Hybrid strain based three-node flat triangular shell elements

Abstract

A series of three flat triangular shell elements with three corner nodes and six degrees-of-freedom per node is proposed. The elements are based on the Hellinger-Reissner hybrid strain formulation. Each of these elements is considered as a combination of a triangular bending element and a plane stress element. The bending component is degenerate and isoparametric adopting the specially designed strain distribution to suppress shear-locking in the “thin” limit. Thus, they are generally applicable to thin and thick shells. The plane stress component is built on the basis of Allman's triangle. Effort has also been directed to study the drilling degress-of-freedom. A scheme that has a more satisfactory physical basis so that the resulting elements are capable of reflecting true normal rotations as well as desirable bending and membrane behaviours is presented. Explicit expressions of all the three element stiffness matrices are derived. They eliminate the need for numerical integration for the element stiffness matrices and thereby improve significantly the computational time. Numerical studies, including those of the obstacle course, are performed and reported in this paper.