Volumetric topology optimization under redundancy constraints

Abstract

With ever-increasing pollution and scarcity of resources, structural optimization, the science of finding the optimal structural arrangements under equilibrium constraints, is becoming an increasing necessity in engineering practice. However, designers are hesitant to adopt a method that is by nature a limit state and thus potentially unreliable. This thesis embeds a level of safety, namely redundancy, within the structural optimization process. Redundancy is the ability to remove a certain number of elements from the structure without losing stability. The thesis translates this constraint into a linear mathematical optimization problem. Then, a topology optimization algorithm is developed that identifies the least volume structure with the ability to remove any element(s) while maintaining stability under the initial loading. Besides the developed algorithm, this thesis shows the relation between the internal forces of redundant structures and their substructures, and in fact shows that it can be expressed linearly when only 1 level of redundancy is provided, and polynomial for higher levels. The algorithm is eventually implemented and extensively analyzed for a series of configurations, showing that redundant optimal shapes have considerably less volume than twice that of the pure volumetric optimal, and hence effectively combine safety with material efficiency. Overall, this thesis constitutes the early stage of a novel structural optimization algorithm that is unique to its volumetric optimization objectives.