Design sensitivity of post-buckling states including material constraints

Abstract

This paper reports theoretical studies on the design sensitivity of problems with geometrically non-linear behavior leading to buckling and post-buckling of thin-walled structural members. For the class of problems considered, buckling occurs in the form of a stable bifurcation, and it is assumed that 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 the material as part of the sensitivity study of equilibrium states along the post-critical path. The investigation employs a discrete model of a structure in terms of generalized coordinates (suitable for finite element analysis) and a single load parameter; and perturbation techniques to classify the 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 sensitivity with respect to changes in a design parameter is discussed. A simple example of a circular plate is presented to illustrate the use of the formulation for the sensitivity with respect to a single design parameter.