Structural Optimization with Reliability Constraints

During the last 25 years considerable progress has been made in the fields of structural optimization and structural reliability theory. In classical deterministic structural optimization all variables are assumed to be deterministic. Due to the unpredictability of loads and strengths of actual structures it is now widely accepted that structural problems are non-deterministic. Therefore, some of the variables have to be modelled as random variables/processes and a reliability-based design philosophy should be used, Comell [1], Moses [2], Ditlevsen [3] and Thoft-Christensen & Baker [ 4]. In this paper we consider only structures which can be modelled as systems of elasto-plastic elements, e.g. frame and truss structures. In section 2 a method to evaluate the reliability of such structural systems is presented. Based on a probabilistic point of view a modern structural optimization problem is formulated in section 3. The formulation is a natural extension of the commonly used formulations in determinstic structural optimization. The mathematical form of the optimization problem is briefly discussed. In section 4 two new optimization procedures especially designed for the reliability-based optimization problem are presented. In some examples in section 5 the optimization procedures are compared.During the last 25 years considerable progress has been made in the fields of structural optimization and structural reliability theory. In classical deterministic structural optimization all variables are assumed to be deterministic. Due to the unpredictability of loads and strengths of actual structures it is now widely accepted that structural problems are non-deterministic. Therefore, some of the variables have to be modelled as random variables/processes and a reliability-based design philosophy should be used, Comell [1], Moses [2], Ditlevsen [3] and Thoft-Christensen & Baker [ 4]. In this paper we consider only structures which can be modelled as systems of elasto-plastic elements, e.g. frame and truss structures. In section 2 a method to evaluate the reliability of such structural systems is presented. Based on a probabilistic point of view a modern structural optimization problem is formulated in section 3. The formulation is a natural extension of the commonly used formulations in determinstic structural optimization. The mathematical form of the optimization problem is briefly discussed. In section 4 two new optimization procedures especially designed for the reliability-based optimization problem are presented. In some examples in section 5 the optimization procedures are compared