Isogeometric shape optimization for scaffold structures

Abstract

The development of materials with specific structural properties is of huge practical interest, for example, for medical applications or for the development of light weight structures in aeronautics. In this article, we combine shape optimization and homogenization for the optimal design of the microstructure in scaffolds. Given the current microstructure, we apply the isogeometric boundary element method to compute the effective tensor and to update the microstructure by using the shape gradient in order to match the desired effective tensor. Extensive numerical studies are presented to demonstrate the applicability and feasibility of the approach.

Isogeometric analysis of diffusion problems on random surfaces

“…As we typically have to compute many realizations of the parametric surface in order to obtain acceptable approximations of the quantities of interest, it is in practice advisable to perform the reinterpolation of each patch and to compute the Karhunen-Loève expansion only with respect to a set of interpolation points. We refer to [26] for the details.…”