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BRIEF NOTES

A Combined Fourier Series–Galerkin Method for the Analysis of Functionally Graded Beams

[+] Author and Article Information
H. Zhu, B. V. Sankar

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611-6250

J. Appl. Mech 71(3), 421-424 (Jun 22, 2004) (4 pages) doi:10.1115/1.1751184 History: Received July 01, 2002; Revised December 05, 2003; Online June 22, 2004
Copyright © 2004 by ASME
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References

Suresh, S., and Mortensen, A., 1998, Fundamentals of Functionally Graded Materials, IOM Communications Ltd., London.
Pindera, M.-J., and Dunn, P., 1995, “An Evaluation of Coupled Microstructural Approach for the Analysis of Functionally Graded Composites via the Finite Element Method,” NASA CR 195455, Lewis Research Center, Cleveland, OH.
Delale,  F., and Erdogan,  F., 1983, “The Crack Problem for a Nonhomogeneous Plane,” ASME J. Appl. Mech., 50, pp. 609–614.
Sankar,  B. V., 2001, “An Elasticity Solution for Functionally Graded Beams,” Compos. Sci. Technol., 61, pp. 689–696.
Sankar,  B. V., and Tzeng,  J. T., 2002, “Thermal Stresses in Functionally Graded Beams,” AIAA J., 40(6), pp. 1228–1232.
Venkataraman, S., and Sankar, B. V., 2001, “Analysis of Sandwich Beams With Functionally Graded Core,” AIAA Paper 2001-1281.
Apetre, N. A., Sankar, B. V., and Venkataraman, S., 2002, “Indentation of a Sandwich Beam With Functionally Graded Core,” AIAA Paper 2002-1683.

Figures

Grahic Jump Location
Transverse shear stress through the thickness of FGM beam for Eh=0.1 E0. The exact solution and that of Galerkin method are indistinguishable.
Grahic Jump Location
Transverse shear stress through the thickness of FGM beam for Eh=10 E0. The exact solution and that of Galerkin method are indistinguishable.
Grahic Jump Location
Normalized axial stress σxx through the thickness of FGM beam for Eh=0.1 E0. The exact solution and that of Galerkin method are indistinguishable.
Grahic Jump Location
Normalized axial stress σxx through the thickness of FGM beam for Eh=10 E0. The exact solution and that of Galerkin method are indistinguishable.
Grahic Jump Location
A FGM beam subjected to symmetric transverse loading

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