Abstract
This paper presents three-dimensional elasticity solutions for an annular sector plate made of transversely isotropic functionally graded material (FGM) subjected to concentrated forces \(\left( X,Y,0 \right) \) or couples \(\left( M_X,M_Y,M_Z\right) \) applied at one of its radial edges. The elastic coefficients can vary arbitrarily through the plate thickness. The analysis was based on the assumed forms of displacements for bending of an FGM plate (Mian and Spencer in J Mech Phys Solids 4:2283–2295, 1998), in which the four analytical functions were constructed properly. Appropriate boundary conditions and end conditions similar to those in the classic plate theory were employed to determine the unknown constants contained in the analytical functions so as to accomplish the analysis. When the material coefficients are all constant, the obtained analytical solutions can be degenerated into those for a homogeneous transversely isotropic annular sector plate, which have never been reported before. The solutions may be further reduced to those for a homogeneous isotropic annular sector plate, among which the ones for concentrated couples \(\left( M_X ,M_Y,0 \right) \) are also new to the literature.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Rogers, T.G., Spencer, A.J.M.: Thermoelastic stress analysis of moderately thick inhomogeneous and laminated plates. Int. J. Solids Struct. 25, 1467–482 (1989)
Rogers, T.G.: Exact three-dimensional bending solutions for inhomogeneous and laminated elastic plates. In: Eason, G., Ogden, R.W. (eds.) Elasticity, Mathematical Methods and Applications, pp. 301–313. Ellis Horwood, Chichester (1990)
Spencer, A.J.M.: Three-dimensional elasticity solutions for stretching of inhomogeneous and laminated plates. In: Eason, G., Ogden, R.W. (eds.) Elasticity, Mathematical Methods and Applications, pp. 347–356. Ellis Horwood, Chichester (1990)
Spencer, A.J.M.: A stress function formulation for a class of exact solutions for functionally graded elastic plates. In: Bahei-el-Din, A.Y., Dvorak, G. (eds.) IUTAM Symposium on Transformation Problems in Composite and Active Materials, pp. 161–172. Kluwer, Dordrecht (1998)
Mian, M.A., Spencer, A.J.M.: Exact solutions for functionally graded and laminated elastic materials. J. Mech. Phys. Solids 4, 2283–2295 (1998)
Spencer, A.J.M., Selvadurai, A.P.S.: Some generalized anti-plane strain problems for an inhomogeneous elastic half space. J. Eng. Math. 34, 403–416 (1998)
Spencer, A.J.M.: Concentrated force solutions for an inhomogeneous thick elastic plate. Z. Angew. Math. Phys. 51, 573–90 (2000)
Reddy, J.N., Wang, C.M., Kitipornchai, S.: Axisymmetric bending of functionally graded circular and annular plates. Eur. J. Mech. A Solids 18, 185–199 (1999)
Nosler, A., Fallah, F.: Reformulation of Mindlin—Reissner governing equations of functionally graded circular plates. Acta Mech. 198, 209–233 (2008)
Li, X.Y., Ding, H.J., Chen, W.Q.: Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load \(\text{qr}^{{\rm k}}\). Int. J. Solids Struct. 45, 191–210 (2008)
Jomehzadeh, E., Saidi, A.R., Atashipour, S.R.: An analytical approach for stress analysis of functionally graded annular sector plates. Mater. Des. 30, 3679–3685 (2009)
Sahraee, S., Saidi, A.R.: Axisymmetric bending analysis of thick functionally graded circular plates using fourth-order shear deformation theory. Eur. J. Mech. A Solids 28, 974–984 (2009)
Fereidoon, A., Mohyeddin, A., Sheikhi, M., Rahmani, H.: Bending analysis of functionally graded annular sector plates by extended Kantorovich method. Comput. Part B Eng. 43, 2172–2179 (2012)
Golmakani, M.E., Alamatian, J.: Large deflection analysis of shear deformable radially functionally graded sector plates on two-parameter elastic foundations. Eur. J. Mech. A Solids 42, 251–265 (2013)
Liu, B., Ferreira, A.J.M., Xing, Y.F., Neves, A.M.A.: Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method. Compos. Struct. 136, 546–553 (2016)
England, A.H., Spencer, A.J.M.: Complex variable solutions for inhomogeneous and laminated elastic plates. Math. Mech. Solids 10, 503–539 (2005)
England, A.H.: Bending solution for inhomogeneous and laminated elastic plates. J. Elast. 82, 129–173 (2006)
England, A.H.: Stiffness coefficients for inhomogeneous elastic plates. Int. J. Eng. Sci. 47, 438–451 (2009)
Yang, B., Ding, H.J., Chen, W.Q.: Elasticity solutions for a uniformly loaded annular plate of functionally graded materials. Struct. Eng. Mech. 30, 501–512 (2008)
Yang, B., Ding, H.J., Chen, W.Q.: Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported. Appl. Math. Model. 36, 488–503 (2012)
Yang, B., Chen, W.Q., Ding, H.J.: Elasticity solutions for functionally graded annular plates subject to biharmonic loads. Arch. Appl. Mech. 84, 51–65 (2014)
Huang, D.J., Yang, B., Chen, W.Q., Ding, H.J.: Analytical solutions for an infinite transversely isotropic functionally graded sectorial plate subjected to a concentrated force or couple at the tip. Acta Mech. 227, 495–506 (2016)
Ding, H.J., Chen, W.Q., Zhang, L.C.: Elasticity of Transversely Isotropic Materials. Springer, Dordrecht (2006)
Yang, B., Ding, H.J., Chen, W.Q.: Elasticity solutions for a uniformly loaded rectangular plate of functionally graded materials with two opposite edges simply supported. Acta Mech. 207, 245–258 (2009)
Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity, 3rd edn. McGraw Hill, New York (1970)
Папкович, П. Ф., Теорня упрутости Ленинграg и Москва: СИОГ (1939)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jiang, J.L., Huang, D.J., Yang, B. et al. Elasticity solutions for a transversely isotropic functionally graded annular sector plate. Acta Mech 228, 2603–2621 (2017). https://doi.org/10.1007/s00707-017-1839-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-017-1839-y