On shape and material optimization of isotropic bodies

• Autorzy: Czarnecki S. , Lewiński T. , Wawruch P.
• Języki publikacji: EN

Abstrakty

EN

This paper deals with the free material design and its two constrained versions constructed by imposing isotropy with (i) independent bulk and shear moduli, and (ii) fixed Poisson’s ratio. In the latter case, the Young modulus is the only design variable. The moduli are viewed as non-negative, thus allowing for the appearance of void domains within the design domain. The paper shows that all these methods reduce to one stress-based problem in which the norm involved reflects the type of the constraints imposed.

Słowa kluczowe

EN

optimum design; elastic moduli; free material design

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2017
• Tom: Vol. 65, iss. 1
• Strony: 3--9
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Czarnecki S.

• Warsaw University of Technology Armii Ludowej 16, 00-637 Warsaw, Poland

autor

Lewiński T.

• Warsaw University of Technology Armii Ludowej 16, 00-637 Warsaw, Poland

autor

Wawruch P.

• Warsaw University of Technology Armii Ludowej 16, 00-637 Warsaw, Poland

Bibliografia

• 1. Bendsøe M.P., Guedes J.M., Haber R.B., Pedersen P., Taylor J.E., An analytical model to predict optimal material properties in the context of optimal structural design, Journal of Applied Mechanics, Transactions of ASME, 61(4): 930–937, 1994, doi: 10.1115/1.2901581.
• 2. Bouchitt´e G., Buttazzo G., Characterization of optimal shapes and masses through Monge-Kantorovich equation, Journal of the European Mathematical Society, 3(2): 139– 168, 2001, doi: 10.1007/s100970000027.
• 3. Czarnecki S., Isotropic material design, Computational Methods in Science and Technology, 21(2): 49–64, 2015, doi: 10.12921/cmst.2015.21.02.001.
• 4. Czarnecki S., Lewiński T., A stress-based formulation of the free material design problem with the trace constraint and single loading condition, Bulletin of the Polish Academy of Sciences: Technical Sciences, 60(2): 191–204, 2012.
• 5. Czarnecki S., Lewiński T., On minimum compliance problems of thin elastic plates of varying thickness, Structural and Multidisciplinary Optimization, 48(1): 17–31, 2013, doi: 10.1007/s00158-013-0893-x.
• 6. Czarnecki S., Lewiński T., A stress-based formulation of the free material design problem with the trace constraint and multiple load conditions, Structural and Multidisciplinary Optimization, 49(5): 707–731, 2014, doi: 10.1007/s00158-013-1023-5.
• 7. 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.
• 8. 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.
• 9. Kocvara M., Stingl M. ˇ , Free material optimization for stress constraints, Structural and Multidisciplinary Optimization, 33(4): 323–335, 2007, doi: 10.1007/s00158-007-0095-5.
• 10. Rychlewski J., On Hooke’s law, Journal of Applied Mathematics and Mechanics, 48(3): 303–314, 1984, doi: 10.1016/0021-8928(84)90137-0.

Uwagi

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