Abstract
Based on England’s expansion formula for displacements, the elastic field in a transversely isotropic functionally graded annular plate subjected to biharmonic transverse forces on its top surface is investigated using the complex variables method. The material parameters are assumed to vary along the thickness direction in an arbitrary fashion. The problem is converted to determine the expressions of four analytic functions α (ζ), β (ζ), ϕ (ζ) and ψ (ζ) under certain boundary conditions. A series of simple and practical biharmonic loads are presented. The four analytic functions are constructed carefully in a biconnected annular region corresponding to the presented loads, which guarantee the single-valuedness of the mid-plane displacements of the plate. The unknown constants contained in the analytic functions can be determined from the boundary conditions that are similar to those in the plane elasticity as well as those in the classical plate theory. Numerical examples show that the material gradient index and boundary conditions have a significant influence on the elastic field.
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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)
Tounsi S.M.A., Mechab M.S.A.H.I., Benyoucef H.H.S.: Two new refined shear displacement models for functionally graded sandwich plates. Arch. Appl. Mech. 81, 1507–1522 (2011)
Cheng Z.Q., Batra R.C.: Three-dimensional thermoelastic deformations of a functionally graded elliptic plates. Compos.: Part B. 31, 97–106 (2000)
Kashtalyan M.: Three-dimensional elastic solutions for bending of functionally graded rectangular plates. Eur. J. Mech. A Solids 23, 853–864 (2004)
Wang Y., Xu R.Q., Ding H.J.: Three-dimensional solution of axisymmetric bending of functionally graded circular plates. Compos. Struct. 92, 1683–1693 (2010)
Birman V., Byrd L.W.: Modeling and analysis of functionally graded materials and structures. ASME Appl. Mech. Rev. 60, 195–216 (2007)
Mian A.M., Spencer A.J.M.: Exact solutions for functionally graded and laminated elastic materials. J. Mech. Phys. Solids 46, 2283–2295 (1998)
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)
England A.H.: Bending solution for inhomogeneous and laminated elastic plates. J. Elast. 82, 129–173 (2006)
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)
Ding H.J., Chen W.Q., Zhang L.C.: Elasticity of Transversely Isotropic Materials. Springer, Dordrecht (2006)
Timoshenko S.P., Goodier J.N.: Theory of Elasticity. 3rd edn. McGraw-Hill, New York (1970)
Young W.C., Budynas R.G.: Roark’s Formulas for Stress and Strain. McGraw-Hill, New York (2002)
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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). https://doi.org/10.1007/s00419-013-0782-1
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DOI: https://doi.org/10.1007/s00419-013-0782-1