Meshless analysis for cracked shallow shell

Abstract

A moderated thick double curved shallow shell with functionally graded materials subjected to static and dynamic loads are investigated by the meshless methods. Shear deformable plate theory is applied and the governing equation with respect to the middle surface is formulated in the Cartesian coordinate system with five degrees of freedom. The numerical solutions of the partial differential equations are obtained by the Finite Block Method in both strong form formulation (Point Collocation Method) and weak form formulation (Meshless Local Petrov-Galerkin) with Lagrange series interpolation and mapping technique. Two-dimensional plane-stress and plate bending problems are coupled in the governing equations. The second-order partial differentials are employed in the algorithm of strong form of governing equations and the first-order derivatives are required only in the weak form. The stress resultant intensity factors are evaluated by the Crack Opening Displacement (COD) and by the Variation Principle Method (VPM) techniques. The Laplace transform method and Durbin's inverse technique are utilized to deal with the crack problems under dynamic load. Comparisons have been made with analytical and numerical solutions with the finite element method in order to demonstrate the accuracy and convergence of the meshless approaches.