Post-buckling of laminated plates using collocation method and Legendre basis functions

In this paper, post-buckling behavior of laminated plates is investigated using mesh-free method. One of the most common powerful numerical methods in recent decades is mesh-free collocation method. Due to wildly oscillating solutions at the endpoints and occurrence of Runge phenomenon in the case of uniform distribution of points, the domain of the problem is discretized with Legendre-gauss-lobatto nodes. In this paper, the classical laminated plate theory is used and different out-of-plane boundary conditions with anti-symmetric cross-ply and angle-ply laminates are investigated. Equations system is introduced by discretizing von-Karman’s compatibility equations and boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Because of large deformations and nonlinear terms in the strain-displacement relations, the nonlinear system of equations is solved by using Newton-Raphson technique. Since number of equations is always more than the number of unknown parameters, the least square technique is used to solve the system of equations. Some results are obtained and compared with those available in the literature.