A non-linear element for analysing elastic frame structures at large deflections

Abstract

A non-linear finite element for analyzing elastic frame structures at large deflections is presented. A co-rotational technique combined with Classical beam theory with the inclusion of the effect of axial forces is adopted. The element nodal force vector is derived from the strain energy of the element. The element tangent stiffness matrix is obtained by differentiating the nodal force vector, with respect to the degree of freedom (d.o.f.). The obtained formulations have a simple and compact mathematical forms which are easy to implement into a computer program. An incremental interactive technique based on Newton-Raphson method is adopted to solve the non-linear equation and to trace the equilibrium paths of the structures. Numerical examples are presented to show the accuracy and efficiency of the proposed formulations.