Hierarchical Topology Optimization of Structures Subjected to Constraints on Material Design

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The hierarchical topology optimization of three-dimensional structures is addressed in this paper. The structure lay-out (macroscale)and material microstructure (microscale) are optimized concurrently to minimize compliance. It is assumed that structure is made upof a periodic cellular material. This two-scale optimization problem is subjected to global/local material resource constraints and tospecific local constraints controlling the perimeter on material microstructure design. To handle local constraints a proper algorithmicstrategy is used combining two versions of MMA (Method of Moving Asymptotes). Local design problems can be solvedindependently and one takes advantage of this property by using parallel computing techniques to speed-up the solution task.Concerning applications one might think on man's made structures but the model is used to gain insight in natural hierarchicalmaterials such as bone. At apparent level (macroscale) bone exhibits two types of tissues in a well-defined arrangement (cortical andtrabecular) while going down on length scale (microscale) one distinguish trabeculae from marrow space. Actually, bone adapts tothe mechanical environment by changing its microstructure and this natural adaptation is simulated in the present work. Further,among morphometric parameters used to characterize trabecular architecture there is the surface-to-volume ratio, which depends onanatomical site of the trabecular region. This biological feature of bone architecture is taken into account in the present study bymeans of a local material design constraint involving perimeter control. The results obtained for a proximal femur bone show a fineagreement with real bone.
Original languageUnknown
Title of host publicationNA
Publication statusPublished - 1 Jan 2008
EventEngOpt 2008 -
Duration: 1 Jan 2008 → …


ConferenceEngOpt 2008
Period1/01/08 → …

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