An approximation technique for design sensitivity analysis of the critical load in non-linear structures

A new technique of approximating design sensitivities of the critical load is presented in this paper. The technique results in stable and reliable estimations of design sensitivities at prebuckling points. Since taking derivatives of an approximated eigenvalue problem gives unstable sensitivities as the point approaches the critical load, the sensitivities are approximated directly from the exact sensitivity expressions. The sensitivities are approximated by applying two common approaches that are used in the critical load estimation and are called &one- and two-point approximationʹ. The reliability and applicability of the proposed technique are demonstrated through several numerical examples of truss and beam structures. Two-point approximation of design sensitivities gives better results than one-point approximation.