MATHEMATICAL ENGINEERING TECHNICAL REPORTS Optimization-Based Stability Analysis of Structures under Unilateral Constraints

This paper discusses an optimization-based technique for determining the stability of a given equilibrium point of the unilaterally constrained structural system, which is subjected to the static load. We deal with the three problems in mechanics sharing the common mathematical properties: (i) structures containing no-compression cables; (ii) frictionless contacts; (iii) elastic-plastic trusses with nonnegative hardening. It is shown that the stability of a given equilibrium point of these structures can be determined by solving a maximization problem of a convex function over a convex set. Based on the difference of convex functions (DC) optimization, we propose an algorithm to solve the stability determination problem, at each iteration of which a second-order cone programming (SOCP) problem is to be solved. The problems presented are solved for various structures to determine the stability of given equilibrium points.