First-order shear deformation theories, one proposed by Reissner and another one by Mindlin, are widely in use, even today, because of their simplicity. In this paper, two new displacement based first-order shear deformation theories involving only two unknown functions, as against three functions in case of Reissner’s and Mindlin’s theories, are introduced. For static problems, governing equations of one of the proposed theories are uncoupled. And for dynamic problems, governing equations of one of the theories are only inertially coupled, whereas those of the other theory are only elastically coupled. Both the theories are variationally consistent. The effectiveness of the theories is brought out through illustrative examples. One of the theories has striking similarity with classical plate theory.
Issue Section:
Technical Papers
1.
Reissner
, E.
, 1944, “On the Theory of Bending of Elastic Plates
,” J. Math. Phys.
0022-2488, 23
, pp. 184
–191
.2.
Reissner
, E.
, 1945, “The Effect of Transverse Shear Deformation on the Bending of Elastic Plates
,” Trans. ASME
0097-6822, 67
, pp. A
-69–A-77
.3.
Mindlin
, R. D.
, 1951, “Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates
,” Trans. ASME
0097-6822, 73
, pp. 31
–38
.4.
Wang
, C. M.
, Lim
, G. T.
, Reddy
, J. N.
, and Lee
, K. H.
, 2001, “Relationships Between Bending Solutions of Reissner and Mindlin Plate Theories
,” Eng. Struct.
0141-0296, 23
(7
), pp. 838
–849
.5.
Krishna Murty
, A. V.
, 1977, “Higher Order Theory for Vibrations of Thick Plates
,” AIAA J.
0001-1452, 15
(12
), pp. 1823
–1824
.6.
Lo
, K. H.
, Christensen
, R. M.
, and Wu
, E. M.
, 1977, “A High-Order Theory of Plate Deformation Part 1: Homogeneous Plates
,” ASME J. Appl. Mech.
0021-8936, 44
(4
), pp. 663
–668
.7.
Kant
, T.
, 1982, “Numerical Analysis of Thick Plates
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 31
(1
), pp. 1
–18
.8.
Bhimaraddi
, A.
, and Stevens
, L. K.
, 1984, “A Higher Order Theory for Free Vibration of Orthotropic, Homogeneous, and Laminated Rectangular Plates
,” ASME J. Appl. Mech.
0021-8936, 51
(1
), pp. 195
–198
.9.
Reddy
, J. N.
, 1984, “A Refined Nonlinear Theory of Plates With Transverse Shear Deformation
,” Int. J. Solids Struct.
0020-7683, 20
(9/10
), pp. 881
–896
.10.
Soldatos
, K. P.
, 1988, “On Certain Refined Theories for Plate Bending
,” ASME J. Appl. Mech.
0021-8936, 55
(4
), pp. 994
–995
.11.
Reddy
, J. N.
, 1990, “A General Non-Linear Third-Order Theory of Plates With Moderate Thickness
,” Int. J. Non-Linear Mech.
0020-7462, 25
(6
), pp. 677
–686
.12.
Hanna
, N. F.
, and Leissa
, A. W.
, 1994, “A Higher Order Shear Deformation Theory for the Vibration of Thick Plates
,” J. Sound Vib.
0022-460X, 170
(4
), pp. 545
–555
.13.
Srinivas
, S.
, Joga Rao
, C. V.
, and Rao
, A. K.
, 1970, “An Exact Analysis for Vibration of Simply-Supported Homogeneous and Laminated Thick Rectangular Plates
,” J. Sound Vib.
0022-460X, 12
(2
), pp. 187
–199
.14.
Vasil’ev
, V. V.
, 1992, “The Theory of Thin Plates
,” Mech. Solids
0025-6544, 27
(3
), pp. 22
–42
.15.
Liew
, K. M.
, Xiang
, Y.
, and Kitipornchai
, S.
, 1995, “Research on Thick Plate Vibration: A Literature Survey
,” J. Sound Vib.
0022-460X, 180
(1
), pp. 163
–176
.16.
Ghugal
, Y. M.
, and Shimpi
, R. P.
, 2002, “A Review of Refined Shear Deformation Theories of Isotropic and Anisotropic Laminated Plates
,” J. Reinf. Plast. Compos.
0731-6844, 21
(9
), pp. 775
–813
.17.
Wang
, J.
, Liew
, K. M.
, Tan
, M. J.
, and Rajendran
, S.
, 2002, “Analysis of Rectangular Laminated Composite Plates via FSDT Meshless Method
,” Int. J. Mech. Sci.
0020-7403, 44
(7
), pp. 1275
–1293
.18.
Xiang
, Y.
, and Reddy
, J. N.
, 2003, “Natural Vibration of Rectangular Plates With an Internal Line Hinge Using the First Order Shear Deformation Plate Theory
,” J. Sound Vib.
0022-460X, 263
(2
), pp. 285
–297
.19.
Liew
, K. M.
, Huang
, Y. Q.
, and Reddy
, J. N.
, 2003, “Vibration Analysis of Symmetrically Laminated Plates Based on FSDT Using the Moving Least Squares Differential Quadrature Method
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 192
(19
), pp. 2203
–2222
.20.
Liew
, K. M.
, He
, X. Q.
, Tan
, M. J.
, and Lim
, H. K.
, 2004, “Dynamic Analysis of Laminated Composite Plates With Piezoelectric Sensor/Actuator Patches Using the FSDT Mesh-Free Method
,” Int. J. Mech. Sci.
0020-7403, 46
(3
), pp. 411
–431
.21.
Peng
, L. X.
, Kitipornchai
, S.
, and Liew
, K. M.
, 2005, “Analysis of Rectangular Stiffened Plates Under Uniform Lateral Load Based on FSDT and Element-Free Galerkin Method
,” Int. J. Mech. Sci.
0020-7403, 47
(2
), pp. 251
–276
.22.
Liew
, K. M.
, Wang
, C. M.
, Xiang
, Y.
, and Kitipornchai
, S.
, 1998, Vibration of Mindlin Plates: Programming the P-Version Ritz Method
, 1st ed., Elsevier Science Oxford
.23.
Shimpi
, R. P.
, 2002, “Refined Plate Theory and Its Variants
,” AIAA J.
0001-1452, 40
(1
), pp. 137
–146
.24.
Jones
, R. M.
, 1999, Mechanics of Composite Materials
, 2nd ed., Taylor and Francis
, Philadelphia
, pp. 63
–67
.25.
Shames
, I. H.
, and Dym
, C. L.
, 1975, Energy and Finite Element Methods in Structural Mechanics
, Hemisphere Publishing
, New York
, pp. 257
–274
.26.
Kabir
, H. R. H.
, 1995, “A Shear-Locking Free Robust Isoparametric Three-Node Triangular Finite Element for Moderately-Thick and Thin Arbitrarily Laminated Plates
,” Comput. Struct.
0045-7949, 57
(4
), pp. 589
–597
.27.
Reddy
, J. N.
, 1997, “On Locking-Free Shear Deformable Beam Finite Elements
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 149
(1–4
), pp. 113
–132
.28.
Ainsworth
, M.
, and Pinchedez
, K.
, 2002, “The hp-MITC Finite Element Method for the Reissner-Mindlin Plate Problem
,” J. Comput. Appl. Math.
0377-0427, 148
(2
), pp. 429
–462
.29.
Xiao
, J. R.
, and McCarthy
, M. A.
, 2003, “Meshless Analysis of Timoshenko Beams Based on a Locking-Free Formulation and Variational Approaches
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 192
(39–40
), pp. 4403
–4424
.30.
Brezzi
, F.
, and Marini
, L. D.
, 2003, “A Nonconforming Element for the Reissner-Mindlin Plate
,” Comput. Struct.
0045-7949, 81
(8–11
), pp. 515
–522
.31.
Averill
, R. C.
, and Reddy
, J. N.
, 1992, “An Assessment of Four-Noded Plate Finite Elements Based On a Generalized Third-Order Theory
,” Int. J. Numer. Methods Eng.
0029-5981, 33
(8
), pp. 1553
–1572
.32.
Srinivas
, S.
, and Rao
, A. K.
, 1970, “Bending, Vibration and Buckling of Simply-Supported Thick Orthotropic Rectangular Plates and Laminates
,” Int. J. Solids Struct.
0020-7683, 6
(11
), pp. 1463
–1481
.33.
Srinivas
, S.
, 1970, “Three Dimensional Analysis of Some Plates and Laminates and a Study of Thickness Effects
,” Ph.D. thesis, Dept. of Aeronautical Engineering, Indian Institute of Science, Bangalore, India.34.
Whitney
, J. M.
, 1973, “Shear Correction Factors for Orthotropic Laminates Under Static Load
,” ASME J. Appl. Mech.
0021-8936, 40
(1
), pp. 302
–304
.35.
Vlachoutsis
, S.
, 1992, “Shear Correction Factors for Plates and Shells
,” Int. J. Numer. Methods Eng.
0029-5981, 33
(7
), pp. 1537
–1552
.36.
Birman
, V.
, and Bert
, C. W.
, 2002, “On the Choice of Shear Correction Factor in Sandwich Structures
,” J. Sandwich Struct. Mat.
, 4
(1
), pp. 83
–95
.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
