Engineering Transactions, 62, 2, pp. 109-130, 2014
10.24423/engtrans.52.2014

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

Karol DASZKIEWICZ
Politechnika Gdańska Wydział Inżynierii Lądowej i Środowiska Katedra Mechaniki Budowli i Mostów
Poland

Jacek CHRÓŚCIELEWSKI
Politechnika Gdańska Wydział Inżynierii Lądowej i Środowiska Katedra Mechaniki Budowli i Mostów
Poland

Wojciech WITKOWSKI
Politechnika Gdańska Wydział Inżynierii Lądowej i Środowiska Katedra Mechaniki Budowli i Mostów
Poland

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.
Keywords: functionally graded shells, nonlinear six-parameter shell theory, Cosserat constitutive equations, micropolar constants, large deflection.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

KOIZUMI M., FGM activities in Japan, Composites Part B 28B, 1-4, 1997.

YAMANOUCHI M., KOIZUMI M., HIRAI T., SHIOTA I., Proceedings for the First International Symposium of Functionally Graded Materials, Japan, 1990.

KREJA I., A literature review on computational models for laminated composite and sandwich panels, Central European Journal of Engineering, 1, 59-80, 2011.

WOO J., MEGUID S.A., Nonlinear analysis of functionally graded plates and shallow shells, International Journal of Solids and Structures 38, 7409-7421, 2001.

GHANNADPOUR S.A.M., ALINIA M.M., Large deflection behavior of functionally graded plates under pressure loads, Composite Structures 75, 67-71, 2006.

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.

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.

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.

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.

ARCINIEGA R.A., REDDY J.N., Large deformation analysis of functionally graded shells, International Journal of Solids and Structures 44, 2036-2052, 2007.

SHEN H.-S., Functionally Graded Materials, Nonlinear Analysis of Plates and Shells, CRC Press, Boca Raton, London, New York, 2009.

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.

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.

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.

COSSERAT E., COSSERAT F., Théorie des corps déformables, Theory of deformable bodies (in French), Librairie Scientifique A. Hermann et Fils, Paris, 1909.

NOWACKI W., Theory of asymmetric elasticity, Pergamon Press, Oxford, 1986.

RUBIN, M.B., Cosserat Theories: Shells, Rods and Points, Kluwer Academic Publishers, Dordrecht, 2000.

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.

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.

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.

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.

WIŚNIEWSKI K., Finite rotation shells: Basic equations and finite elements for Reissner kinematics, Springer, Berlin, 2010.

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.

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.

DASZKIEWICZ K., Analiza nieliniowa powłok z materiałów gradientowych w ośrodku mikropolarnym. Nonlinear analysis of functionally graded shells in micropolar elasticity (in Polish), In: Wiedza i eksperymenty w budownictwie, J. Bzówka (Ed.), Wydawnictwo Politechniki Śląskiej, Gliwice, 765-772, 2014.

DASZKIEWICZ K., CHRÓŚCIELEWSKI J., WITKOWSKI W., Wpływ parametrów materiałowych ośrodka mikropolarnego na geometrycznie nieliniową analizę MES powłok z materiałów o funkcyjnej gradacji właściwości materiałowych, The influence of micropolar material constants on MES geometrically nonlinear analysis of FGM shells (in Polish), In: XIII Konferencja Naukowo-Techniczna TKI 2014, Techniki Komputerowe w Inżynierii, Abstracts, Wydawnictwo WAT, Warszawa, 45-46, 2014.

REDDY J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, London, New York, Washington D.C., 2003.

KUGLER S., FOTIU P.A., MURIN J., The numerical analysis of FGM shells with enhanced finite elements, Engineering Structures, 49, 920-935, 2013.

PIETRASZKIEWICZ W. BADUR J., Finite rotations in the description of continuum deformation, International Journal of Engineering Science, 21, 1097–1115, 1983.

JEONG J, RAMEZANI H., MÜNCH I., NEFF P., A numerical study for linear isotropic Cosserat elasticity with conformally invariant curvature, Z. Angew. Math. Mech. 89, 7, 552–569, 2009.

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.

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.

HSL, A collection of Fortran codes for large-scale scientific computation, http://www.hsl.rl.ac.uk/.

BASAR Y., DING Y., Finite rotation elements for the nonlinear analysis of thin shell structures, International Journal of Solids and Structures, 26, 83-97, 1990.

SANSOUR C., BEDNARCZYK H., The Cosserat surface as a shell model, theory and finite-element formulation, Computational Methods in Applied Mechanics and Engineering, 120, 1-32, 1995.

EBERLEIN R., WRIGGERS P., Finite element concepts for finite elastoplastic strains and isotropic stress response in shells: theoretical and computational analysis, Computer Methods in Applied Mechanics and Engineering, 171, 243-279, 1999.




DOI: 10.24423/engtrans.52.2014