Abstract
In this study, we consider the problem of nonlinearly tapered annular plate with a free edge. The supported edge may be simply supported, clamped or elastically restrained against rotation. Exact expressions of deflection, moment-resultants, and stresses are presented for nonuniform thickness. We compare the results of the Kirchhoff plate theory and the Mindlin plate theory. It is shown that the Kirchhoff plate theory and the Mindlin plate theory provide approximately the same results for the positive values of the thickness factor, but the difference between the deflections diverges as the thickness increases at the inner edge. We also propose that the Kirchhoff plate theory may be used in the region of −0.4 ≤ α < 1 and the Mindlin plate theory must be used for α < −0.4.
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References
Chung K.C., Wang C.M. (2002) Optimal design of stepped circular plates with allowance for the effect of transverse shear deformation. Int. J. Mech. Sci. 44, 1163–1177
Conway H.D. (1948) Bending of symmetrically loaded circular plates with variable thickness. ASME J. Appl. Mech. 15, 1–6
Conway H.D. (1949) Note on the bending of circular plates of variable thickness. ASME J. Appl. Mech. 16, 209–210
Levinson M. (1980) An accurate simple theory of the statics and dynamics of elastic plates. Mech. Res. Comm. 7, 343–350
Liu T., Kitipornchai S., Wang C.M. (2001) Bending of linearly tapered annular Mindlin plates Int. J. Mech. Sci. 43, 265–278
Ma L.S., Wang T.J. (2004) Relationship between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory. Int. J. Solid Struct. 41, 85–101
Mindlin R.D. (1951) Influence of rotary inertia and shear in flexural motion of isotropic, elastic plates. J. Appl. Mech. 18, 1031–1036
Nelson R.B., Lorch D.R. (1974) A refined theory for laminated orthotropic plates. ASME J. Appl. Mech. 41, 177–183
Reddy J.N. (1974) Energy and Variational Methods in Applied Mechanics. Wiley, Canadax
Reddy J.N. (1984) A simple higher-order theory for laminated composite plates. ASME J. Appl. Mech. 51, 745–752
Reddy J.N. (1999) Axisymmetric bending of functionally graded circular and annular plates. Eur. J. Mech. A/Solids. 18, 185–199
Reddy J.N. (1999) Theory and Analysis of Elastic Plates. Taylor & Francis, Philadelphia
Reissner E. (1945) The effect of transverse shear deformation on the bending of elastic plates. ASME J. Appl. Mech. 12, A69–A77
Timoshenko, S.P., Woinowsky-Krieger, S.: Theory of Plates and Shells. McGraw-Hill (1959)
Ventsel, E., Krauthammer, T.: Thin Plates and Shells: Theory, Analysis, and Applications. CRC (2001)
Wang C.M. (1997) Relationships between Mindlin and Kirchhoff bending solutions for tapered circular and annular plates. Eng. Struct. 19, 255–258
Wang C.M., Lim G.T. (2000) Bending Solutions of sectorial Mindlin plates from Kirchhoff plates. J. Eng. Mech. 126, 367–372
Wang C.M., Reddy J.N., Lee K.H. (2000) Shear Deformable Beams and Plates: Relationships with Classical Solutions. Elsevier, The Netherlands
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Ozer, H. A comparative analysis of Mindlin and Kirchhoff bending solutions for nonlinearly tapered annular plate with free edges. Arch Appl Mech 77, 393–405 (2007). https://doi.org/10.1007/s00419-006-0095-8
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DOI: https://doi.org/10.1007/s00419-006-0095-8