Non-classical effects in non-linear analysis of pretwisted anisotropic strips

Abstract

The literature on classical analysis of anisotropic beams assumes that all 1D “moment strain” measures (i.e. twist and bending curvatures) are of the same order of magnitude, resulting in a linear cross-sectional analysis. The present paper treats the situation in which one or more of the 1D moment strain measures may be larger than the other(s), resulting in a non-linear cross-sectional analysis. This type of non-classical analysis is needed, for example, in problems where the trapeze effect is important, such as in rotor blades. As a precursor to complicated non-linear sectional analysis of arbitrary cross sections, a non-linear sectional analysis is presented for an anisotropic strip with small pretwist, based on the dimensional reduction of laminated shell theory to a non-linear one-dimensional theory using the variationalasymptotic method. Results obtained from this strip-beam analysis are compared with available theoretical and experimental results for a problem in which the trapeze effect is important. In order to demonstrate the usage of the results in the analysis of structures made of an arbitrary geometrical combination of pretwisted generally anisotropic strips, a closed-form expression is derived for the torsional buckling of a column with a cruciform cross section.