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

2000 ◽  
Vol 35 (2) ◽  
pp. 93-103 ◽  
Author(s):  
Hui-Shen Shen
Keyword(s):  
Thermal Loading ◽  
Lateral Pressure ◽  
Plate Theory ◽  
Perturbation Technique ◽  
Laminated Plates ◽  
Graphical Form ◽  
Elastic Foundations ◽  
Non Linear ◽  
Shear Deformable ◽  
Two Parameter

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.

Postbuckling of composite laminated plates under biaxial compression combined with lateral pressure and resting on elastic foundations

1998 ◽  
Vol 33 (4) ◽  
pp. 253-261 ◽  
Author(s):  
H-S Shen
Keyword(s):  
Lateral Pressure ◽  
Plate Theory ◽  
Perturbation Technique ◽  
Laminated Plates ◽  
Combined Loading ◽  
Graphical Form ◽  
Biaxial Compression ◽  
Elastic Foundations ◽  
Plate Aspect Ratio ◽  
Limiting Case

A postbuckling analysis is presented for a simply supported, composite laminated rectangular plate subjected to biaxial compression combined with lateral pressure and resting on a two-parameter (Pasternak-type) elastic foundation. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the classical laminated plate theory, including plate-foundation interaction. The analysis uses a perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of antisymmetric angle-ply and symmetric cross-ply laminated plates subjected to combined loading and resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influence played by a number of effects, among them foundation stiffness, the plate aspect ratio, the total number of plies, fibre orientation and initial lateral pressure, is studied. Typical results are presented in dimensionless graphical form.

A Composite Plate Theory for Arbitrary Laminate Configurations

1987 ◽  
Vol 54 (1) ◽  
pp. 181-189 ◽  
Author(s):  
A. Toledano ◽  
H. Murakami
Keyword(s):  
Composite Plate ◽  
Plate Theory ◽  
Piecewise Linear ◽  
Present Theory ◽  
Laminated Plates ◽  
Stress Distributions ◽  
Laminated Plate ◽  
Individual Layer ◽  
Mixed Variational Principle ◽  
Shear Deformable

In order to improve the accuracy of in-plane responses of shear deformable composite plate theories, a new laminated plate theory was developed for arbitrary laminate configurations based upon Reissner’s (1984) new mixed variational principle. To this end, across each individual layer, piecewise linear continuous displacements and quadratic transverse shear stress distributions were assumed. The accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by Pagano (1969). A comparison with the exact solutions obtained for symmetric, antisymmetric, and arbitrary laminates indicates that the present theory accurately estimates in-plane responses, even for small span-to-thickness ratios.

scholarly journals Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations

2019 ◽  
Vol 25 (9) ◽  
pp. 1507-1520 ◽  
Author(s):  
Hui-Shen Shen ◽  
Y Xiang ◽  
Yin Fan
Keyword(s):  
Large Amplitude ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Perturbation Approach ◽  
Elastic Foundations ◽  
Vibration Responses ◽  
Uniform Temperature Field ◽  
Thermal Postbuckling

This paper investigates the small- and large-amplitude vibrations of thermally postbuckled graphene-reinforced composite (GRC) laminated plates resting on elastic foundations. The piecewise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the plate. The anisotropic and temperature-dependent material properties of the FG-GRC layers are estimated through the extended Halpin–Tsai micromechanical model. Based on the Reddy's higher order shear deformation plate theory and the von Kármán strain–displacement relationships, the motion equations of the plates are derived. The foundation support, the thermal effect, and the initial deflection caused by thermal postbuckling are also included in the derivation. A two-step perturbation approach is applied to determine the thermal postbuckling equilibrium paths as well as the nonlinear vibration solutions for the FG-GRC laminated plates. The numerical illustrations concern small- and large-amplitude vibration characteristics of thermally postbuckled FG-GRC laminated plates under a uniform temperature field. The effects of graphene reinforcement distributions and foundation stiffnesses on the vibration responses of FG-GRC laminated plates are examined in detail.

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