Quadrilateral membrane element family formulated by the quadrilateral area coordinate method

The quadrilateral area coordinate (QAC) method is a new tool for developing quadrilateral finite element models. Compared with those traditional elements using isoparametric coordinates, models formulated by QAC method are less sensitive to mesh distortion. In this paper, a family of quadrilateral membrane elements with 4–8 nodes are successfully developed by employing the QAC method, the generalized conforming conditions and internal parameters. All the displacement fields of these elements possess second-order completeness in Cartesian coordinates, so they are more accurate and robust in various distorted meshes. Numerical results show that the presented elements exhibit excellent performance in all benchmark problems, such as MacNeal’s beam, thin curved beam problems, etc., which the traditional isoparametric elements can not easily achieve. The efficiency of the QAC method for developing simple, effective and reliable serendipity plane membrane elements is again demonstrated.