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Elastoplastic Analysis of a Functionally Graded Material Beam Subjected to Uniformly Distributed Load

Published online by Cambridge University Press:  10 December 2019

L. J. Xue Open the ORCID record for L. J. Xue [Opens in a new window] ,
X. Y. Bian ,
J. J. Feng  and
J. N. Liu
L. J. Xue
Affiliation:
Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, Tianjin University of TechnologyTianjin, China
X. Y. Bian
Affiliation:
Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, Tianjin University of TechnologyTianjin, China
J. J. Feng*
Affiliation:
National Demonstration Center for Experimental Mechanical and Electrical Engineering Education (Tianjin University of Technology) Tianjin, China
J. N. Liu
Affiliation:
National Demonstration Center for Experimental Mechanical and Electrical Engineering Education (Tianjin University of Technology) Tianjin, China
*
*Corresponding author (jjfeng@tju.edu.cn)
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Abstract

The elastoplastic behavior of a Functionally Graded Material (FGM) simply supported beam consisting of elastic material A and elastoplastic material B under uniformly distributed load is investigated. A power function is used to describe the volume fractions of the constituent materials, and the average stress of the FGM beam is obtained by using the averaging method. This method can avoid the assumption of the varying properties of the whole material, and can consider the different Possion’s ratios of the different constituent materials. What’s more, only the elastoplastic material B in the FGM beam will yield, and the yield function is determined by the stress of material B only, rather than the average stress of the whole material. The method used in this work is more closer to the real material than the method by assuming the variation of the whole properties of FGM. The theoretical results show a good agreement with the finite element results, which indicates that the method provided in this work is valid. With this method, the variation of the elastic and plastic areas, the stress distribution on the cross section, variation of the curvature and neutral layer, and the residual stress distribution of the FGM beam are discussed through numerical results. This work can provide a new way for the design and in-depth investigation of FGM material.

Keywords

Functionally graded materialBeamElastoplasticUniformly distributed load
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 1 , February 2020 , pp. 73 - 85
Copyright
Copyright © 2019 The Society of Theoretical and Applied Mechanics 

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References

REFERENCES

Niino, M., and Maeda, S., “Recent Development Status of Functionally Gadient Materials,” ISIJ International, 30, pp.699–703 (1990).CrossRefGoogle Scholar
Suresh, S., and Mortensen, A., “Fundamentals of Functionally Graded Materials,” IOM Communications. London (1998).Google Scholar
Miyamoto, Y., Kaysser, W. A., Rabin, B. H., Kawasaki, A., and Ford, R.G., “Functionally Graded Materials: Design, Processing and Applications,” Kluwer Academic. Dordrecht (1999).Google Scholar
Paulino, G. H., Jin, Z. H., and Dodds, R. H., “Failure of Functionally Graded Materials,” Elsevier Science Ltd. New York (2003).CrossRefGoogle Scholar
Noda, N., “Thermal Stresses in Functionally Graded Material,” Journal of Thermal Stresses, 22, pp.477–512 (1999).CrossRefGoogle Scholar
Mantese, J. V., Schubring, N. W., and Micheli, A. L., “Stress-induced Polarization-graded Ferroelectrics,” Applied Physics Letters, 81(6), pp.1068–1070 (2002).CrossRefGoogle Scholar
Sankar, B. V., “An Elasticity Solution for Functionally Graded Beams,” Composites Science and Technology, 61, pp.689–696 (2001).CrossRefGoogle Scholar
Ding, H. J., Huang, D. J., and Chen, W. Q., “Elasticity Solutions for Plane Anisotropic Functionally Graded Beams,” International Journal of Solids and Sturctures, 44, pp.176–196 (2007).CrossRefGoogle Scholar
Ma, L. S., and Lee, D. W., “A Further Discussion of Nonlinear Mechanical Behavior for FGM Beams Under In-plane Thermal Loading,” Composite Structures, 93, pp.831–842 (2011).CrossRefGoogle Scholar
Sallai, B. O., Tounsi, A., Mechab, I., Bachir, B. M., Meradjah, M., and Adda, B. E. A., “A Theoretical Analysis of Flexional Bending of Al/Al2O3 S-FGM Thick Beams,” Computational Materials Science, 44, pp.1344–1350 (2009).Google Scholar
Mirzababaee, M., Tahani, M., and Zebarjad, S. M., “A New Approach for The Analysis of Functionally Graded Beams,” Journal of Achievements in Materials and Manufacturing Engineering, 17, pp. 265–268 (2006).Google Scholar
Kang, Y. A., and Li, X. F., “Bending Behavior of Functionally Graded Cantilever Beam with Power-law Non-linearity Subjected to An End Force,” International Journal of Non-Linear Mechanics, 44, pp.696–703 (2009).CrossRefGoogle Scholar
Yaghoobi, H., and Fereidoon, A., “Influence of Neutral Surface Position on Deflection of Functionally Graded Beam under Uniformly Distributed Load,” World Applied Sciences Journal, 10(3), pp.337–341 (2010).Google Scholar
Simsek, M., “Static Analysis of A Functionally Graded Beam Under A Uniformly Distributed Load by Ritz Method,” International Journal of Engineering and Applied Sciences, 1(3), pp.1–11 (2009).Google Scholar
Qu, J. M., and Cherkaoui, M., “Fundamentals of micromechanics of solids,” John Wiley &Sons, Inc. New Jersey (2006).CrossRefGoogle Scholar
Sayman, O., “An Elastic-plastic Thermal Stress Analysis of Aluminum Metal-matrix Composite Beams,” Composite Structures, 53, pp.419–425 (2001).CrossRefGoogle Scholar