Acta Mechanica Solida Sinica

, Volume 20, Issue 2, pp 95–102

# Three-dimensional analysis of functionally graded plate based on the Haar wavelet method

• Chun Zhang
• Zheng Zhong
Article

## Abstract

A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. With good features in treating singularities, Haar series solution converges rapidly for arbitrary distributions, especially for the case where the material properties change rapidly in some regions. Through numerical examples the influences of the ratio of material constants on the top and bottom surfaces and different material gradient distributions on the structural response of the plate to mechanical stimuli are studied.

## Key words

functionally graded material rectangular plate Haar wavelet three-dimensional analysis

## References

1. [1]
Sankar, B.V., An elasticity solution for functionally graded beams. Composites Science and Technology, 2001, 61(5): 689–696.
2. [2]
Kashtalyan, M., Three-dimensional elasticity solution for bending of functionally graded rectangular plates. European Journal of Mechanics A/Solids, 2004, 23: 853–864.
3. [3]
Zhong, Z. and Shang, E.T., Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate. International Journal of Solids and Structures, 2003, 40: 5335–5352.
4. [4]
Yu, T. and Zhong, Z., A general solution of a clamped functionally graded cantilever-beam under uniform loading. Acta Mechanica Solida Sinica, 2006, 27(1): 15–20.Google Scholar
5. [5]
Cao, Z.Y., Nonlinear dynamic analysis of functionally graded material plates. Acta Mechanica Solida Sinica, 2006, 27(1): 21–25.Google Scholar
6. [6]
Chen, C.F. and Hsiao, C.H., Haar wavelet method for solving lumped and distributed-parameter systems. IEE Proc.-Control Theory Appl., 1997, 144(1): 87–94.
7. [7]
Hsiao, C.H. and Wang, W.J., State analysis of time-varying singular nonlinear systems via Haar wavelets. Mathematics and Computers in Simulation, 1999, 51: 91–100.
8. [8]
Reddy, J.N., Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering, 2000, 47: 663–684.

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2007

## Authors and Affiliations

• Chun Zhang
• 1
• 2
• Zheng Zhong
• 1
1. 1.School of Aerospace Engineering and Applied mechanicsTongji UniversityShanghaiChina
2. 2.School of Civil Engineering and ArchitectureNanchang UniversityNanchangChina