Efficient equilibrium-based stress recovery for isogeometric laminated curved structures

Abstract

This work extends the stress recovery for laminated composite solid plates, proposed in [1,2], to curved structures. Based on 3D Isogeometric Analysis (IGA) computations and equilibrium, this procedure uses a single element through the thickness in combination with a calibrated layer-by-layer integration rule or a homogenized approach, allowing for an inexpensive and accurate approximation in terms of in-plane stresses (and their derivatives), while through-the-thickness stress components are poorly approximated. Relying on the high-order continuity properties of IGA shape functions, an accurate out-of-plane stress state can also be recovered by means of direct integration of the equilibrium equations in strong form. The a posteriori step application, which is straightforward in the context of solid plates, is not trivial in the case of curved geometries. In fact, the notion of in-plane and out-of-plane directions is not clear when modeling this kind of structures in the global reference system, while adopting curvilinear coordinates to express the equilibrium gives rise to additional coupled terms that require an iterative process to resolve the balance of momentum equation. Therefore, we propose to apply the recovery locally, which, despite leading to more elaborated stress derivative terms because of the increasing geometry complexity, still allows for a direct reconstruction as the resolvent system is uncoupled. Several numerical results show the good performance of this approach particularly for composite stacks with significant radius-to-thickness ratio and number of plies.