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Solution of the Thermoelastic Problem for a Two-Dimensional Curved Beam with Bimodular Effects

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  • 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)

  • Meng-Qiao Zhang

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

  • Bo Pang

    (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)

Abstract

In classical thermoelasticity, the bimodular effect of materials is rarely considered. However, all materials will present, in essence, different properties in tension and compression, more or less. The bimodular effect is generally ignored only for simple analysis. In this study, we theoretically analyze a two-dimensional curved beam with a bimodular effect and under mechanical and thermal loads. We first establish a simplified model on a subarea in tension and compression. On the basis of this model, we adopt the Duhamel similarity theorem to change the initial thermoelastic problem as an elasticity problem without the thermal effect. The superposition of the special solution and supplement solution of the Lamé displacement equation enables us to satisfy the boundary conditions and stress continuity conditions of the bimodular curved beam, thus obtaining a two-dimensional thermoelastic solution. The results indicate that the solution obtained can reduce to bimodular curved beam problems without thermal loads and to the classical Golovin solution. In addition, the bimodular effect on thermal stresses is discussed under linear and non-linear temperature rise modes. Specially, when the compressive modulus is far greater than the tensile modulus, a large compressive stress will occur at the inner edge of the curved beam, which should be paid with more attention in the design of the curved beams in a thermal environment.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:3002-:d:892858
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    References listed on IDEAS

    as
    1. 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.
    2. Ahmed E. Abouelregal & Marin Marin, 2020. "The Size-Dependent Thermoelastic Vibrations of Nanobeams Subjected to Harmonic Excitation and Rectified Sine Wave Heating," Mathematics, MDPI, vol. 8(7), pages 1-13, July.
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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. Mohamed A. Attia & Ammar Melaibari & Rabab A. Shanab & Mohamed A. Eltaher, 2022. "Dynamic Analysis of Sigmoid Bidirectional FG Microbeams under Moving Load and Thermal Load: Analytical Laplace Solution," Mathematics, MDPI, vol. 10(24), pages 1-22, December.

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