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On an extended Kantorovich method for the mechanical behavior of functionally graded solid/annular sector plates with various boundary conditions

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Abstract

Based on the first-order shear deformation plate theory, two approaches within the extended Kantorovich method (EKM) are presented for a bending analysis of functionally graded annular sector plates with arbitrary boundary conditions subjected to both uniform and non-uniform loadings. In the first approach, EKM is applied to the functional of the problem, while in the second one EKM is applied to the weighted integral form of the governing differential equations of the problem as presented by Kerr. In both approaches, the system of ordinary differential equations with variable coefficients in r direction and the set of ordinary differential equations with constant coefficients in \(\theta \) direction are solved by the generalized differential quadrature method and the state space method, respectively. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified with the available published works in the literature. It is observed that the first approach is applicable to all supports with an excellent accuracy while the second approach does not give acceptable results for a plate with a free edge. Furthermore, various response quantities in FG annular sector plates with different boundary conditions, material constants, and sector angles are presented which can be used as a benchmark.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, P.O. Box 14588-89694, Tehran, Iran

    Famida Fallah & Ali Khakbaz

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  1. Famida Fallah
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  2. Ali Khakbaz
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Correspondence to Famida Fallah.

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Fallah, F., Khakbaz, A. On an extended Kantorovich method for the mechanical behavior of functionally graded solid/annular sector plates with various boundary conditions. Acta Mech 228, 2655–2674 (2017). https://doi.org/10.1007/s00707-017-1851-2

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  • DOI: https://doi.org/10.1007/s00707-017-1851-2

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