(A) study on polyhedral elements by means of the smoothed finite element method for elastic problems

Abstract

The polyhedral elements by means of the node or edge-based smoothed finite element method is proposed within the framework of linear and nonlinear elasticity. The polyhedral elements are allowed to have an arbitrary number of nodes or faces, and so retain a good geometric adaptability. The strain smoothing technique and implicit shape functions based on the linear point interpolation makes the element formulation simple and straightforward. For linear elasticity, the resulting polyhedral elements are free from the excessive zero-energy modes, and yield robust solutions very much insensitive to mesh distortion. Several numerical examples within the framework of linear elasticity demonstrate the accuracy and convergence behavior. The proposed polyhedral elements in general yield solutions of better accuracy and faster convergence rate than those of the conventional finite element methods. In addition, the polyhedral elements is extended to nonlinear elasticity with the updated Lagrangian approach. Through several numerical examples, the edge-based smoothed finite element method using the polyhedral elements is spatially stable and shows more accurate solution than the other finite element methods for nonlinear elasticity, while non-physical hourglass deformation modes are found for the node-based smoothed finite element method. In order to overcome the volumetric locking, the smoothing domain-based selective edge/elemental cell-based smoothed finite element method and the nodal cell based smoothed finite element method with mixed formulation are developed. The schemes provide good solutions in comparison with the previous works in the literatures [48, 49].