Simultaneous design of optimal shape and local cubic material characteristics

• Autorzy: Czubacki, R. , Lewiński, T. , Ganghoffer, J. F.
• Języki publikacji: EN

Abstrakty

EN

This paper deals with the minimum compliance problem of the femur bone made of a nonhomogeneous elastic material with cubic symmetry. The elastic moduli as well as the trajectories of anisotropy directions are design variables. The isoperimetric condition determines the value of the cost of the design expressed as the integral of the trace of the Hooke’s tensor. The optimum design is found for a selected design domain and a single load case. The optimal cubic material characteristics are reflected by the properties of the underlying microstructure. Admissible microstructures are reconstructed, thus delivering a deeper insight into the optimum design. The obtained microstructures are second- rank laminates composed of an isotropic material and voids. To eliminate the degeneracy of the design at least three load cases should be considered.

Słowa kluczowe

EN

topology optimization; cubic material design; discrete homogenization

• Czasopismo: Engineering Transactions
• Rocznik: 2017
• Tom: Vol. 65, iss. 1
• Strony: 11--17
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Czubacki, R.

• Warsaw University of Technology Faculty of Civil Engineering Department of Structural Mechanics and Computer Aided Engineering Armii Ludowej 16, 00-637 Warszawa, Poland,

autor

Lewiński, T.

• Warsaw University of Technology Faculty of Civil Engineering Department of Structural Mechanics and Computer Aided Engineering Armii Ludowej 16, 00-637 Warszawa, Poland

autor

Ganghoffer, J. F.

• Warsaw University of Technology Faculty of Civil Engineering Department of Structural Mechanics and Computer Aided Engineering Armii Ludowej 16, 00-637 Warszawa, Poland

Bibliografia

• 1. Czarnecki S., Isotropic material design, Computational Methods in Science and Technology, 21(2): 49–64, 2015, doi: 10.12921/cmst.2015.21.02.001.
• 2. Czarnecki S., Wawruch P., The emergence of auxetic material as a result of optimal isotropic design, Physica Status Solidi B, 252(7): 1620–1630, 2015, doi: 10.1002/ pssb.201451733.
• 3. Czubacki R., Lewiński T., Topology optimization of spatial continuum structures made of non-homogeneous material of cubic symmetry, Journal of Mechanics of Materials and Structures, 10(4): 519–535, 2015, doi: 10.2140/jomms.2015.10.519.
• 4. Goda I., Ganghoffer J.-F., Czarnecki S., Wawruch P., Lewiński T., Optimal internal architectures of femoral bone based on relaxation by homogenization and isotropic material design, Mechanics Research Communications, 76: 64–71, 2016, doi: 10.1016/j.mechrescom.2016.06.007.
• 5. Lewiński T., Telega J.J., Plates, laminates and shells: asymptotic analysis and homogenization, World Scientific, Singapore, 2000.
• 6. Walpole L.J., Fourth-rank tensors of the thirty-two crystal classes: multiplication tables, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 391(1800): 149–179, 1984, doi 10.1098/rspa.1984.0008.
• 7. Telega J.J., Galka A., Tokarzewski S., Effective moduli of trabecular bone, Acta of Bioengineering and Biomechanics, 1(1): 53–57, 1999.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).