Assessment of generalized finite elements in nonlinear analysis

Abstract

This paper presents two different formulations for in-plane generalized finite elements for geometrical non-linear analysis. The results from analyses which employ the proposed elements are also presented. One of the proposed elements has one additional degree of freedom at each node and shows good performance for analysis in which bending deformation is dominant. The other can reproduce quadratic deformation mode with only corner nodes and it 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 obtained by a simple extension of standard FEM. The convergence of analytical solutions and the robustness against element distortion are investigated and the results are compared with those of standard displacement based first and second order elements. In most cases, the proposed elements provide good solution convergence which is similar to, if not better than, those of conventional second order elements. Additionally, it is also shown that high-precision solutions can be obtained even if the mesh is strongly distorted.