Geometrically Nonlinear Analysis of Functionally Graded Shells Based on 2-D Cosserat Constitutive Model

Daszkiewicz, K.; Chróścielewski, J.; Witkowski, W.

Artykuł - szczegóły

Tytuł artykułu

Geometrically Nonlinear Analysis of Functionally Graded Shells Based on 2-D Cosserat Constitutive Model

Autorzy

Daszkiewicz K. , Chróścielewski J. , Witkowski W.

Wybrane pełne teksty z tego czasopisma

http://et.ippt.gov.pl/

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Warianty tytułu

Języki publikacji

Abstrakty

In this paper geometrically nonlinear analysis of functionally graded shells in 6-parameter shell theory is presented. It is assumed that the shell consists of two constituents: ceramic and metal. The mechanical properties are graded through the thickness and are described by power law distribution. Formulation based on 2-D Cosserat constitutive model is used to derive constitutive relation for functionally graded shells. Numerical results for typical benchmark geometries of smooth and irregular FGM shells under mechanical loading are presented. The influence of power-law exponent and micropolar material constants on the overall behaviour of functionally graded shells is investigated.

Słowa kluczowe

functionally graded shells nonlinear six-parameter shell theory Cosserat constitutive equations micropolar constants large deflection

ugięcie duże powłoki równania konstytutywne

Wydawca

Instytut Podstawowych Problemów Techniki PAN

Czasopismo

Engineering Transactions

Rocznik

2014

Tom

Vol. 62, iss. 2

Strony

109--130

Opis fizyczny

Bibliogr. 34 poz., rys., tab., wykr.

Twórcy

autor

Daszkiewicz K.

kardaszk@pg.gda.pl

Gdańsk University of Technology Faculty of Civil and Environmental Engineering Department of Structural Mechanics Narutowicza 11/12, 80-233 Gdańsk

autor

Chróścielewski J.

Gdańsk University of Technology Faculty of Civil and Environmental Engineering Department of Structural Mechanics Narutowicza 11/12, 80-233 Gdańsk

autor

Witkowski W.

Gdańsk University of Technology Faculty of Civil and Environmental Engineering Department of Structural Mechanics Narutowicza 11/12, 80-233 Gdańsk

Bibliografia

1. Koizumi M., FGM activities in Japan, Composites Part B, 28B, 1–4, 1997, http://www.sciencedirect.com/science/article/pii/S1359836896000169.
2. Kreja I., A literature review on computational models for laminated composite and sandwich panels, Central European Journal of Engineering, 1, 59–80, 2011, http://link.springer.com/article/10.2478%2Fs13531-011-0005-x.
3. Woo J., Meguid S.A., Nonlinear analysis of functionally graded plates and shallow shells, International Journal of Solids and Structures, 38, 7409–7421, 2001, http://www.sciencedirect.com/science/article/pii/S0020768301000488.
4. Ghannadpour S.A.M., Alinia M.M., Large deflection behavior of functionally graded plates under pressure loads, Composite Structures, 75, 67–71, 2006, http://www.sciencedirect.com/science/article/pii/S0263822306001188.
5. Chi S., Chung Y., Mechanical behavior of functionally graded material plates under transverse load – Part I: Analysis, International Journal of Solids and Structures, 43, 3657–3674, 2006, http://www.sciencedirect.com/science/article/pii/S0020768305002052.
6. Chi S., Chung Y., Mechanical behavior of functionally graded material plates under transverse load – Part II: Numerical results, International Journal of Solids and Structures, 43, 3675–3691, 2006, http://www.sciencedirect.com/science/article/pii/S0020768305002040.
7. Yang J., Shen H-S., Non-linear analysis of functionally graded plates under transverse and in-plane loads, International Journal of Nonlinear Mechanics, 38, 467–482, 2003, http://www.sciencedirect.com/science/article/pii/S0020746201000701.
8. Ma L.S., Wang T.J., Nonlinear bending and postbuckling of functionally graded circular plates under mechanical and thermal loadings, International Journal of Nonlinear Mechanics, 40, 3311–3330, 2003, http://www.sciencedirect.com/science/article/pii/S0020768303001185.
9. Arciniega R.A., Reddy J.N., Large deformation analysis of functionally graded shells, International Journal of Solids and Structures, 44, 2036–2052, 2007, http://www.sciencedirect.com/science/article/pii/S0020768306003428.
10. Shen H.-S., Functionally Graded Materials, Nonlinear Analysis of Plates and Shells, CRC Press, Boca Raton, London, New York, 2009.
11. Mania R.J., Dynamic response of FGM thin plate subjected to combined loads, [in:] Shell Structures: Theory and Applications, Vol. 3, 377–380, W. Pietraszkiewicz and J. Górski [Eds.], CRC Press, London, 2014.
12. Zhang D.-G., Nonlinear bending analysis of FGM rectangular plates with various supported boundaries resting on two-parameter elastic foundations, Archive of Applied Mechanics, 84, 1, 1–20, 2014, http://link.springer.com/article/10.1007%2Fs00419-013-0775-0.
13. Chróścielewski J., Makowski J., Pietraszkiewicz W., Statyka i Dynamika Powłok Wielopłatowych, Statics and dynamics of multifold shells: Nonlinear theory and finite element method (in Polish), Wydawnictwo IPPT PAN, Warsaw, 2004.
14. Cosserat E., Cosserat F., Th´eorie des corps d´eformables, Theory of deformable bodies (in French), Librairie Scientifique A. Hermann et Fils, Paris, 1909.
15. Nowacki W., Theory of asymmetric elasticity, Pergamon Press, Oxford, 1986.
16. Rubin M.B., Cosserat Theories: Shells, Rods and Points, Kluwer Academic Publishers, Dordrecht, 2000.
17. Altenbach J., Altenbach H., Eremeyev V.A., On generalized Cosserat-type theories of plates and shells: a short review and bibliography, Archive of Applied Mechanics, 80, 73–92, 2010, https://hal.archives-ouvertes.fr/hal-00827365.
18. Chróścielewski J., Makowski J., Stumpf H., Genuinely resultant shell finite elements accounting for geometric and material non-linearity, Int. J. Numer. Meth. Eng., 35, 63–94, 1992, http://onlinelibrary.wiley.com/doi/10.1002/nme.1620350105/abstract.
19. Chróścielewski J., Witkowski W., 4-node semi-EAS element in 6–field nonlinear theory of shells, International Journal for Numerical Methods in Engineering, 68, 1137–1179, 2006, http://onlinelibrary.wiley.com/doi/10.1002/nme.1740/abstract.
20. Konopińska W., Pietraszkiewicz W., Exact resultant equilibrium conditions in the non-linear theory of branching and self-intersecting shells, International Journal of Solids and Structures, 44, 352–369, 2007, http://www.sciencedirect.com/science/article/pii/S0020768306001405.
21. Wiśniewski K., Finite rotation shells: Basic equations and finite elements for Reissner kinematics, Springer, Berlin, 2010, http://link.springer.com/book/10.1007%2F978-90-481-8761-4.
22. Chróścielewski J., Kreja I., Sabik A., Witkowski W., Modeling of composite shells in 6-parameter nonlinear theory with drilling degree of freedom, Mech. Adv. Mater. Struct., 18, 403–419, 2011, http://www.tandfonline.com/doi/abs/10.1080/15376494.2010.524972#.U7SDhrE09I0.
23. Burzyński S., Chróścielewski J., Witkowski W., Elastoplastic material law in 6- parameter nonlinear shell theory, [in:] Shell Structures: Theory and Applications, Vol. 3, 377–380, W. Pietraszkiewicz and J. Górski [Eds.], CRC Press, London, 2014.
24. Burzyński S., Chróścielewski J., Witkowski W., Elastoplastic law of Cosserat type in shell theory with drilling rotation, Mathematics and Mechanics of Solids, DOI: 10.1177/1081286514554351, http://mms.sagepub.com/content/early/2014/10/16/1081286514554351.
25. Daszkiewicz K., Nonlinear analysis of functionally graded shells in micropolar elasticity [in Polish: Analiza nieliniowa powłok z materiałów gradientowych w ośrodku mikropolarnym], [in:] Wiedza i eksperymenty w budownictwie, J. Bzówka [Ed.], Wydawnictwo Politechniki Śląskiej, Gliwice, 765–772, 2014.
26. Daszkiewicz K., Chróścielewski J., Witkowski W., The influence of micropolar material constants on MES geometrically nonlinear analysis of FGM shells [in Polish: Wpływ parametrów materiałowych ośrodka mikropolarnego na geometrycznie nieliniową analizę MES powłok z materiałów o funkcyjnej gradacji właściwości materiałowych], [in:] XIII Konferencja Naukowo-Techniczna TKI 2014, Techniki Komputerowe w Inżynierii, Abstracts, Wydawnictwo WAT, Warszawa, 45–46, 2014.
27. Reddy J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, London, New York, Washington D.C., 2003.
28. Kugler S., Fotiu P.A., Murin J., The numerical analysis of FGM shells with enhanced finite elements, Engineering Structures, 49, 920–935, 2013, http://www.sciencedirect.com/science/article/pii/S0141029613000035.
29. Pietraszkiewicz W., Badur J., Finite rotations in the description of continuum deformation, International Journal of Engineering Science, 21, 1097–1115, 1983, http://www.sciencedirect.com/science/article/pii/0020722583900502.
30. Jeong J., Ramezani H., Munch I., Neff P. ¨ , A numerical study for linear isotropic Cosserat elasticity with conformally invariant curvature, Z. Angew. Math. Mech., 89, 7, 552–569, 2009, http://onlinelibrary.wiley.com/doi/10.1002/zamm.200800218/abstract.
31. Lakes R.S., Experimental microelasticity of two porous solids, International Journal of Solids Structures, 22, 1, 55–63, 1986, http://www.sciencedirect.com/science/article/pii/0020768386901034.
32. Lakes R.S., Experimental methods for study of Cosserat elastic solids and other generalized elastic continua, [in:] Continuum models for materials with micro-structure, 1–22, Mhlhaus H. [Eds.], Wiley, 1995, http://silver.neep.wisc.edu/∼lakes/CossRv.pdf.
33. Khabbaz R.S., Manshadi B.D., Abedian A., Nonlinear analysis of FGM plates under pressure loads using higher-order shear deformation theories, Composite Structures, 89, 333–344, 2009, http://www.sciencedirect.com/science/article/pii/S0263822308002055.
34. Pietraszkiewicz W., Konopińska V., Drilling couples and refined constitutive equations in the resultant geometrically non-linear theory of elastic shells, International Journal of Solids Structures, 51, 11–12, 2133–2143, 2014, http://www.sciencedirect.com/science/article/pii/S0020768314000705

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-1485ca18-c896-4c25-9446-74beaf0c7451