A cost-effective isogeometric approach for composite plates based on a stress recovery procedure

Abstract

This paper introduces a cost-effective strategy to simulate the behavior of laminated plates by means of isogeometric 3D solid elements. Exploiting the high continuity of spline functions and their properties, a proper out-ofplane stress state is recovered from a coarse displacement solution using a post-processing step based on the enforcement of equilibrium in strong form.Appealing results are obtained and the method is shown to be particularly effective on slender composite stacks with a large number of layers.

Fast assembly of Galerkin matrices for 3D solid laminated composites using finite element and isogeometric discretizations

“…Finally, substituting (A.10) into (A.8), and including the Assumptions 2 and 3, the stiffness matrix terms can be rearranged in the same way as we did for (25), and the P ijs l,αβ matrices (26) become The termsC αβ,l are computed following (A.11) and particularizingĈ for every material layer l, with l = 1, . .…”

“…This approach has been recently extended in [51] to the case of collocation methods. In [25], despite the use of single element through the thickness, the stiffness matrix assembly cost is still high, due to the use of layerwise quadrature schemes along the lamina thickness (the number of quadrature points scales linearly with the number of layers).…”

Fast and accurate elastic analysis of laminated composite plates via isogeometric collocation and an equilibrium-based stress recovery approach

“…As interlaminar delamination and other fracture processes rely mostly on out-of-plane components, a proper through-the-thickness stress description is required. In order to recover a more accurate stress state, we perform a postprocessing step based on the equilibrium equations, following [23], relying on the higher regularity granted by IGA shape functions. This procedure, which takes its roots in [19,25,63,73], has already been proven to be successful for IGA-Galerkin.…”

“…For this kind of structures also simple loading conditions, such as traction or bending, cause a complex 3D stress state because of the difference in the material properties between the layers, which may lead to delamination, con-sequently requiring an accurate stress evaluation through the thickness (see, e.g., [65,70]). As an alternative to two-dimensional theories, often insufficiently accurate to depict delamination and interlaminar damage, and to layerwise theories, which typically show an high computational cost, a novel method combining an isogeometric analysis (IGA) Galerkin approach with a stress-recovery technique has been recently proposed in [23]. Introduced in 2005 by Hughes et al [36], IGA aims at integrating design and analysis employing shape functions typically belonging to Computer Aided Design field (such as, B-Splines and NURBS).…”

“…This method is significantly less expensive compared to a layerwise approach since employs a considerably lower number of degrees of freedom. The post-processing approach, first proposed in [23], takes inspiration from recovery techniques which can be found in [16,19,25,42,63,73] and is based on the direct integration of the equilibrium equations to compute the out-of-plane stress components from the in-plane ones directly derived from a coarse displacement solution.…”