Quadrilateral Axisymmetric Elements Formulated by the Area Coordinate Method

Abstract

In this paper, two displacement-based 4-node quadrilateral axisymmetric elements are presented by the quadrilateral area coordinate method (QACM) [1,2] and generalized conforming conditions. Firstly, by using nodal and perimeter version generalized conforming conditions for axisymmetric problems, the fundamental displacement fields formulated by the QACM are established; secondly, the internal displacement fields (also expressed by the QACM) are constructed by nodal conforming conditions. The resulting element is denoted as AQACQ6. Then, further modification [3] for the internal strain matrix of element AQACQ6 is performed, and another new element AQACA6M, which can pass the strict form constant stress/strain patch test, is thus obtained. It can be shown that the displacement fields of these two new elements both possess second-order completeness in global coordinates. Several numerical examples show that both elements exhibit excellent performance for various tests of almost incompressible and mesh distortion problems. The efficiency of the QACM and the generalized conforming theory for developing simple, effective and reliable finite elements is again demonstrated.