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Strain gradient effects on the thermoelastic analysis of a functionally graded micro-rotating cylinder using generalized differential quadrature method

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Abstract

In this paper, a strain gradient elasticity formulation for capturing the size effect in micro-scaled structures is presented to analyze the thermoelastic response of a functionally graded micro-rotating cylinder. The temperature distribution in the micro-rotating cylinder is analytically obtained by solving the steady-state, one-dimensional and axisymmetric Fourier heat conduction equation. For a functionally graded micro-rotating cylinder, except Poisson’s ratio, all mechanical and thermal properties such as elastic modulus, density and thermal expansion coefficient are assumed to vary through the thickness according to a power-law distribution. The thermomechanical governing differential equation is obtained as a fourth-order ordinary differential equation in terms of mechanical displacement. The generalized differential quadrature method is used for the solution of thermal stresses, strains and displacement in the micro-rotating cylinder under internal and external pressure. At first, numerical results are presented for the micro-rotating cylinder to validate the generalized differential quadrature method. Then, the results obtained from the strain gradient elasticity are compared to the classical elasticity solution. Furthermore, numerical results illustrate the effects of non-homogeneity constant, thermal field and rotation on the distribution of Von Mises stress, Von Mises strain and radial displacement. It is perceived that the mentioned parameters have considerable effects on the distribution of stress, strain and displacement.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, 78137-33385, Islamic Republic of Iran

    Mohammad Hosseini

  2. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, 91775-1111, Islamic Republic of Iran

    Ali Dini

  3. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, 76169-14111, Islamic Republic of Iran

    Mojtaba Eftekhari

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  1. Mohammad Hosseini
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  2. Ali Dini
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  3. Mojtaba Eftekhari
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Correspondence to Mohammad Hosseini.

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Hosseini, M., Dini, A. & Eftekhari, M. Strain gradient effects on the thermoelastic analysis of a functionally graded micro-rotating cylinder using generalized differential quadrature method. Acta Mech 228, 1563–1580 (2017). https://doi.org/10.1007/s00707-016-1780-5

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  • DOI: https://doi.org/10.1007/s00707-016-1780-5

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