Development of two-dimensional elements with a central circular hole

Abstract

Two new two-dimensional (2D) elements, one is a eight-node rectangular and the other is a eight-node circular element each with a central circular hole, have been developed using complex potentials to define stress and strain functions. These new elements can be combined with the conventional elements, e.g., isoparametric elements, with no modifications required. Two numerical examples were employed to illustrate the potential accuracy and versatility of the proposed elements. The results obtained using these two elements are in good agreement with the theoretical results. Moreover, the proposed rectangular element performs better than the proposed circular element.