Design sensitivity of post-buckling states including material constraints

This paper reports theoretical studies on the design sensitivity of problem s with geometrically non-linear behavior leading to buckling and post-buckl ing of thin-walled structural members. For the class of problems considered , buckling occurs in the form of a stable bifurcation, and it is assumed th at changes in the design parameters do not break the bifurcation behavior. The specific focus of the research is the first yield or first failure of t he material as part of the sensitivity study of equilibrium states along th e post-critical path. The investigation employs a discrete model of a struc ture in terms of generalized coordinates (suitable for finite element analy sis) and a single load parameter; and perturbation techniques to classify t he critical state and to approximate the post-critical path. The problem of material behavior is modeled by means of constraints on the post-critical path, based on a yield criterion. For simplicity, the presentation uses the von Mises yield criterion, but other more complex criteria, such as those employed in composite materials (first-ply failure) can also be represented . Two forms of the constraints are formulated, and the problem of sensitivi ty with respect to changes in a design parameter is discussed. A simple exa mple of a circular plate is presented to illustrate the use of the formulat ion for the sensitivity with respect to a single design parameter. (C) 2000 Elsevier Science S.A. All rights reserved.