Development of a shell element with pressure variation through the thickness

Abstract

A shell formulation was developed from a three-dimensional solid. The shell element is an isoparametric element, and has four corner nodes at which there are three displacement and three rotations, independently. Therefore, the element formulation includes the transverse shear deformation and the transverse normal deformation. In addition, the formulation consists of separate components of the mean stress and deviatoric stresses because the Gurson constitutive model for void growth is based on the mean stress and the dilatation. As a result, the Gurson void model can be implemented in the shell formulation at the next stage. The shell element uses the reduced integration along the inplane axes and full integration along the transverse direction If more accuracy is required along the thickness of the shell, a large number of integration points can be selected in the direction. Verification of the shell element was performed for a plate problem and a shell problem whose analytical solutions were available. The next phase of this work is to implement the Gurson model in the shell element. Once those are successfully completed, the module will be incorporated into the DYSMAS program.