Abstract
In conjunction with the homogenization theory and the finite element method, the mathematical models for designing the corss-section of composite shafts by maximizing the torsion rigidity are developed in this paper. To obtain the extremal torsion rigidity, both the cross-section of the macro scale shaft and the representative microstructure of the composite material are optimized using the new models. The micro scale computational model addresses the problem of finding the periodic microstructures with extreme shear moduli. The optimal microstructure obtained with the new model and the homogenization method can be used to improve and optimize natural or artificial materials. In order to be more practical for engineering applications, cellular materials rather than ranked materials are used in the optimal process in the existence of optimal bounds for the elastic properties. Moreover, the macro scale model is proposed to optimize the cross-section of the torsional shaft based on the tailared composites. The validating optimal results show that the models are very effective in obtaining composites with extreme elastic properties, and the cross-section of the composite shaft with the extremal torsion rigidity.
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The project supported by the National Natural Science Foundation of China (10172078 and 10102018)
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Zhen, Y., Changchun, W. & Hua, L. Homogenization-based topology design for pure torsion of composite shafts. Acta Mech Sinica 19, 241–246 (2003). https://doi.org/10.1007/BF02484486
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DOI: https://doi.org/10.1007/BF02484486