Gradient‐based determination of principal design influences on composite structures

Abstract

This work deals with the computation of design sensitivities of elastic solid‐shell structures extended to anisotropic layered composite structures. Design sensitivities concerning fiber angles and layer thicknesses are derived and quantitatively determined in the context of the finite element method. The anisotropic analysis model is founded on a sophisticated solid‐shell formulation based on reduced integration and is extended to discretize the composite with only one element over the element thickness by means of multiple integration points. This can be understood as a special case of equivalent‐single‐layer theories. Examination of system response sensitivity matrices using methods from principal component analysis, such as singular value decomposition, is used to identify crucial design changes corresponding to major changes in the structural behavior of the composite. This procedure is termed as sensitivity based design exploration. Results are discussed by reference to simple academic examples.