Sensitivity analysis of thin-walled members, problems and applications

A review of problems related to sensitivity analysis of thin walled members with open monosymmetric or bisymmetric cross-section is presented. The restraints imposed on angle of cross-section rotation, transverse displacement and cross-section warping are taken into account. The consideration is based upon the classical theory of thin-walled beams with nondeformable cross-section. The first variations of state variables due to a change of the design variable are investigated. Arbitrary displacement, internal force or reaction of the member subject to static load, critical buckling load, frequency and mode of torsional vibration are assumed to be the state variables. The dimensions of the cross-section, the material constants, the restraints stiffness, and their locations, position of the member ends are taken as the design variables. Accuracy of the approximate changes of the state variables achieved by sensitivity analysis is also discussed.