynomials and natural B-splines. Then, it is extended to more basis and blending functions. In addition to the well-known ‘Lagrangian’-type elements, equivalent ‘Bézierian’-type elements are introduced. Tensor product B-splines and aspects of NURBS isogeometric formulation are given. In addition to quadrilaterals, triangular macroelements based on Barnhill’s interpolation are presented for the first time. The review coversapplications of CAD-based macroelements in conjunction with the Galerkin-Ritz formulation, the Boundary Element Method, as well as recent Global Collocation procedures. A numerical example on a vibrating membrane elucidates the performance of the CAD-based global interpolation and depicts its superiority over the conventional finite element method.