A Hybrid Force Method/Stiffness Matrix Method for the Analysis of Thin-Walled Composite Frames

Abstract

A novel method for the analysis of frames constructed of thin-walled members of anisotropic composite materials is presented in this paper. The method accounts for non-isotropic coupling effects that exist in composite material beams due to the anisotropy of the composite material laminates that form the thin-walled cross-section. The method also accounts for warping effects known to be significant in thin-walled members. The analysis is performed by the direct stiffness matrix method utilizing a new approach that divides each thin-walled member of the frame into one-dimensional warping-beam superelements and non-warping conventional beam elements. The element stiffness matrices for these two one-dimensional beam elements are obtained by a numerical procedure that is based on the classical force method of analysis. The stiffness matrices of both beam elements are 12 × 12 matrices corresponding to the six degrees of freedom per node required for conventional space frame analysis. The remarkable feature of this representation is that warping is accounted for without introducing additional degrees of freedom to account for the bimoment and warping twist in the members. This is accomplished by use of the warping-beam superelement that linearizes the regions of non-uniform torsion in the thin-walled beam. Examples of space frame structures constructed of thin-walled composite material I-beams are presented to demonstrate the method. Results of analyses using the proposed method are compared with those obtained from two-dimensional finite element models.