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Finite element based bending analysis of rectangular FGM plates using first-order shear deformation theory

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Abstract

FEM based bending analysis of rectangular FGM plates with different boundary conditions under various transverse loads is investigated based on the first-order shear deformation theory (FSDT). Three different FGM models of P-FGM, S-FGM and E-FGM are considered. Moreover, various types of transverse loads including uniformly distributed lateral load, concentrated point load at center of the plate, hydrostatic load, distributed triangular prism type load, uniformly strip type distributed load and sinusoidal type of loads are considered. Also, three types of elements including 4-node, 8-node and 9-node quadrilateral plate elements have been used in the FEM formulation applying the FSDT. An FEM mesh sensitivity analysis has been performed on the obtained results for a simply supported P-FGM square plate with different power-law indices under uniform lateral load. The obtained results have been validated through comparing them with the results in the literature for special cases. Then, the effect of changes of different parameters, including power-law index for P-FGM, S-FGM and also E-FGM, element types and number of elements used, types of boundary conditions on all edges, various transverse loads, aspect ratio of rectangular pale and Young’s modulus of materials on the bending results for the non-dimensional center deflection and also 3-D deformed shape of the FGM rectangular plates, have been studied and discussed. The obtained results show that the FEM based modeling with Q8 element type using FSDT is reliable, accurate, really simple and efficient in solving the bending behavior of thin to medium-thick FGM plates compared to the other analytical higher order shear deformation theories (HSDT) and models with much further complexity. Moreover, it is seen that the FGM power-law index influences the bending deformation of the plate vividly.

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Abbreviations

E m :

Modulus of elasticity of metal rich surface of FGM plate

E c :

Modulus of elasticity of ceramic rich surface of FGM plate

Φ x :

Rotation of transverse section in the x-z plane around the x axis not assumed to be kept normal to the mid-plane x-y of the plate after bending deformation

Φ y :

Rotation of transverse section in the y-z plane around the y axis not assumed to be kept normal to the mid-plane x-y of the plate after bending deformation

N i :

Shape functions of the quadrilateral plate element

\(\bar{w}\) :

Non-dimensional center deflection of the plate

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Authors and Affiliations

  1. Department of Mechanical Engineering, Parand Branch, Islamic Azad University, Parand, Iran

    Ahmad Mamandi

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  1. Ahmad Mamandi
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Correspondence to Ahmad Mamandi.

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The author of this paper declares that he has no conflict of interest.

Ahmad Mamandi is an Associate Professor of Aerospace Engineering, Parand Branch, Islamic Azad University, Parand, Iran. His research interests include nonlinear vibrations, recent theories of beams, plates and shells, FEM modeling, MEMS/NEMS, aeroelasticity, fracture mechanics and fatigue analysis of structures.

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Mamandi, A. Finite element based bending analysis of rectangular FGM plates using first-order shear deformation theory. J Mech Sci Technol 37, 2491–2506 (2023). https://doi.org/10.1007/s12206-023-0425-6

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  • DOI: https://doi.org/10.1007/s12206-023-0425-6

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