Equilibrated Basis Functions for Static Analysis of In-plane Heterogeneous Laminated Composite Plates in Boundary and Meshfree Approaches

Abstract

In this paper, static analysis of in-plane heterogeneous laminated composite plates is studied using equilibrated basis functions in a meshfree style based on first order shear deformation theory. The governing equations are satisfied through a weighted residual integration over a fictitious rectangular domain submerging the main domain of the plate. The integration is decomposed into a set of 1D pre-evaluated ones, which removes the need for numerical integration during the solution progress and considerably reduces the computational costs. The resulted bases may be implemented both in a boundary form and in a meshless local approach. Proper correlation between adjacent nodes in the meshless form ensures complete continuity of both the deformation and the stress components throughout the plate domain. Boundary conditions are applied independently of the equilibrium satisfaction through a simple collocation technique, which drastically decreases the required effort. The achieved results, compared with those presented in the literature or by commercial codes, reveal proper accuracy and convergence of the method. A comparative study on the effect of in-plane heterogeneity of the stiffness coefficients is also presented after verification of the method.