Semi-analytical solution for three-dimensional vibration of functionally graded circular plates

2007 ◽  
Vol 196 (49-52) ◽  
pp. 4901-4910 ◽  
Author(s):  
G.J. Nie ◽  
Z. Zhong
Keyword(s):  
Analytical Solution ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Circular Plates

A Parallel Domain Decomposition BEM Algorithm for Three-Dimensional Exponentially Graded Elasticity

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
J. E. Ortiz ◽  
W. A. Shelton ◽  
V. Mantič ◽  
R. Criado ◽  
L. J. Gray ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Domain Decomposition ◽  
Functionally Graded Material ◽  
Computational Cost ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Functionally Graded ◽  
Graded Material ◽  
High Computational Cost ◽  
Exponentially Graded

A parallel domain decomposition boundary integral algorithm for three-dimensional exponentially graded elasticity has been developed. As this subdomain algorithm allows the grading direction to vary in the structure, geometries arising from practical functionally graded material applications can be handled. Moreover, the boundary integral algorithm scales well with the number of processors, also helping to alleviate the high computational cost of evaluating the Green’s functions. For axisymmetric plane strain states in a radially graded material, the numerical results for cylindrical geometries are in excellent agreement with the analytical solution deduced herein.

Semi-Analytical Solution for Functionally Graded Solid Circular and Annular Plates Resting on Elastic Foundations Subjected to Axisymmetric Transverse Loading

2012 ◽  
Vol 4 (2) ◽  
pp. 205-222 ◽  
Author(s):  
A. Behravan Rad
Keyword(s):  
Elastic Foundation ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Circular Plates ◽  
Linear Elastic ◽  
Edge Conditions ◽  
The One ◽  
Foundation Plate

AbstractIn this paper, the static analysis of functionally graded (FG) circular plates resting on linear elastic foundation with various edge conditions is carried out by using a semi-analytical approach. The governing differential equations are derived based on the three dimensional theory of elasticity and assuming that the mechanical properties of the material vary exponentially along the thickness direction and Poisson’s ratio remains constant. The solution is obtained by employing the state space method (SSM) to express exactly the plate behavior along the graded direction and the one dimensional differential quadrature method (DQM) to approximate the radial variations of the parameters. The effects of different parameters (e.g., material property gradient index, elastic foundation coefficients, the surfaces conditions (hard or soft surface of the plate on foundation), plate geometric parameters and edges condition) on the deformation and stress distributions of the FG circular plates are investigated.

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