On Geometry of Truss

Abstract

It has been shown, by a number of examples, that it is possible to obtain rational designs by introducing a geometrical variation of trussed structures into the design process. To determine the effective geometrical configuration, two kinds of parameters, cross sectional areas and nodal coordinates, need to be taken into account in the optimization procedure. The treatment of nodal coordinates apparently results in the increase of the number of design variables, which often induces some difficulties in the application of mathematical programming. Large scale optimization problems generally have a poor convergency to require excessive computation time or memory capacity. For such problems, U. Kirsch proposed a decomposition approach and showed its efficiency by some design examples. In this paper, a search for least-weight geometry is carried out by a two-step treatment based on Kirsch's approach. The cross sectional areas are assumed to be completely dependent on and determined from the set of nodal coordinates. Then, two design approaches are considered. The first approach is the deterministic method based on the allowable stress criterion. The other is the probabilistic method, where the safety is examined by the system failure probability. Also, the influence of buckling constraints and the number of employed nodes on geometry are discussed through some numerical examples.