Study on discrete optimization techniques in reliability-based optimization of truss structures

The paper deals with application of two optimization techniques to solve mixed (discrete–continuous) reliability-based optimization (RBO) problem of truss structures. The mixed RBO problem is formulated as the minimization of structural volume subjected to the constraints on the values of componental reliability indices determined by FORM approach. The cross-sectional areas of truss bars and coordinates of the specified truss nodes are considered as discrete and continuous design variables, respectively. The specified allowable reliability indices are associated with limit states in the form of the admissible displacements of the chosen truss nodes, admissible stress or local buckling of the elements as well as a global loss of stability. Two optimization techniques, namely: transformation and controlled enumeration methods are employed to solve the optimization problem. The transformation method allows to transform the mixed optimization problem into the continuous one. Two numerical examples: 10 bar planar truss and spatial truss dome are used to illustrate the proposed methodology of solution. Results obtained by both methods are compared and appropriate conclusions are drawn.