Effects of microscale material randomness on the attainment of optimal structural shapes

Classical procedures of shape optimization of engineering structures implicitly assume the existence of a hypothetical perfectly homogeneous continuum - they do not recognize the presence of any microscale material randomness. By contrast, the present study investigates this aspect for the paradigm of a Michell truss with minimum compliance (maximum stiffness) that has a prescribed weight. The problem involves a stochastic generalization of the topology optimization method implemented in the commercial Altair's OptiStruct computer code. In particular, this generalization allows for the dependence of each finite element's stiffness matrix on the actual microstructure contained in the given element's domain. Contrary to intuition, stochastic material properties may improve the compliance of optimal design. This is because the optimization is performed on a given random distribution, so that the design process has an opportunity to choose 'stiffer' cells and discard those with weaker material. The paper does not aim for a robust design process, but tries to answer a simpler intermediate question: how the random fluctuation of material properties influences a structure that has been designed using classical continuum-based optimization algorithms.