Discrete optimization of trusses with stability constraints

The paper deals with discrete optimization of elastic trusses with geometric nonlinear behaviour and constraints on stability. The problem consists of minimizing the weight of the structure and choosing the optimal cross-sectional areas of members so that external loads do not cause a loss of stability. Member cross-sections are selected from a discrete set of available sections. Element stresses, element stability and global structural stability constraints are considered. An enumeration method according to the increasing value of the objective function is applied. The numerical examples concern the optimization of shallow truss structures when snap-through can occur. The discrete optimal solutions ahve been compared with the results of continuous design variables optimization. The influence of small initial imperfections of geometry on discrete optimal designs has been examined.