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Application of Ritz method to large amplitude rapid surface heating of FGM shallow arches

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Abstract

In this article, thermally induced vibrations of shallow functionally graded material arches is considered and analyzed. The arch is subjected to sudden thermal loading on one surface while the other surface is kept at a constant temperature. Based on the uncoupled thermoelasticity assumptions, the one-dimensional heat conduction equation is established and numerically solved using the finite difference method and Crank–Nicolson marching scheme. The classical theory of curved beams is used to drive the equations of motion, where the curvature of the beam is assumed to be constant. The strain–displacement relationships are based on the von Kármán nonlinear theory based on the shallow arch theory of Donnell. The governing equations are obtained based on the Hamilton principle and converted to a set of nonlinear algebraic equations via the polynomial Ritz method. The obtained equations are nonlinear and solved using the \(\beta \)-Newmark time marching scheme and the Newton–Raphson method. Comparison of the numerical results is done with other existing results for the case of isotropic homogeneous shallow arches where well agreement is obtained. The effects of different parameters on the numerical results are presented and provided in graphical presentations.

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Authors and Affiliations

  1. Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran

    M. M. Khalili, A. Keibolahi & M. R. Eslami

  2. Faculty of Engineering, Shahrekord University, Shahrekord, Iran

    Y. Kiani

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  1. M. M. Khalili
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  2. A. Keibolahi
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  3. Y. Kiani
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Correspondence to Y. Kiani.

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Khalili, M.M., Keibolahi, A., Kiani, Y. et al. Application of Ritz method to large amplitude rapid surface heating of FGM shallow arches. Arch Appl Mech 92, 1287–1301 (2022). https://doi.org/10.1007/s00419-022-02106-4

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