An enhancement of overlapping finite elements. (February 2022) - Lee, Sungkwon; Bathe, Klaus-Jürgen
Highlights: We present a novel development of overlapping finite elements. The elements are no longer based on a function used in meshless solution schemes. We identify the required numerical integration. We also study the geometric distortion-insensitivity, conditioning of the equations. The results of illustrative example solutions show the excellent performance of the elements. Abstract: We present a novel further development of overlapping finite elements. The formulation of the enhanced elements is based on the earlier published elements but has an important new ingredient which renders the enhanced formulation more effective with respect to the evaluation of the element matrices and the solution of the governing finite element equations. The novel ingredient is that the elements are no longer based on a function used in meshless solution schemes; hence the elements provide more generality and ease of use. We first give the formulation which is applicable to two- and three-dimensional analyses of solids, give new insights, and then present an evaluation considering the required numerical integration, geometric distortion-insensitivity and the conditioning of the resulting finite element equations. In the study of the element characteristics, we also give some illustrative example solutions that show the performance of the elements in linear static analyses of two- and three-dimensional solids.