Nonlinear Analysis of Cable-strut Structures as a Mixed Complementarity Problem

Abstract

This paper proposes a computation-oriented approach for determining the structural response of cable-strut systems under prescribed, not necessarily monotonic, loading histories. A feature of such structures, and one that is often a source of computational difficulty, is the possible slackening and retensioning of the cables. The methodology used in the present work to deal robustly and efficiently with this behavior is to express the element (cable or strut) constitutive law in a special mathematical format known as “complementarity”. Mathematically, this represents the perpendicularity of two-sign constrained vectors. Mechanically, it can be used to capture precisely the unilateral behavior of cables (viz. they can only support tension) and also the irreversible yielding of struts. We outline how these cable and strut laws can be combined with classical equilibrium and compatibility relations to provide a formulation in rates. Numerical solution of this problem is carried out by converting the rate problem into a finite incremental form leading to a special class of problems known in the mathematical programming literature as a “mixed complementarity problem” (MCP). Two examples are given to illustrate application of the approach proposed.