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An iterative finite element based topology optimization method based on prescribed material redistribution (PMR) has recently been demonstrated to effectively identify optimal topologies for single material structures. Through the application of a family of Beta probability density and cumulative distribution functions, the method provides a gradual transition from a unimodal distribution of uniform intermediate density to a bimodal distribution of void and fully dense regions. In this paper, the PMR method is extended to dual material structures in which the tensile member strength differs from the compressive member strength. Evolution to topologies which satisfy dual material optimality criteria is ensured through the introduction of local fictitious moduli based on the local stress state. For validation, both analytically derived solutions and a numerical dual material truss optimization procedure are applied. The truss optimization procedure is based on an assumed topology for which the optimal joint coordinates and member cross-sectional areas are determined using a quasi-Newton method and fully stressed design conditions. Validation problems considered include a two-bar dual material cantilever, a dual material truss structure subjected to combined loading, and dual material shear loaded frame structures with pre-existing members. For each case, validation is provided by correlating PMR results with results obtained from the dual material truss optimization procedure. It is demonstrated that for all cases considered, the PMR method provides a reliable tool for the identification of minimum weight dual material structures. ©2010 by ASME.
Taggart, David G., Denis Jahns, Arun Nair, and Peter Dewhurst. "Application of the PMR topology optimization scheme to dual material structures." ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) 3, PARTS A AND B (2010): 1109-1118. doi:10.1115/IMECE2010-39082.
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I found one hundred and thirty-five "a"s in the provided passage.
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