Penalty Finite Element Formulation for Curved Elastica

Abstract
A simple penalty finite element formulation is presented for the large‐rotation and postbuckling analyses of curved beams. The analytical formulation is based on a form of Reissner's large‐deformation theory with the transverse shear deformation and the extensibility of the center line constrained through the use of the penalty method. Reduced integration is used in evaluating the elemental arrays, and a procedure is outlined for determining the critical points in the solution path. Numerical results are presented to demonstrate the effectiveness of the finite elements developed.