Bending Solution of Plates on Winkler Foundation by Element-Free Galerkin Method Based on Mindlin Plate Theory

Element-free Galerkin method (EFGM) is successfully applied to solve the bending problem of plates on a Winkler foundation. The shape function which is characteristic of high-time continuity is formulated by means of weight function. A way to incorpor- ate the self-adaptive influential radius in weight function is proposed. Based on variational principle, this paper derives control equation for the bending of plates on a Winkler foundation from Mindlin-Reissner plate theory. Using penalty function mothed, assembled stiffness matrix which is real symmetry positive definite matrix is deduced. This method can solve the bending problem of plates with different boundary conditions on a Winkler foundation. The corresponding computer programs of EFGM and post-process programs are also developed. Numerical examples show that EFGM solving the bending of plates on a Winkler found is reasonable and feasible. This present study provides a newly effective numerical method for the Winkler foundation bending problem and expands the application field of EFGM.