Author(s)

S. Šilih & S. Kravanja

Abstract

This paper presents the synthesis of trusses using Mixed-Integer Non-Linear Programming (MINLP). The discrete/continuous non-convex and non-linear optimization problems are solved by the Modified OA/ER algorithm. The Hiearchical superelement approach (HSA) is introduced for the discrete topology optimization of trusses in order to reduce the number of topology alternatives. For the solution of truss synthesis problems, which include a high number of discrete/binary variables, we applied multilevel MINLP strategies. The Sequential Two-Phase (STP) strategy was developed for topology, shape and standard dimension optimization of trusses. A numerical example at the end of the paper shows the suitability of the proposed approach. 1 Introduction The paper presents the Mixed-Integer Non-Linear Programming (MINLP) optimization approach to the synthesis of trusses. The solution of discrete/continuous and non-linear optimization problems is discussed with respect to the simultaneous topology, shape and standard dimension optimization of trusses. In the context of truss synthesis, the discrete optimization problems can be divided into two main spheres of activity. The first one is topology optimization with the object of obtaining the optimal number and configuration of structural elements (bars), while the second one is a discrete dimension optimization problem, where cross-sections of elements are forced to have discrete, in many cases standard dimensions. A wide range of different optimization techniques has been employed in order to solve the topology optimization problem of trusses, e.g. Genetic Algorithm (GA) [1], [2], the GA linked with Non-Linear

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