Shape optimization using adaptive high-order finite elements

Abstract

In recent years, the state of the art in shape optimization has advanced due to new approaches proposed by various researchers. A fundamental difficulty in shape optimization is that the original finite element mesh may become invalid during large shape changes. Automatic remeshing and “velocity field” approaches are most commonly used for conventionalh-type finite element analysis to address this problem.

In this paper, we describe a different approach to shape optimization based on the use of high-orderp-type finite elements tightly coupled to a parameterized computational geometry module. The advantages of this approach are as follows.

Accurate results can be obtained with much fewer finite elements, so large shape changes are possible without remeshing.

Automatic adaptive analysis may be performed so that accurate results are achieved at each step of the optimization process.

Since the elements derive their geometric mapping from the underlying geometry, the fundamental equivalent of “velocity field” element shape updating may be readily achieved.

Results are presented for sizing and shape optimization with this approach and contrasted with previous results from the literature.