Degenerated plate-shell elements with refined transverse shear strains

Abstract

Although traditional three-dimensional plate-shell elements relax the constraint so that normal cross-sections remain normal to the neutral plane during transverse shear deformation, the section is still constrained to remain plane. The work reported here relaxes this constraint by introducing shape functions across the thickness to approximate the transverse shear strain field in the thickness direction. These shape functions are treated in the manner of generalized angles undergoing small deformations. They are added as new degrees of freedom to the ordinary displacement field of the degenerated shell elements. The field is still able to simulate large deformation behavior of the element. Each shape function yields two independent variables, one in each direction. In this work, two types of shape functions are proposed allowing a parabolic transverse shear strain, as well as an unsymmetric transverse shear strain distribution in the thickness direction. These two modes of deformation are particularly important in the case of diffused material failure in shell structures. Displacement field representation and finite element formulation based on a total Lagrangian approach are given. Examples are presented demonstrating the applicability of this element in a variety of problems.