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Semi-Analytical Solution for Functionally Graded Solid Circular and Annular Plates Resting on Elastic Foundations Subjected to Axisymmetric Transverse Loading

Semi-Analytical Solution for Functionally Graded Solid Circular and Annular Plates Resting on Elastic Foundations Subjected to Axisymmetric Transverse Loading
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Year:    2012

Author:    A. Behravan Rad

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 2 : pp. 205–222

Abstract

In this paper, the static analysis of functionally graded (FG) circular plates resting on linear elastic foundation with various edge conditions is carried out by using a semi-analytical approach. The governing differential equations are derived based on the three dimensional theory of elasticity and assuming that the mechanical properties of the material vary exponentially along the thickness direction and Poisson's ratio remains constant. The solution is obtained by employing the state space method (SSM) to express exactly the plate behavior along the graded direction and the one dimensional differential quadrature method (DQM) to approximate the radial variations of the parameters. The effects of different parameters (e.g., material property gradient index, elastic foundation coefficients, the surfaces conditions (hard or soft surface of the plate on foundation), plate geometric parameters and edges condition) on the deformation and stress distributions of the FG circular plates are investigated.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.10-m11104

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 2 : pp. 205–222

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Functionally graded circular plate elastic foundation differential quadrature method state-space method.

Author Details

A. Behravan Rad

  1. Thermo-magneto-elasticity analysis of variable thickness annular FGM plates with asymmetric shear and normal loads and non-uniform elastic foundations

    Behravan Rad, Ahmad | Shariyat, Mohammad

    Archives of Civil and Mechanical Engineering, Vol. 16 (2016), Iss. 3 P.448

    https://doi.org/10.1016/j.acme.2016.02.006 [Citations: 38]

  2. Three-dimensional magneto-elastic analysis of asymmetric variable thickness porous FGM circular plates with non-uniform tractions and Kerr elastic foundations

    Behravan Rad, A. | Shariyat, M.

    Composite Structures, Vol. 125 (2015), Iss. P.558

    https://doi.org/10.1016/j.compstruct.2015.02.049 [Citations: 65]

  3. Hygroelasticity analysis of an elastically restrained functionally graded porous metamaterial circular plate resting on an auxetic material circular plate

    Behravan-Rad, A. | Jafari, M.

    Applied Mathematics and Mechanics, Vol. 41 (2020), Iss. 9 P.1359

    https://doi.org/10.1007/s10483-020-2651-7 [Citations: 11]

  4. A modified axisymmetric ordinary state-based peridynamics with shear deformation for elastic and fracture problems in brittle solids

    Zhang, Ting | Zhou, Xiaoping

    European Journal of Mechanics - A/Solids, Vol. 77 (2019), Iss. P.103810

    https://doi.org/10.1016/j.euromechsol.2019.103810 [Citations: 29]

  5. Piezomagnetic Behavior of Functionally Graded Cylinders under Non-Axisymmetric Hygrothermal Loading: Interplay between Loading Contribution, Material Properties, and Elastic Response

    Eftekhari, Malihe | Hosseini, Mohammad | Eftekhari, Mojtaba

    Mechanics of Solids, Vol. (2024), Iss.

    https://doi.org/10.1134/S0025654424602520 [Citations: 0]

  6. Thermo-mechanical behavior of 2D functionally graded porous-auxetic metamaterial rotating disk with an auxetic foundation

    Behravanrad, Ahmad | Jafari, Mohammad

    Aerospace Science and Technology, Vol. 145 (2024), Iss. P.108829

    https://doi.org/10.1016/j.ast.2023.108829 [Citations: 13]

  7. A powerful numerical approach for the axisymmetric bending response of shear deformable two-directional functionally graded (2D-FG) plates with variable thickness

    Noori, Ahmad Reshad | Temel, Beytullah

    Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 235 (2021), Iss. 22 P.6370

    https://doi.org/10.1177/09544062211010837 [Citations: 6]

  8. Thermo-elastic analysis of functionally graded circular plates resting on a gradient hybrid foundation

    Behravan Rad, A.

    Applied Mathematics and Computation, Vol. 256 (2015), Iss. P.276

    https://doi.org/10.1016/j.amc.2015.01.026 [Citations: 17]

  9. Thermoporoelasticity analysis of variable thickness and elastically restrained functionally graded auxetic metamaterial circular plate resting on an auxetic material circular plate

    Behravanrad, Ahmad | Jafari, Mohammad

    Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 235 (2021), Iss. 16 P.3036

    https://doi.org/10.1177/0954406220958432 [Citations: 4]

  10. Static analysis of non-uniform 2D functionally graded auxetic-porous circular plates interacting with the gradient elastic foundations involving friction force

    Behravan Rad, A.

    Aerospace Science and Technology, Vol. 76 (2018), Iss. P.315

    https://doi.org/10.1016/j.ast.2018.01.036 [Citations: 72]

  11. Effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular plate with variable hybrid foundation

    Behravanrad, Ahmad | Jafari, Mohammad

    Mechanics Based Design of Structures and Machines, Vol. (2024), Iss. P.1

    https://doi.org/10.1080/15397734.2024.2361138 [Citations: 0]