Three-dimensional elasticity solution for simply supported rectangular plates with variable thickness

2008 ◽  
Vol 43 (3) ◽  
pp. 165-176 ◽  
Author(s):  
Y-P Xu ◽  
D Zhou
Keyword(s):  
Variable Thickness ◽  
Three Dimensional ◽  
Rectangular Plates ◽  
Elasticity Solution ◽  
Simply Supported ◽  
Three Dimensional Elasticity

Three-dimensional elasticity solution of simply supported functionally graded rectangular plates with internal elastic line supports

2009 ◽  
Vol 44 (4) ◽  
pp. 249-261 ◽  
Author(s):  
Y P Xu ◽  
D Zhou
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Lower Surface ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Elastic Line ◽  
Simply Supported ◽  
Three Dimensional Elasticity

This paper studies the stress and displacement distributions of simply supported functionally graded rectangular plates with internal elastic line supports. The Young's modulus is graded through the thickness following the exponential law and the Poisson's ratio is kept constant. On the basis of three-dimensional elasticity theory, the solutions of displacements and stresses of the plate under static loads, which exactly satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the internal elastic line supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients in the solutions are then determined by the boundary conditions on the upper and lower surfaces of the plate. Convergence and comparison studies demonstrate the correctness and effectiveness of the proposed method. The effect of variations in Young's modulus on the displacements and stresses of rectangular plates and the effect of internal elastic line supports on the mechanical properties of plates are investigated.

Exact Elasticity Solution for Laminated Anisotropic Cylindrical Shells

1993 ◽  
Vol 60 (1) ◽  
pp. 41-47 ◽  
Author(s):  
K. Bhaskar ◽  
T. K. Varadan
Keyword(s):  
Shell Theory ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Elasticity Solution ◽  
Transverse Loading ◽  
Cylindrical Bending ◽  
Simply Supported ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
Anisotropic Cylindrical Shell

An exact three-dimensional elasticity solution is obtained for cylindrical bending of simply-supported laminated anisotropic cylindrical shell strips subjected to transverse loading. Displacements and stresses are presented for different angle-ply layups and radius-to-thickness ratios, so as to serve as useful benchmark results for the assessment of various two-dimensional shell theories. Finally, in the light of these results, the accuracy of the Love-type classical shell theory is examined.

A Study on Free Vibrational Response of Functionally Graded Nanocomposite Sandwich Plates Reinforced by Randomly Oriented Straight Carbon Nanotubes

2016 ◽  
Vol 880 ◽  
pp. 77-82
Author(s):  
Vahid Tahouneh
Keyword(s):  
Carbon Nanotube ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Reinforced Composites ◽  
Technical Literature ◽  
Simply Supported ◽  
Vibrational Response ◽  
Three Dimensional Elasticity

This paper is motivated by the lack of studies in the technical literature concerning to the three dimensional vibration analysis of thick laminated rectangular plates with continuously graded carbon nanotube-reinforced (CGCNTR) sheets. The formulations are based on the three-dimensional elasticity theory. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The structure is supported by an elastic foundation with Winkler’s (normal) and Pasternak’s (shear) coefficients. The material properties of the functionally graded carbon nanotube reinforced composites are graded along the thickness and estimated through Mori-Tanaka method.

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