Structural Topology Optimization with Stress Constraint Considering Loading Uncertainties

This paper deals with the consideration of loading uncertainties in topology optimization via a fundamental optimization problem setting. Variability of loading in engineering design is realized e.g. in the action of various load combinations. In this study this phenomenon is modelled by the application of two mutually excluding (i.e. alternating) forces such that the magnitudes and directions are varied parametrically in a range. The optimization problem is stated as to find the minimum volume (i.e. the minimum weight) load-bearing elastic truss structure that transfers such loads acting at a fix point of application to a given line of support provided that stress limits are set. The aim of this paper is to numerically determine the layout, size, and volume of the optimal truss and to support the numerical results by appropriate analytical derivations. We also show that the optimum solution is non-unique, which affects the static determinacy of the structure as well. In this paper we also create a truss-like structure with rigid connections based on the results of the truss optimization and analyse it both as a bar structure (frame model) and a planar continuum (disk) structure to compare with the truss model. The comparative investigation assesses the validity of computational models and proves that the choice affects design negatively since rigidity of connections resulted by usual construction technologies involve extra stresses leading to significant undersizing.