A Trefftz based meshfree local method for bending analysis of arbitrarily shaped laminated composite and isotropic plates

AR. Motamedi, B. Boroomand, N. Noormohammadi

Engineering Analysis with Boundary Elements. 143:237-262.

Abstract

A simple meshfree method is developed in the context of Trefftz approaches to solve bending problem of arbitrarily shaped laminated composite and isotropic plates. Widely used deformation theories including classical plate theory, first-order and third-order shear deformation theory are adapted to the method, so the solution range contains thin to thick plates without any restrictions on geometry, genus, layer sequences or boundary conditions. The solution domain is discretized by a set of nodes at which the degrees of freedom are defined. A sub-domain (cloud) centered at each node and containing several adjacent nodes is considered, over which the corresponding Partial Differential Equation (PDE) is split into homogeneous and particular parts. The solution of the homogeneous PDE is formed using a series of exponential basis functions capable of exactly satisfying the PDE, thus putting the method in the context of Trefftz approaches. The boundary conditions are applied in a point-wise manner without the need for boundary meshes. No integration is enforced throughout the solution procedure. By investigating several sample problems compared the literature or the Finite Element Method (FEM), perfect agreement and high convergence rate have been appeared, while the required nodes in the present method is considerably fewer than FEM.