An efficient 3D enhanced strain element with Taylor expansion of the shape functions

Further development of three dimensional tri-linear elements based on a modified enhanced strain methodology is presented. The new formulation employs Taylor expansions of the derivatives of the isoparametric and enhanced shape functions in local coordinates. With this approach, only nine enhanced modes are needed for developing a dilatational-locking free element. Furthermore, the formulation permits a symbolic integration of the element tangent matrix, and more efficient static condensation procedure due to uncoupling of the enhanced modes. Good results in the analysis of thin shell structures, using only one 3D element in the thickness direction of the shell, are also presented.