Geometrically Nonlinear Analyses Using 2-Dimensional Generalized Finite Element Enriched by the Quadratic Deformation Mode

Abstract

A formulation of a novel in-plane generalized finite element, which can be used in geometrically nonlinear analysis, is presented and some analyses are conducted using the proposed element. The presented element has four nodes, and four additional degrees of freedom are added on each node. As a result, this element can reproduce the quadratic deformation mode with only corner nodes and has no linear dependency, which is a well known problem of generalized finite elements. The formulation is based on the rate form of the virtual work principle and is obtained by a simple extension of the standard FEM. The convergence of the analysis solution and its robustness for element distortion are investigated, and the results are compared with those of standard-displacement-based first- and second-order elements. The proposed element provides solution convergence as good as or better than those of the conventional second-order elements. In addition, it is shown that an accurate solution is obtained when the mesh is strongly distorted.