Non-linear bending of shear deformable laminated plates under lateral pressure and thermal loading and resting on elastic foundations

Abstract

A non-linear bending analysis is presented for a simply supported shear deformable composite laminated plate subjected to a combined uniform lateral pressure and thermal loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on Reddy's higher-order shear deformation plate theory, including the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the load-deflection curves and load-bending moment curves. Numerical examples are presented that relate to the performances of antisymmetric angleply and symmetric cross-ply laminated plates subjected to thermomechanical loading and resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influences due to a number of effects e.g. foundation stiffness, plate aspect ratio, total number of plies, fibre orientation and initial thermal bending stress, are studied. Typical results are presented in a dimensionless graphical form.

Keywords

large deflection shear deformable composite laminated plate Pasternak-type elastic foundation higher-order shear deformation plate theory Galerkin-perturbation technique

Get full access to this article

View all access options for this article.

References

Argyris

Tenek

Linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method. Comput. Meth. Appl. Mechanics Engng, 1994, 113, 207–251.

Lin

R. M.

Lim

M. K.

Large deflection analysis of plates under thermal loading. Comput. Meth. Appl. Mechanics Engng, 1994, 117, 381–390.

Yeh

F. H.

Liu

W. H.

Nonlinear analysis of rectangular orthotropic plates. Int. J. Mech. Sci., 1991, 33, 563–578.

Huang

N. N.

Tauchert

T. R.

Large deformation of antisymmetric angle-ply laminates resulting from nonuniform temperature loading. J. Thermal Stresses, 1988, 11, 287–297.

Zaghloul

S. A.

Kennedy

J. B.

Nonlinear analysis of unsymmetrically laminated plates. J. Engng Mechanics, ASCE, 1975, 101, 169–185.

Niyogi

A. K.

Nonlinear bending of rectangular orthotropic plates. Int. J. Solids Structs, 1973, 9, 1133–1139.

Iyengar

K. T.S.

Naqvi

M. M.

Large deflection of rectangular plates. Int. J. Non-Linear Mechanics, 1966, 1, 109–122.

Yamaki

Influence of large amplitudes on flexural vibrations of elastic plates. Z. Angew. Math. Mech., 1961, 41, 501–510.

Wang

C. T.

Bending of rectangular plates with large deflections. Technical Note 1462, National Advisory Committee for Aeronautics, 1948.

10.

Levy

Bending of rectangular plates with large deflections. Technical Note 737, National Advisory Committee for Aeronautics, 1942.

11.

Ganapathi

Polit

Touratier

A C° eight-node membrane-shear-bending element for geometrically nonlinear (static and dynamic) analysis of laminates. Int. J. Numer. Meth. Engng, 1996, 39, 3453–3474.

12.

Savithri

Varadan

T. K.

Large deflection analysis of laminated composite plates. Int. J. Non-Linear Mechanics, 1993, 28, 1–12.

13.

Turvey

G. J.

Osman

M. Y.

Elastic large deflection analysis of isotropic rectangular Mindlin plates. Int. J. Mech. Sci., 1990, 32, 315–328.

14.

Singh

Sadasiva Rao

T. V. K.

Large deflection behaviour of thick composite plates. Composite Structs, 1987, 8, 13–29.

15.

Gorji

On large deflection of symmetric composite plates under static loading. Proc. Instn Mech. Engrs, Part C, Journal of Mechanical Engineering Science, 1986, 200 (C1), 13–19.

16.

Putcha

N. S.

Reddy

J. N.

A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates. Comput. Structs, 1986, 22, 529–538.

17.

Reddy

J. N.

Chao

W. C.

Large-deflection and large-amplitude free vibrations of laminated composite material plates. Comput. Structs, 1981, 13, 341–347.

18.

Reddy

J. N.

Chao

W. C.

Nonlinear bending of thick rectangular laminated composite plates. Int. J. Non-Linear Mechanics, 1981, 16, 291–301.

19.

Pica

Wood

R. D.

Hinton

Finite element analysis of geometrically nonlinear plate behaviour using a Mindlin formulation. Comput. Structs, 1980, 11, 203–215.

20.

Sinha

S. N.

Large deflections of plates on elastic foundations. J. Engng Mechanics, ASCE, 1963, 89, 1–24.

21.

Berger

H. M.

A new approach to the analysis of large deflections of plates. Trans. ASME, J. Appl. Mechanics, 1955, 22, 465–472.

22.

Yang

H. T. Y.

Flexible plate finite element on elastic foundation. J. Structural Division, ASCE, 1970, 96, 2083–2101.

23.

Ghosh

P. K.

Large deflection of a rectangular plate resting on a Pasternak-type elastic foundation. Trans. ASME, J. Appl. Mechanics, 1977, 44, 509–511.

24.

Chia

C. Y.

Nonlinear Analysis of Plates, 1980 (McGraw-Hill, New York).

25.

Shen

H. S.

Thermomechanical post-buckling analysis of imperfect laminated plates using a higher-order shear-deformation theory. Comput. Structs, 1998, 66, 395–409.

26.

Reddy

J. N.

Mechanics of Laminated Composite Plates: Theory and Analysis, 1997 (CRC Press, Boca Raton, Florida).

27.

Shen

H. S.

Thermal post-buckling analysis of imperfect laminated plates using a higher-order shear-deformation theory. Int. J. Non-Linear Mechanics, 1997, 32, 1035–1050.

28.

Turvey

G. J.

Uniformly loaded, simply supported, antisymmetrically laminated, rectangular plate on a Winkler-Pasternak foundation. Int. J. Solids Structs, 1977, 13, 437–444.