A simplified triangular shell element with a necking criterion for 3-D sheet-forming analysis

Abstract

A 3-node triangular shell element with only 3 translational degrees of freedom per node is presented, in which the out-of-plane displacement is the only d.o.f. considered for bending. The bending stiffness matrix of the element is derived by assuming constant curvature normal to the boundary with adjacent elements. An explicit dynamic time integration scheme is implemented for sheet forming analysis. The authors have incorporated in the numerical analysis their necking criterion based on the intrinsic Forming-Limit Stress Diagram.