Acta Mechanica Solida Sinica

, Volume 23, Issue 2, pp 167–174 | Cite as

Three-Dimensional Static Analyses for FGM Plates with Medium Components and Different Net Structures

  • Hongmei Cheng
  • Zhiyuan Cao


A new microelement method for the analyses of functionally graded structures was proposed. The key of this method is the maneuverable combination of two kinds of elements. Firstly, the macro elements are divided from the functionally graded material structures by the normal finite elements. In order to reflect the functionally graded distributions of materials and the microconstitutions in each macro-element, the microelement method sets up the dense microelements in every macro-element, and translates the degrees of freedom of all microelemental nodes to the same as the normal finite elements by the compatibility conditions. This microelement method can fully reflect the micro constitutions and different components of materials, and its computational elements are the same as the normal finite elements, so it is an effective numerical method for the analyses of the functionally graded material structures. The three-dimensional analyses of functionally graded plates with medium components and different micro net structures are given by using the microelement method in this paper. The differences of the stress contour in the plane of functionally graded plates with different net microstructures are especially given in this paper.

Key words

functionally graded materials medium components different net structures three-dimensional analyses microelement method span-scale analyses 


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  1. [1]
    Koizumi, M., The concept of FGM. Ceramic Trans, Functionally Gradient Materials, 1993, 34: 3–10.Google Scholar
  2. [2]
    Hirai, T. and Chen, L., Recent and prospective development of functionally graded materials in Japan. Materials Science Forum, 1999, 308–311: 509–514.CrossRefGoogle Scholar
  3. [3]
    Markworth, A.J. and Ramesh, K.S., Review modelling studies applied to functionally graded materials. Journal of Materials Science, 1995, 30: 2183–2193.CrossRefGoogle Scholar
  4. [4]
    Wang, H.M., Liu, C.B. and Ding, H.J., Exact solution and transient behavior for torsional vibration of functionally graded finite hollow cylinders. Acta Mechanica Sinica, 2009, 25(4): 555–563.CrossRefGoogle Scholar
  5. [5]
    Obata, Y. and Noda, N., Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a FGM. Journal of Thermal Stresses, 1994, 17: 471–487.CrossRefGoogle Scholar
  6. [6]
    Cheng, Z.Q. and Batra, R.C., 3-D thermoelastic deformations of a FGM elliptic plate. Composites, Part B, 2000, 31: 97–106.CrossRefGoogle Scholar
  7. [7]
    Praveen, G.N. and Reddy, J.N., Nonlinear transient thermoelastic analysis of FGM ceramic-metal plates. International Journal of Solids and Structures, 1998, 35(33): 4457–4476.CrossRefGoogle Scholar
  8. [8]
    Tanigawa, Y., Matsumoto, M. and Akat, T., Optimization problem of material composition for nonhomogeneous plate to minimize thermal stress. Trans of the Japan Society of Mechanical Engineers, Series A, 1996, 62: 115–122.CrossRefGoogle Scholar
  9. [9]
    Hao, T.H., Crack tip field in functionally gradient material with exponential variation of elastic constants in two directions. Acta Mechanica Sinica, 2005, 21(6): 601–607.CrossRefGoogle Scholar
  10. [10]
    Tanigawa, Y., Some basic thermoelastic problems for nonhomogeneous structural materials. ASME, Applied Mechanics Reviews, 1995, 48(6): 287–300.CrossRefGoogle Scholar
  11. [11]
    Huang, G.Y., Wang, Y.S. and Yu, S.W., A new multilayered model for in-plane fracture analysis of functionally graded materials. Acta Mechanica Sinica, 2005, 37(1): 1–8.Google Scholar
  12. [12]
    Cheng, Z.Q. and Lim, C.W., Kitipornchai S. 3-D asymptotic approach to inhomogeneous and laminated piezoelectric plates. International Journal of Solids and Structures, 2000, 37: 3153–3175.CrossRefGoogle Scholar
  13. [13]
    Lim, C.W. and He, L.H., Exact solution of a compositionally graded piezoelectric layer under uniform stretch, bending and twisting. International Journal of Mechanical Sciences, 2001, 43: 2479–2492.CrossRefGoogle Scholar
  14. [14]
    Yang, J. and Shen, H.S., Dynamic response of initially stressed functionally graded rectangular thin plates. Composite Structure, 2001, 54: 497–508.CrossRefGoogle Scholar
  15. [15]
    Shen, H.S., Bending, buckling and vibration of functionally graded composite material plates and shells. Advances in Mechanics, 2004, 34(1): 53–60.Google Scholar
  16. [16]
    Yang, Z.G., Zhong, Z. and Dai, Y., Three dimensional elasticity analysis of a functionally graded rectangular plate. Chinese Quarterly of Mechanics, 2004, 25(1): 15–20.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  1. 1.State Key Laboratory for Geomechanics & Deep Underground Engineering, School of Mechanics, Architecture and Civil EngineeringChina University of Mining and TechnologyXuzhouChina
  2. 2.School of Aerospace Engineering and Applied MechanicsTongji UniversityShanghaiChina

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