Remarks on Linear and Nonlinear Variational Design Sensitivity Analysis

Abstract

Theoretical formulations and numerical methods for variational design sensitivity analysis have been investigated since almost two decades leading to two major formulations, i.e. the material derivative approach, see e.g. [1], and the domain parametrization approach, see e.g. [2]. Recently, the author described a third viewpoint which takes elements from both forementioned approaches and yields an advanced presentation of variational design sensitivity analysis within nonlinear computational mechanics [5].

An integrated formulation of direct and design sensitivity analysis can be obtained by tracing and separating geometrical and physical mappings. This approach is based on a differential geometry setting of continuum mechanics using convected coordinates. The fundamental ideas are outlined.

Furthermore, a nonlinear elastic, isotropic damage law as well as the subsequent sensitivity analysis are described in order to demonstrate the efficiency of the proposed theoretical and computational formulations.