p-Version of FEM and Shape Optimal Design

by K. Izadpanah, MacNeal-Schwendler Corp, United States,
G. A. Dilley, MacNeal-Schwendler Corp, United States,
Y. K. Shyy, MacNeal-Schwendler Corp, United States,
C. Fleury, MacNeal-Schwendler Corp, United States,

Document Type: Proceeding Paper

Part of: Computer Utilization in Structural Engineering


This paper presents some research results obtained recently in using the p-version of the finite element method (FEM) for shape optimal design. It is shown that the p-version 2-D elastic element can be extended to employ part of a Bezier or B-spline curve as its element side. This new element has been tested successfully with the patch test. Moreover, it is compatible, has no preferred direction, and contains all the required rigid body modes. Preliminary results of some classical shape optimal design problems indicate that optimal shapes can be obtained with fewer degrees of freedom when compared to the h-version FEM. As with the h-version, ten iterations are sufficient for the convergence of the optimization process in most of the problems.

Subject Headings: Finite element method | Structural design | Degrees of freedom | Optimization models | Structural analysis | Computer analysis | Elastic analysis | Spline (mathematics)

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