Analysis of Thin Plates by the Element-Free Galerkin Method

A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into “finite elements”. The satisfaction of the C1 continuity requirements are easily met by EFG since it requires only C1 weights; therefore, it is not necessary to resort to Mindlin-Reissner theory or to devices such as discrete Kirchhoff theory. The requirements of consistency are met by the use of a quadratic polynomial basis. A subdivision similar to finite elements is used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Lagrange multipliers. It is shown, that high accuracy can be achieved for arbitrary grid geometries, for clamped and simply-supported edge conditions, and for regular and irregular grids. Numerical studies are presented which show that the optimal support is about 3.9 node spacings, and that high-order quadrature is required.