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

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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.

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  1. Sankar, B.V., An elasticity solution for functionally graded beams. Composites Science and Technology, 2001, 61(5): 689–696.

    Article  Google Scholar 

  2. Kashtalyan, M., Three-dimensional elasticity solution for bending of functionally graded rectangular plates. European Journal of Mechanics A/Solids, 2004, 23: 853–864.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. Cao, Z.Y., Nonlinear dynamic analysis of functionally graded material plates. Acta Mechanica Solida Sinica, 2006, 27(1): 21–25.

    Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  8. Reddy, J.N., Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering, 2000, 47: 663–684.

    Article  Google Scholar 

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Project supported by the National Natural Sciences Foundation of China (No. 10432030).

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Zhang, C., Zhong, Z. Three-dimensional analysis of functionally graded plate based on the Haar wavelet method. Acta Mech. Solida Sin. 20, 95–102 (2007).

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