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

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. 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.

A multiscale separated representation to compute the mechanical behavior of composites with periodic microstructure

“…n at the same time. The interested reader can refer to [22] for more details. The computational cost is given only for sake of illustration because it depends strongly on the implementation.…”

A reduced model to simulate the damage in composite laminates under low velocity impact

“…In particular the use of the extended finite element method (XFEM) should be investigated to model damages without modifying the mesh. The proposed approach developed in plate structures could be extended to shell structures with the strategy proposed in [12].…”

“…The advantage is that 3D solutions can be obtained with a computational cost characteristic of standard 2D solutions [11]. This approach has been applied to composites shell structures [12] and have been improved using high order interpolation in the thickness [13,14]. In this work the PGD will be adapted to simulate a low velocity impact on a composite laminate involving damages.…”

Advanced separated spatial representations for hardly separable domains

“…A parametric 3D elastic solution of beams involved in frame structures was proposed in [18]. The same approach was extensively considered in structural plate and shell models in [19][20][21][22][23][24] and [25].…”