The strain-smoothed 4-node quadrilateral finite element

Recently, the strain-smoothed element (SSE) method has been developed for 3-node triangular and 4-node tetrahedral solid elements. The method was also applied for enhancing the membrane performance of a 3-node triangular shell element (MITC3+ element). Using the SSE method, convergence behaviors of the finite elements were significantly improved without additional degrees of freedom. However, the application of the SSE method is limited to constant strain finite elements such as 3-node triangular and 4-node tetrahedral elements. In this paper, the SSE method is applied to a 4-node quadrilateral finite element. Doing so, the piecewise linear shape functions are employed instead of standard bilinear shape functions. The proposed strain-smoothed 4-node quadrilateral element passes all the basic tests, and shows a significantly improved accuracy in various numerical examples. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The strain-smoothed element (SSE) method has been developed and applied to improve the convergence behavior of finite elements, limited to constant strain elements. In this paper, the SSE method was successfully applied to a 4-node quadrilateral finite element using piecewise linear shape functions, resulting in significantly improved accuracy.