Truss Structure Optimization for Two Design Variable Elements Using Genetic Algorithms with Stress and Failure Probability Constraints

Engineering structures need to satisfy certain criteria such that it may function properly. This paper presents the results of a study on trusses which need to satisfy optimal conditions, i.e. lowest cost possible with maximal performance. The trusses considered were statically indeterminate steel structures with multi-system of loading. The cost is here represented by the material volume of the structure and the maximal performance is reflected by the high working stresses within allowable stress limits. The material strength was modeled as a random variable with a Log Normal distribution. Beside stresses, the structures are also required to meet a failure probability of P_f=10^-3, which may occur locally within the elements as well as globally on the structure as a whole. The complexity of optimization problems depends in general on the number of the considered variables. The larger the number of variables considered, the more complicated becomes the solution process. Therefore, cases of single variable elements as well as multi variables ones were considered in this study. Optimization problems are usually solved applying iterative procedures, frequently resorting to mathematical programming. In these procedures the process usually converges to unreliable solutions; it even may completely bogged down with no solution at all. To circumvent this problem, iteration was carried out applying Genetic Algorithms where the process proceeds in a stochastic manner. Genetic Algorithms usually deliver reliable solutions.