3D simulation of laminated shell structures using the Proper Generalized Decomposition

Abstract

Numerical simulations of composite structures are generally performed using multi-layered shell elements in the context of the finite elements method. This strategy has numerous advantages like a low computation time and the capability to reproduce the comportment of composites in most of cases. The main restriction of this approach is that they require an approximation of the comportment in the thickness. This approximation is generally no more valid near the boundary and loading conditions and when non linear phenomena like delamination occurs in the thickness. This paper explores an alternative to shell computation using the framework of the Proper Generalized Decomposition that is based on a separated representation of the solution. The idea is to solve the full 3D solid problem separating the in-plane and the out-of-plane spaces. Practically, a classical shell mesh is used to describe the in-plane geometry and a simple 1D mesh is used to deal with the out-of-plane space. This allows to represents complex fields in the thickness without the complexity and the computation cost of a solid mesh which is particularly interesting when dealing with composite laminates.