Eigenanalysis and continuum modelling of an asymmetric beam-like repetitive structure

An asymmetric repetitive pin-jointed structure, based upon a 3-D NASA framework, is analysed using a state variable transfer matrix technique. A conventional transfer matrix cannot be constructed due to the singularity of one partition of the stiffness matrix; instead, a cell (rather than cross-sectional) state vector consisting of displacements only is employed, leading to a generalised eigenvalue problem. The asymmetry of the structure leads to tension-torsion and bending-shear couplings, which may be explained in terms of the tension-shear coupling of a single face of the structure. Equivalent continuum beam properties and coupling coefficients are determined, and the effect of (a)symmetry discussed as a trade between, for example, tension-Poisson's ratio contraction for a symmetric structure, against tension-torsion coupling for the asymmetric. (C) 2004 Elsevier Ltd. All rights reserved.