Postbifurcation Equilibrium Paths Modified by Nonlinear Configuration-Dependent Conservative Loading Using Nonsmooth Analysis*

Abstract

ABSTRACT This paper discusses the effect of deformation-sensitive loading devices because the nature of loading is generally not perfectly dead, being independent of the deflections that occur. This paper presents the effect of nonlinear variable load. Postbifurcation equilibrium paths and structural tangent stiffness are modified on the basis of a polygonal approximation and nonsmooth analysis. The effects of dead and variable loads are compared. Configuration-dependent loading devices can be characterized by some load-deflection functions, much like the nature of material behavior can be characterized by stress-strain functions. The effect of a deformation-sensitive load is similar to that of the material. Consequently, in the stability analysis of structures, a configuration-dependent loading program can be handled like material behavior. Thus, in the tangent stiffness of the structure, much like the tangent modulus of the material, the tangent modulus of the load appears. Previous research has shown that nonlinear material behavior can be handled using nonsmooth analysis—approximating nonlinear material functions by polygonals. In this paper, this method and its results are extended to the case of nonlinear loading programs. The present analysis is based on earlier work in which a complete stability analysis was introduced for dead-loaded structures that have polygonal constitutive law, namely nonsmooth material functions and non-smooth internal potential. The aim of this paper is to extend these results to cases involving nonlinear configuration-dependent conservative loading by introducing nonsmooth loading functions.