The generalised constrained finite strip method for thin-walled members in shear

Abstract The constrained finite strip method (cFSM) is an extension of the semi-analytical finite strip method (SAFSM) of structural analysis of thin-walled members, where consideration of the displacement fields utilised and of various mechanical criteria allows constraint matrices to be formed. The application of these constraint matrices to the linear buckling eigenvalue problem of the SAFSM results in deformation fields that satisfy the considered criteria and, therefore, isolate particular modes. Through careful selection of the mechanical criteria, the deformation fields obtained may be restricted to particular buckling modes. This is referred to as modal decomposition. While the cFSM has been applied to modal decomposition of thin-walled, prismatic members under the action of longitudinal normal stresses, it has yet to be applied to such members under the action of shear stresses. Recent work using the SAFSM to analyse the buckling behaviour of thin-walled, prismatic members under applied shear stresses, notably by Hancock and Pham, has shown that the issues of potentially indistinct minima or multiple minima in the signature curve can occur under this loading, as they did for compression and bending. This paper briefly presents the derivation of a SAFSM that permits coupling between longitudinal series terms of sines and cosines and also considers membrane instability due both to shear stresses and transverse normal stresses. It then presents the application of the cFSM to such a finite strip and results are produced for members under shear stresses. While the results are presented for members with unrestrained ends (equivalent to infinitely long members), simplification via removal of the degrees of freedom not present in typical FSM formulations would allow finite length members with simply-supported ends to be analysed.