Three-dimensional elasticity solution of functionally graded rectangular plates with variable thickness

2009 ◽  
Vol 91 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Yepeng Xu ◽  
Ding Zhou
Keyword(s):  
Variable Thickness ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Elasticity Solution ◽  
Three Dimensional Elasticity

Three-dimensional elasticity analysis of functionally graded rotating cylinders with variable thickness profile

2011 ◽  
Vol 226 (3) ◽  
pp. 585-594 ◽  
Author(s):  
E Ghafoori ◽  
M Asghari
Keyword(s):  
Variable Thickness ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Numerical Results ◽  
Constant Thickness ◽  
Rotating Cylinders ◽  
Hollow Structures ◽  
Thickness Profile ◽  
Axisymmetric Structure ◽  
Three Dimensional Elasticity

A three-dimensional elasticity solution for the analysis of functionally graded rotating cylinders with variable thickness profile is proposed. The axisymmetric structure has been divided in several divisions in the radial direction. Constant mechanical properties and thickness profile are assumed within each division. The solution is considered for four different thickness profiles, namely constant, linear, concave, and convex. It is shown that the linear, concave, and convex thickness profiles have smaller stress values compared to a constant thickness profile. The effects of various grading indices as well as different boundary conditions, namely solid, free–free hollow and fixed–free hollow structures are discussed. A series of numerical results using zirconia as outer surface ceramic and aluminium as inner surface metal are presented. Parametric study has then been carried out to give a better understanding of how different stress, strain, and displacement components change along radial and axial directions of the rotating structures. Numerical results show that for a given grading index, the structures with a concave thickness profile have the smaller circumferential strain and stress compared to other thickness profiles.

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.

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