Analysis of composite plates using element free galerkin method

Abstract

Meshfree methods are a new class of numerical analysis methods that rectify some drawbacks of traditional mesh-based methods like FDM, FEM, BEM & FVM. Composite plates are quite common in aerospace industries and are subject to hostile operating conditions making them prone to cracks and their propagation. Hence meshfree methods have a possible application in the crack propagation of composite laminates. In this work, the Element free Galerkin Method- one of the most popular meshfree methods- is applied to isotropic and composite plates and the behavior of the plates is studied under plane stress and transverse bending. The isotropic plates are analysed using Kirchoff’s plate theory and the laminates are analysed using Classical Laminate Theory. To implement the EFG method for analysis of plate, a computer code is developed and executed in MATLAB platform. The current formulation is validated with the exact solutions. The dependence of the performance of the methods on the parameters concerning these methods is analysed and the ways to find optimal parameters are discussed. It is found that EFGM gives excellent results. However, it is dependent heavily on the parameters like support domain size. It is found that the polynomial basis and weight function are the most critical parameters and must be chosen as per the structural theory used. The support domain size, the quadrature order and nodal density also affect the results significantly.