An Efficient 4-Node Plane Hybrid/Mixed Element with Tensorial Formulation

The paper is mainly concerned with developing a kind of tensorial formulation scheme for low- order hybrid/mixed finite elements based on Hellinger-Reisser variational principle. By making use of the invariance properties of tensors, the disadvantages due to coordinates transformation are totally avoided. Also, inmatchingthe derived strain field, which is in tensorial form, a properselection ofthe optimal stress field is successfully achieved on the basis of“the consistency of one stress parameter with one independent deformation mode”. Thus, a 4-node plane quadrilateral element is obtained. Numerical simulations reveal the remarkable characteristics of the present elements, such as invariance, robustness, having no zero energy,etc.