A high order cell-based smoothed finite element method using triangular and quadrilateral elements

Abstract

This paper presents a novel high-order cell-based smoothed finite element method (CS-FEM) using 6 nodes triangular (T6) and 8 nodes quadrilateral (Q8) elements. In addition, high-order quadrilateral transition elements (Q5 and Q6) are also developed based on this method. In this method, the high order strain field in each smoothing domain is constructed using pick-out theory. And the strain field is represented by a complete polynomial. Both triangular and quadrilateral high order CS-FEM are formulated without the need to dividing the elements into smaller smoothing cells. Since there is no mapping and derivation in computation, so high-order CS-FEM has better adaptability to mesh distortion. The performance of high-order CS-FEM is examined in great detail, using a number of numerical examples. And it is found that CS-FEM results agrees with finite element method (FEM) counterpart. In addition, we found also that the edge-nodes of the high-order elements in a CS-FEM model can be quite freely placed, which is not possible in a standard high-order FEM model. All the high-order CS-FEM models are implemented through User-defined Element Library (UEL) in ABAQUS, which greatly improves work efficiency.