×

Discrete double directors shell element for the functionally graded material shell structures analysis. (English) Zbl 1423.74585

Summary: In this paper, the accuracy and the efficiency of the 3d-shell model based on a double directors shell element for the functionally graded material (FGM) shell structures analysis is studied. The vanishing of transverse shear strains on top and bottom faces is considered in a discrete form. Thus, the third-order shear deformation plate theory (TSDT) is a particular case of the discrete double directors shell model (DDDSM) used in the present work. The DDDSM is introduced to remove the shear correction factors, when using the first-order shear deformation theory (FSDT), and improve an excellent performance when compared with other works. This model can be used for static, free vibration and buckling analyses of FGM. The convergence of the proposed model is compared to other well-known formulations found in the literature.

MSC:

74K25 Shells
74S05 Finite element methods applied to problems in solid mechanics

Software:

MUL2
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Vel, S. S.; Batra, R. C., Three-dimensional exact solution for the vibration of functionally graded rectangular plates, J. Sound Vib., 272, 703-730, (2004)
[2] Ferreira, A. J.M.; Roque, C. M.C.; Jorge, R. M.N.; Fasshaueret, G. E.; Batra, R. C., Analysis of functionally graded plates by a robust meshless method, Mech. Adv. Mater. Struct., 14, 8, 577-587, (2007)
[3] Matsunaga, H., Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory, Compos. Struct., 82, 499-512, (2008)
[4] Carrera, E.; Brischetto, S.; Cinefra, M.; Soave, M., Effects of thickness stretching in functionally graded plates and shells, Composites B, 42, 123-133, (2011)
[5] Neves, A. M.A.; Ferreira, A. J.M.; Carrera, E.; Cinefra, M.; Roque, C. M.C.; Jorge, R. M.N.; Soares, C. M.M., A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates, Compos. Struct., 94, 1814-1825, (2012)
[6] Xiang, S.; Kang, G. W., A nth-order shear deformation theory for the bending analysis on the functionally graded plates, Eur. J. Mech. A Solids, 37, 336-343, (2013) · Zbl 1347.74060
[7] Simo, J. C.; Fox, D. D.; Rifai, M. S., On a stress resultant geometrically exact shell model. part II: the linear theory; computational aspects, Comput. Methods Appl. Mech. Engrg., 73, 53-92, (1989) · Zbl 0724.73138
[8] Woo, J.; Meguid, S. A., Nonlinear analysis of functionally graded plates and shallow shells, Int. J. Solids Struct., 38, 7409-7421, (2001) · Zbl 1010.74034
[9] Reddy, J. N., Analysis of functionally graded plates, Internat. J. Numer. Methods Engrg., 47, 663-684, (2000) · Zbl 0970.74041
[10] Mantari, J. L.; Oktem, A. S.; Soares, C. G., Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory, Compos. Struct., 94, 37-49, (2011)
[11] Chien, H. T.; Loc, V. T.; Dung, T. T.; Nguyen-Thoi, T.; Nguyen-Xuan, H., Analysis of laminated composite plates using higher-order shear deformation plate theory and node-based smoothed discrete shear gap method, Appl. Math. Model., 36, 5657-5677, (2012) · Zbl 1254.74079
[12] Mantari, J. L.; Soares, C. G., Optimized sinusoidal higher order shear deformation theory for the analysis of functionally graded plates and shells, Composites B, 56, 126-136, (2014)
[13] Sansour, C.; Bednarczyk, H., The Cosserat surface as a shell model, theory and finite-element formulation, Comput. Methods Appl. Mech. Engrg., 120, 1-32, (1995) · Zbl 0851.73038
[14] Başar, Y.; Ding, Y.; Schltz, R., Refined shear-deformation models for composite laminates with finite rotations, Int. J. Solids Struct., 30, 2611-2638, (1993) · Zbl 0794.73036
[15] Başar, Y.; Itskov, M.; Eckstein, A., Composite laminates: nonlinear interlaminar stress analysis by multi-layer shell elements, Comput. Methods Appl. Mech. Engrg., 185, 367-397, (2000) · Zbl 0981.74061
[16] Brank, B.; Carrera, E., A family of shear-deformable shell finite elements for composite structures, Comput. Struct., 76, 287-297, (2000)
[17] Brank, B.; Korelc, J.; Ibrahimbegovic, A., Nonlinear shell problem formulation accounting for through-the-thickness stretching and its finite element implementation, Comput. Struct., 80, 699-717, (2002)
[18] Brank, B., Non linear shell models with seven kinematic parameters, Comput. Methods Appl. Mech. Engrg., 194, 2336-2362, (2005) · Zbl 1082.74050
[19] F. Dammak, Formulation isoparamétrique généralisée en analyse linéaire et non linéaire des coques par éléments finis, Ph.D. Dissertation, Laval University, Québec, Canada, 1996.
[20] Reddy, J. N., On refined computational models of composite laminates, Internat. J. Numer. Methods Engrg., 27, 361-382, (1989) · Zbl 0724.73234
[21] Dammak, F.; Abid, S.; Gakwaya, A.; Dhatt, G., A formulation of the non linear discrete Kirchhoff quadrilateral shell element with finite rotations and enhanced strains, Eur. J. Comput. Mech., 14, 1-26, (2005)
[22] Zenkour, A. M., Generalized shear deformation theory for bending analysis of functionally graded plates, Appl. Math. Model., 30, 67-84, (2006) · Zbl 1163.74529
[23] Dhatt, G.; Touzot, G., Une présentation de la méthode des éléments finis, (1981), Maloine S.A. Editeur, Paris et Les Presses de l’Université Laval Québec · Zbl 0534.65067
[24] Bathe, K. J.; Dvorkin, E., A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation, Internat. J. Numer. Methods Engrg., 21, 367-383, (1985) · Zbl 0551.73072
[25] Nguyen, T. T.; Sab, K.; Bonnet, G., First-order shear deformation plate models for functionally graded materials, Compos. Struct., 83, 25-36, (2008)
[26] Carrera, E.; Brischetto, S.; Robaldo, A., Variable kinematic model for the analysis of functionally graded material plates, AIAA J., 46, 194-203, (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.