An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape

An element free Galerkin (EFG) method is proposed to analyze the natural frequencies of composite laminates of complicated shape. The present method uses moving least squares (MLS) approximation to construct shape functions based on a set of nodes scattered in the problem domain. The dynamic equations of the system are formulated using the Lagrangian equation. The essential boundary conditions are imposed using their weak forms with Lagrange multipliers. Orthogonal transformation technique is used to implement the essential boundary conditions in the eigenvalue equation. The present EFG method is coded in Fortran. Numerical examples are presented for plates of square, elliptical and complicated shapes with different boundary conditions.