A mesh-free method for static and free vibration analyses of thin plates of complicated shape

Abstract

A mesh-free method is presented to analyze the static deflection and the natural frequencies of thin plates of complicated shape. The present method uses moving least-squares (MLS) interpolation to construct shape functions based on a set of nodes arbitrarily distributed in the analysis domain. Discrete system equations are derived from the variational form of system equation. For static analysis, a penalty method is presented to enforce the essential boundary conditions. For frequency analysis of free vibration, the essential boundary conditions are represented through a weak form and imposed using orthogonal transformation techniques. The present EFG method together with techniques for imposing boundary conditions is coded in Fortran. Numerical examples are presented for rectangular, elliptical, polygonal and complicated plates to demonstrate the convergence and efficiency of the present method.