Assumed strain formulation for the four‐node quadrilateral with improved in‐plane bending behaviour

A new assumed strain quadrilateral element with highly accurate in‐plane bending behaviour is presented for plane stress and plane strain analysis. The basic idea of the formulation consists in identification of various modes of deformation and then in proper modification of the strain field in some of these modes. In particular, the strain operator corresponding to the in‐plane bending modes is modified to simulate the strain field resulting from the assumptions usually made in structural mechanics. The modification of the strain field leads to the assumed strain operator on the element level. As a result, the so‐called shear and membrane locking phenomena are alleviated. The element exhibits remarkable success in bending‐ dominated problems even when severely distorted and high aspect ratio meshes are used. Another advantage of the present assumed strain element is that locking for nearly incompressible materials is also mitigated. While this assumed strain element passes the patch test only for the parallelogram shapes, the element provides convergent solutions as long as the initially general form of the element approaches a parallelogram shape with the refinement of the mesh.