DOI 10.1007/s00158-003-0304-9

Effects of microscale material randomness on the attainment of optimal structural shapes T. Liszka, M. Ostoja-Starzewski Abstract 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 mate-rial randomness. By contrast, the present study inves-tigates 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 im-plemented in the commercial Altair’s OptiStruct com-puter code. In particular, this generalization allows for the dependence of each finite element’s stiffness matrix on the actual microstructure contained in the given ele-ment’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 op-portunity to choose ‘stiffer ’ cells and discard those with weaker material. The paper does not aim for a robust de-sign process, but tries to answer a simpler intermediate question: how the random fluctuation of material prop-erties influences a structure that has been designed using classical continuum-based optimization algorithms. Key words optimal structures, random microstructur