Four-node incompatible plane and axisymmetric elements with quadratic completeness in the physical space

In this paper, four-node incompatible elements with quadratic completeness in the physical space are developed for plane and axisymmetric problems. Various revision techniques of the incompatible strain matrix or shape function are proposed to guarantee the incompatible elements to pass the constant stress patch test. In contrast with other elements in the same level, the present one gives reasonable stress solutions without any stress recovery such as the bilinear extrapolation and least square approximation. Numerical examples are given to investigate the accuracy, sensitivity to mesh distortion and locking in the incompressible calculation of the present method when irregular coarse meshes are used