Analyzing Bending Problems of Plates on Elastic Foundations via Improved Element-Free Galerkin Method

Abstract

In this study, by combining the orthonormal basis functions and the traditional moving least-squares (MLS) approximation, thus the new approximation function is established by using the improved moving least-squares (IMLS) approximation, and the corresponding formula derivation is given in Section 2. Afterwards, the equilibrium, geometrical and physical equations of bending problems of plates on elastic foundations are presented respectively, and the equivalent functional of such problems is established with the essential boundary condition imposed by using the penalty method, thus the calculation formula of numerical solution are derived using the improved element-free Galerkin (IEFG) method with IMLS approximation. In numerical examples, we verify the convergence of the IEFG method by increasing the number of nodes. In comparison with the EFG method, the IEFG method converges faster. Moreover, the smaller error and higher calculation speed are obtained by selecting the IEFG method for solving three numerical examples.