Nonlinear bending analysis of composite plates using mesh free method and Legendre basis functions

Nonlinear bending analysis of thin rectangular composite plates with arbitrary boundary conditions requires the use of numerical methods. One of the most common numerical methods in recent decades is meshfree collocation method with legendre basis functions. The meshfree method means that does not require the generation of meshes as in the finite element method, but only requires a scattered set of nodes to descretize the domain of interest. The nodes used in the present research are legendre-gauss-lobatto points. Classical laminated plate theory is used for developing equilibrium equations that it produces acceptable results for thin plates. In this paper, the equilibrium equations are solved directly by substituting the displacement fields with equivalent finite legendre polynomials. Equations system is obtained by discretizing the equilibrium equations and boundary conditions with finite legendre polynomials. Nonlinear terms are caused by the product of variables in the equilibrium equations and the nonlinear set of equations is solved by Newton-Raphson technique. Since the 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 for composite plates with different boundary conditions are computed and compared with those available in the literature, wherever possible.