EQUILIBRIUM PATHS OF POLYGONALLY ELASTIC STRUCTURES

Stability analysis of structures having polygonally elastic material i s presented. The polygonal material model can be used for approximatin g any nonlinearly elastic behavior or originally polygonal behavior. A discrete model is considered, in which perfectly rigid elements are c onnected to each other by springs that represent material characterist ics. The behavior of the springs is governed by uniaxial arbitrary non -decreasing stress-strain polygons with horizontal and vertical jumps. The stability analysis presented is based on potential energy. Since the material law is polygon-like, the related strain energy is a nonsm ooth function, for which, since the material is reversible, it is a co nvex function. Thus, a nonsmooth convex analysis is needed. The stabil ity analysis presented in this paper is global, and related to the tot al domain of the possible deflections. Equilibrium paths of one-dimens ional problems are analyzed. Finally,-a visual presentation of the det ailed nonsmooth stability analysis is introduced. This paper is the fi rst part of a series of three papers related to nonsmooth stability. T he nonsmooth nonconvex (dissipative) problems and nonsmooth damage wit h localization are detailed in Refs. 1 and 2, respectively.