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

Abstract

A novel approach which combines isogeometric collocation and an equilibriumbased stress recovery technique is applied to analyze laminated composite plates. Isogeometric collocation is an appealing strong form alternative to standard Galerkin approaches, able to achieve high order convergence rates coupled with a significantly reduced computational cost. Laminated composite plates are herein conveniently modeled considering only one element through the thickness with homogenized material properties. This guarantees accurate results in terms of displacements and in-plane stress components.To recover an accurate out-of-plane stress state, equilibrium is imposed in strong form as a post-processing correction step, which requires the shape functions to be highly continuous. This continuity demand is fully by isogeometric analysis properties, and excellent results are obtained using a minimal number of collocation points per direction, particularly for increasing values of length-to-thickness plate ratio and number of layers.

A New Nodal Stress Recovery Technique in Finite Element Method Using Colliding Bodies Optimization Algorithm

“…Since generally analysis steps are computed in elements, the whole domain Ω reduces to each element domain, and the square of L 2 the norm of the overall domain will be obtained by summing element contributions as formulating in Eq. (17).…”

“…Wang et al [15] employed superconvergence analysis for solving Maxwell's equations and Yuan et al [16] developed a new adaptive finite element method (AFEM) based on element energy projection method. This field advanced by efforts of Patton et al [17] on laminated composite plastic and endeavors of Chi et al [18]. Caldern et al [19], Kim and Jang [20], Sracic and Elke [21], Boffi and Gastaldi [22], Prato Torres et al [23], Ganis et al [24] and Song et al [25] advanced this field by essays and all of them performed efforts on applications of error estimation and the AFEM.…”

Effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear-deformable beams with varying curvature and torsion

“…Laminated composite plates have been recently addressed in [45]. Nonlinear planar Kirchhoff rods were formulated in [46].…”

Accurate equilibrium-based interlaminar stress recovery for isogeometric laminated composite Kirchhoff plates

“…Therefore, the proposed modeling strategy is coupled with a post-processing technique which directly relies on equilibrium and grants a highly accurate prediction of the out-of-plane stress state even from a very coarse 2D displacement solution (e.g., using one high-order element to model the plate mid-plane). The adopted postprocessing technique takes its origin in [21,22,23] and has already been proven to provide good results for 3D solid plates in the context of both IGA Galerkin [24] and collocation [25] methods (but also of methods based on Radial Basis Functions [26]). The effectiveness of the proposed approach relies on the capability to obtain accurate in-plane results with only one element through the thickness and on the possibility to compute accurate stresses and stress derivatives from the obtained displacement field, thanks to the shape function higher-order in-plane continuity properties.…”