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One- and Two-Dimensional Analytical Solutions of Thermal Stress for Bimodular Functionally Graded Beams under Arbitrary Temperature Rise Modes

Author

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  • Xuan-Yi Xue

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China)

  • Si-Rui Wen

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China)

  • Jun-Yi Sun

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China
    Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China)

  • Xiao-Ting He

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China
    Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China)

Abstract

In this study, we analytically solved the thermal stress problem of a bimodular functionally graded bending beam under arbitrary temperature rise modes. First, based on the strain suppression method in a one-dimensional case, we obtained the thermal stress of a bimodular functionally graded beam subjected to bending moment under arbitrary temperature rise modes. Using the stress function method based on compatibility conditions, we also derived two-dimensional thermoelasticity solutions for the same problem under pure bending and lateral-force bending, respectively. During the solving, the number of unknown integration constants is doubled due to the introduction of bimodular effect; thus, the determination for these constants depends not only on the boundary conditions, but also on the continuity conditions at the neutral layer. The comparisons indicate that the one- and two-dimensional thermal stress solutions are consistent in essence, with a slight difference in the axial stress, which exactly reflects the distinctions of one- and two-dimensional problems. In addition, the temperature rise modes in this study are not explicitly indicated, which further expands the applicability of the solutions obtained. The originality of this work is that the one- and two-dimensional thermal stress solutions for bimodular functionally graded beams are derived for the first time. The results obtained in this study may serve as a theoretical reference for the analysis and design of beam-like structures with obvious bimodular functionally graded properties in a thermal environment.

Suggested Citation

  • Xuan-Yi Xue & Si-Rui Wen & Jun-Yi Sun & Xiao-Ting He, 2022. "One- and Two-Dimensional Analytical Solutions of Thermal Stress for Bimodular Functionally Graded Beams under Arbitrary Temperature Rise Modes," Mathematics, MDPI, vol. 10(10), pages 1-22, May.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1756-:d:820660
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    References listed on IDEAS

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    1. Fengkai Gao & Dongmin Yu & Qiang Sheng, 2022. "Analytical Treatment of Unsteady Fluid Flow of Nonhomogeneous Nanofluids among Two Infinite Parallel Surfaces: Collocation Method-Based Study," Mathematics, MDPI, vol. 10(9), pages 1-13, May.
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    Cited by:

    1. Yi-Lun Liao & Shao-Chen Tseng & Ching-Kong Chao, 2023. "Interfacial Stresses for a Coated Irregularly Shaped Hole Embedded in an Infinite Solid under Point Heat Singularity," Mathematics, MDPI, vol. 11(4), pages 1-20, February.
    2. Xiao-Ting He & Xiao-Guang Wang & Bo Pang & Jie-Chuan Ai & Jun-Yi Sun, 2023. "Variational Solution and Numerical Simulation of Bimodular Functionally Graded Thin Circular Plates under Large Deformation," Mathematics, MDPI, vol. 11(14), pages 1-23, July.
    3. Xiao-Ting He & Meng-Qiao Zhang & Bo Pang & Jun-Yi Sun, 2022. "Solution of the Thermoelastic Problem for a Two-Dimensional Curved Beam with Bimodular Effects," Mathematics, MDPI, vol. 10(16), pages 1-22, August.

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