Elasticity Solutions for Plates

Bhaskar, K.; Varadan, T. K.

doi:10.1007/978-3-030-69424-1_10

K. Bhaskar³ &
T. K. Varadan³

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Abstract

As stated in Chap. 1, elasticity solutions for plate problems, wherein the structure is treated as a three-dimensional continuum, are valuable because they provide a standard benchmark against which the accuracy of two-dimensional engineering theories can be judged. The purpose of this chapter is to give an overview of some such solutions selected from the literature so as to point out the deficiencies of CPT and possible improvements.

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Notes

1.
K. Bhaskar, T. K. Varadan, Theory of Isotropic/Orthotropic Elasticity, Ane Books/CRC Press, 2009.
2.
For a more complete discussion, see: K.Bhaskar, T.K.Varadan, Theory of Isotropic/Orthotropic Elasticity, Ane Books/CRC, 2009.
3.
S. Srinivas, A. K. Rao, C. V. Joga Rao, Flexure of simply supported thick homogeneous and laminated rectangular plates, ZAMM – Jl. of Applied Mathematics and Mechanics, 49(8), 1969, 449–458.
4.
S. Srinivas, A. K. Rao, Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates, International Jl. of Solids and Structures, 6, 1970, 1463–1481.
5.
N. J. Pagano, Exact solutions for rectangular bidirectional composites and sandwich plates, Jl of Composite Materials, 4, 1970, 20–34.
6.
N. J. Pagano, A. S. D. Wang, Further study of composite laminates under cylindrical bending, Jl. of Composite Materials, 5, 1971, 521–528.
7.
S. Savithri, T. K. Varadan, Laminated plates under uniformly distributed and concentrated loads, ASME Jl. of Applied Mechanics, 59, 1992, 211–214.
8.
T. K. Varadan, K. Bhaskar, Elasticity solutions for cross-ply plates under localized surface moments, Jl. of the Aeronautical Society of India, 53(3), 2001, 154–159.
9.
N. J. Pagano, Influence of shear coupling in cylindrical bending of anisotropic laminates, Jl. of Composite Materials, 4, 1970, 330–343.
10.
S. Srinivas, C. V. Joga Rao, A. K. Rao, An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates, Jl. of Sound and Vibration, 12(2), 1970, 187–199.
11.
A. T. Jones, Exact natural frequencies for cross-ply laminates, Jl. of Composite Materials, 4, 1970, 476–491.
12.
A. K. Noor, Free vibrations of multilayered composite plates, AIAA Jl., 11, 1973, 1038–1039.
13.
A. K. Noor, W. S. Burton, Three-dimensional solutions for antisymmetrically laminated anisotropic plates, ASME Jl. of Applied Mechanics, 57, 1990, 182–188.
14.
S. Srinivas, A. K. Rao, Buckling of thick rectangular plates, AIAA Jl., 7, 1969, 1645–1646.
15.
A. Chattopadhyay, H. Gu, Exact elasticity solution for buckling of composite laminates, Composite Structures, 50, 2000, 29–35.
16.
S. Srinivas, A. K. Rao, Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates, International Jl. of Solids and Structures, 6, 1970, 1463–1481.
17.
S. Srinivas, A. K. Rao, Flexure of thick rectangular plates, ASME Jl. of Applied Mechanics, 40, 1973, 298–299.
18.
S. S. Vel, R. C. Batra, Analytical solution for rectangular thick laminated plates subjected to arbitrary boundary conditions, AIAA Jl., 37, 1999, 1464–1473.
19.
I. A. Okumura, Y. Oguma, Series solutions for a transversely loaded and completely clamped thick rectangular plate based on the three-dimensional theory of elasticity, Archive of Applied Mechanics, 68, 1998, 103–121.
20.
T. Kant, E. Hinton, Mindlin plate analysis by segmentation method, ASCE Jl. of Engineering Mechanics, 109(2), 1983, 537–556;
G. Prathap, C. Ramesh Babu, Accurate force evaluation with a simple, bilinear, plate bending element, Computers and Structures, 25(2), 1987, 259–270.
21.
S. Srinivas, A. K. Rao, C. V. Joga Rao, Flexure of simply supported thick homogeneous and laminated rectangular plates, ZAMM – Jl. of Applied Mathematics and Mechanics, 49(8), 1969, 449–458.
22.
S. Srinivas, A. K. Rao, Flexure of thick rectangular plates, ASME Jl. of Applied Mechanics, 40, 1973, 298–299.
23.
K. Rajaiah, A. K. Rao, A note on the reaction at simply supported square corners, ASME Jl. of Applied Mechanics, 45(1), 1978, 217–218.
24.
K. Bhaskar, T. K. Varadan, J. S. M. Ali, Thermoelastic solutions for orthotropic and anisotropic composite laminates, Composites Part B, 27B, 1996, 415–420.
25.
See, for example: V. B. Tungikar, K. M. Rao, Three-dimensional exact solution of thermal stresses in rectangular composite laminate, Composite Structures, 27, 1994, 419–430.

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Department of Aerospace Engineering, Indian Institute of Technology, Madras, Chennai, India
K. Bhaskar & T. K. Varadan

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Bhaskar, K., Varadan, T.K. (2021). Elasticity Solutions for Plates. In: Plates. Springer, Cham. https://doi.org/10.1007/978-3-030-69424-1_10

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DOI: https://doi.org/10.1007/978-3-030-69424-1_10
Published: 08 May 2021
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-69423-4
Online ISBN: 978-3-030-69424-1
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