Solid‐shell formulations based on reduced integration – investigations of anisotropic material behaviour at large deformations

Abstract

AbstractSome years ago, a family of continuum finite elements based on reduced integration (e.g. [1], [2]) was investigated. Many engineering problems with isotropic material behaviour were considered and these elements showed accurate results while being more efficient than similar three‐dimensional formulations based on full integration. The objective of the present contribution is to extend the analysis to layered structures with anisotropic material behaviour undergoing large deformations. Here, we follow an ansatz which is similar to so called equivalent single layer theories, i.e., we model the inhomogeneous material as a continuum using solely one solid‐shell element over the thickness. Therefore, we introduce an additional mapping procedure which enables both, the usage of a certain quadrature rule within each layer of the composite and the consideration of layers with different thickness. A benchmark problem from the literature shows that the new developed ingredient within the solid‐shell concept leads to accurate results in terms of the global response of anisotropic structures at large deformations.