全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

Stress and Strain Analysis of Functionally Graded Rectangular Plate with Exponentially Varying Properties

DOI: 10.1155/2013/206239

Full-Text   Cite this paper   Add to My Lib

Abstract:

The bending of rectangular plate made of functionally graded material (FGM) is investigated by using three-dimensional elasticity theory. The governing equations obtained here are solved with static analysis considering the types of plates, which properties varying exponentially along direction. The value of Poisson’s ratio has been taken as a constant. The influence of different functionally graded variation on the stress and displacement fields was studied through a numerical example. The exact solution shows that the graded material properties have significant effects on the mechanical behavior of the plate. 1. Introduction Recently, a new category of composite materials known as functionally graded materials (FGMs) has attracted the interest of many researchers. The FGMs are heterogeneous composite materials in which the mechanical properties vary continuously in certain direction. FGMs are used in many engineering applications such as aviation, rocketry, missiles, chemical, aerospace, and mechanical industries. Therefore, composites that are made of FGMs were considerably attractive in recent years. Several studies have been performed to analyze the behavior of functionally graded beam, plates, and shells. Hadi et al. [1, 2] studied an Euler-Bernoulli and Timoshenko beam made of functionally graded material subjected to a transverse loading at which Young’s modulus of the beam varies by specific function. Reddy [3] has analyzed the static behavior of functionally graded rectangular plates based on his third-order shear deformation plate theory. Cheng and Batra [4] have related the deflections of a simple supported functionally graded polygonal plate given by the first-order shear deformation theory and a third-order shear deformation theory to an equivalent homogeneous Kirchhoff plate. Cheng and Batra [5] also presented results for the buckling and steady state vibrations of a simple supported functionally graded polygonal plate based on Reddy’s plate theory. Loy et al. [6] studied the vibration of functionally graded cylindrical shells by using Love’s shell theory. Analytical 3D solutions for plates are useful because provided benchmark results to assess the accuracy of various 2D plate theories and finite element formulations. Cheng and Batra [7] used the method of asymptotic expansion to study the 3D thermoelastic deformations of a functionally graded elliptic plate. Recently, Vel and Batra [8] have presented an exact 3D solution for the thermoelastic deformation of functionally graded simple supported plates of finite dimensions. Reiter et al.

References

[1]  A. R. Daneshmehr, A. Hadi, and S. M. N. Mehrian, “Investigation of elastoplastic functionally graded Euler-Bernoulli beam subjected to distribute transverse loading,” Journal of Basic and Applied Scientific Research, vol. 2, no. 10, pp. 10628–10634, 2012.
[2]  A. Hadi, A. R. Daneshmehr, S. M. N. Mehrian, M. Hosseini, and F. Ehsani, “Elastic analysis of functionally graded timoshenko beam subjected to transverse loading,” Technical Journal of Engineering and Applied Sciences, vol. 3, no. 13, pp. 1246–1254, 2013.
[3]  J. N. Reddy, “Analysis of functionally graded plates,” International Journal for Numerical Methods in Engineering, vol. 47, no. 1–3, pp. 663–684, 2000.
[4]  Z.-Q. Cheng and R. C. Batra, “Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories,” Archives of Mechanics, vol. 52, no. 1, pp. 143–158, 2000.
[5]  Z.-Q. Cheng and R. C. Batra, “Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates,” Journal of Sound and Vibration, vol. 229, no. 4, pp. 879–895, 2000.
[6]  C. T. Loy, K. Y. Lam, and J. N. Reddy, “Vibration of functionally graded cylindrical shells,” International Journal of Mechanical Sciences, vol. 41, no. 3, pp. 309–324, 1999.
[7]  Z.-Q. Cheng and R. C. Batra, “Three-dimensional thermoelastic deformations of a functionally graded elliptic plate,” Composites Part B: Engineering, vol. 31, no. 2, pp. 97–106, 2000.
[8]  S. S. Vel and R. C. Batra, “Exact solution for thermoelastic deformations of functionally graded thick rectangular plates,” AIAA Journal, vol. 40, no. 7, pp. 1421–1433, 2002.
[9]  T. Reiter, G. J. Dvorak, and V. Tvergaard, “Micromechanical models for graded composite materials,” Journal of the Mechanics and Physics of Solids, vol. 45, no. 8, pp. 1281–1302, 1997.
[10]  Y. Tanigawa, “Theoretical approach of optimum design for a plate of functionally gradient materials under thermal loading,” in Thermal Shock and Thermal Fatigue Behavior of Advanced Ceramics, vol. 241 of Nato Science Series E, pp. 171–180, 1992.
[11]  K. Tanaka, Y. Tanaka, K. Enomoto, V. F. Poterasu, and Y. Sugano, “Design of thermoelastic materials using direct sensitivity and optimization methods. Reduction of thermal stresses in functionally gradient materials,” Computer Methods in Applied Mechanics and Engineering, vol. 106, no. 1-2, pp. 271–284, 1993.
[12]  K. Tanaka, Y. Tanaka, H. Watanabe, V. F. Poterasu, and Y. Sugano, “An improved solution to thermoelastic material design in functionally gradient materials: Scheme to reduce thermal stresses,” Computer Methods in Applied Mechanics and Engineering, vol. 109, no. 3-4, pp. 377–389, 1993.
[13]  Z. H. Jin and N. Noda, “Minimization of thermal stress intensity factor for a crack in a metal ceramic mixture, Ceramic Trans,” Functionally Graded Material, vol. 34, pp. 47–54, 1993.
[14]  N. Noda and Z. H. Jin, “Thermal stress intensity factors for a crack in a strip of a functionally gradient material,” International Journal of Solids and Structures, vol. 30, no. 8, pp. 1039–1056, 1993.
[15]  Z. H. Jin and N. Noda, “Transient thermal stress intensity factors for a crack in a semi-infinite plate of a functionally gradient material,” International Journal of Solids and Structures, vol. 31, no. 2, pp. 203–218, 1994.
[16]  Y. Obata and N. Noda, “Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material,” Journal of Thermal Stresses, vol. 17, no. 3, pp. 471–487, 1994.
[17]  Y. Obata, N. Noda, and T. Tsuji, “Steady thermal stresses in a functionally gradient material plate,” Transactions of the JSME, vol. 58, pp. 1689–1695, 1992.
[18]  G. N. Praveen and J. N. Reddy, “Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates,” International Journal of Solids and Structures, vol. 35, no. 33, pp. 4457–4476, 1998.
[19]  J. N. Reddy and C. D. Chin, “Thermomechanical analysis of functionally graded cylinders and plates,” Journal of Thermal Stresses, vol. 21, no. 6, pp. 593–626, 1998.
[20]  M. M. Najafizadeh and M. R. Eslami, “Buckling analysis of circular plates of functionally graded materials under uniform radial compression,” International Journal of Mechanical Sciences, vol. 44, no. 12, pp. 2479–2493, 2002.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133