Analyzing of thick plates with cutouts using the meshless (EFG) method based on higher order shear deformation theories for solving shear-locking issue

Abstract

Although the finite element method (FEM) is a well-established method for modelling the thick plates, in some cases FEM encounters some difficulties such as shear locking and decrease in the accuracy of results caused by stress concentration around the openings. In this paper for the first time, the EFG method based on the higher-order shear deformation theories is developed for analysis of thick plates with cutout to overcome these drawbacks. It should be mentioned that the EFG method does not need any mesh generation in problem domain and its boundaries. The Radial Point Interpolation method (RPIM) is used to discrete the problem domain. Several numerical examples are analyzed using proposed method and effects of aspect ratios, boundary conditions and location of cutout are discussed in details. Results show that by choosing the appropriate shape functions for the deflection and rotations, the presented EFG method has successfully overcome the shear-locking problem. Based on numerical results, the best position of circular cutout, which minimizes the maximum deflection is determined. The approximate equations for determination of maximum deflection are presented using the cubic polynomial method. Numerical implementations show that the presented method has high efficiency, good accuracy and easy implementation.