Discrete optimal weight design of geometrically nonlinear truss-structures - Csébfalvi, Anikó (Computer Assisted Methods in Engineering and Science, 1999)
In this paper, we introduce a new branch-and-bound type method, for discrete minimal weight design of geometrically nonlinear truss structure subject to constraints on member stresses and nodal displacements when the member cross-sectional areas are available from a discrete set of a given catalogue. The discrete optimization problem can be formulated as a tree search procedure. The initial - unfeasible - node of the searching tree is obtained by decreasing the relaxed cross-sectional areas to the closest discrete catalogue value. Each node of the branch-and-bound searching tree is characterized by the weight of the structure, the actual value of the infeasibility penalty function, and the minimal relaxed additional weight, that is needed to obtain a feasible structure from the given state. The proposed method involves an exterior point method to determine the relaxed solution of the minimum weight design problem. The algorithm seems computationally attractive and has been tested on a large number of examples. Numerical results are presented for a well-known test problem.