Analysis of thin-walled anisotropic frames by the direct stiffness method

Abstract

The stiffness matrix for a one-dimensional beam element for use in a direct stiffness matrix method for analysing thin-walled anisotropic frames is presented in this paper. Thin-walled beams are widely used as structural components and stiffeners in aerospace and civil engineering applications. The stiffness matrices for two 2-noded 12 degrees of freedom beam elements, one of which accounts for warping and anisotropic coupling only and called a “warping superelement”, and the other a “non-warping element”, are developed numerically. The warping superelement is used in the region of the beam where warping is considered critical. The length of this region, which is dependent on the geometric and mechanical properties of the beam cross-section, is determined using a technique that utilizes equivalent one-dimensional mechanical properties of the composite material panels in the cross-section. The non-warping element is used outside of this critical region. Numerical examples of a thin-walled space frame structure are presented to demonstrate the use of the beam model. Results obtained using the proposed model are compared with numerical results obtained from 2-D finite element analysis.