A bilinear shell element based on a refined shallow shell model

A four‐node shell finite element of arbitrary quadrilateral shape is developed and applied to the solution of static and vibration problems. The element incorporates five generalized degrees of freedom per node, namely the three displacements of the curved middle surface and the two rotations of its normal vector. The stiffness properties of the element are defined using isoparametric principles in a local co‐ordinate system with axes approximately parallel to the edges of the element. The formulation is based on a modern, refined variant of the shallow shell models found from the classical books on shell theory. In addition, the bending behavior of the element is improved with numerical modifications, which include mixed interpolation of the membrane and transverse shear strains. The numerical experiments show that the element is able to compete in accuracy with the highly reputable bilinear elements of the commercial codes ABAQUS and ADINA. The new formulation even outperforms its commercial rivals in problems with strong layers such as vibration problems or problems with concentrated loads. Copyright © 2009 John Wiley & Sons, Ltd.