Stiffness Matrix for Geometric Nonlinear Analysis

Abstract

A new stiffness matrix for the analysis of thin walled beams is derived. Starting from the principle of virtual displacements, an updated Lagrangian procedure for nonlinear analysis is developed. Inclusion of nonuniform torsion is accomplished through adoption of the principle of sectorial areas for cross‐sectional displacements. This requires incorporation of a warping degree of freedom in addition to the conventional six degrees of freedom at each end of the element. Problems encountered in the use of this and similar matrices in three‐dimensional analysis are described.