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Advances in Materials Research Volume 9, Number 1, March 2020 , pages 63-98 DOI: https://doi.org/10.12989/amr.2020.9.1.063 |
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Bending and free vibration analysis of functionally graded beams on elastic foundations with analytical validation |
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Lazreg Hadji and Fabrice Bernard
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| Abstract | ||
| The novelty of this paper is the use of a simple higher order shear and normal deformation theory for bending and free vibration analysis of functionally graded material (FGM) beams on two-parameter elastic foundation. To this aim, a new shear strain shape function is considered. Moreover, the proposed theory considers a novel displacement field which includes undetermined integral terms and contains fewer unknowns with taking into account the effects of both transverse shear and thickness stretching. Different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. In addition, the effect of different micromechanical models on the bending and free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams for which properties vary continuously across the thickness according to a simple power law. Hamilton's principle is used to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio, foundation parameter, the volume fraction of porosity and micromechanical models on the displacements, stresses, and frequencies. | ||
| Key Words | ||
| functionally graded material; elastic foundation; shear deformation theory; bending; free vibration; stretching effect | ||
| Address | ||
| (1) Lazreg Hadji: Laboratory of Geomatics and Sustainable Development, University of Tiaret,14000 Tiaret, Algeria; (2) Lazreg Hadji: Department of Mechanical Engineering, University of Tiaret, BP 78 Zaaroura, 14000 Tiaret, Algeria; (3) Fabrice Bernard: University of Rennes, INSA Rennes, Laboratory of Civil Engineering and Mechanical Engineering, France. | ||
