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Thermoelasticity theory and the decomposed form of thick plates for extensional deformation

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Abstract

Without employing ad hoc stress assumptions, the decomposed form of thermoelastic plates for an extensional deformation is proposed on the basis of thermoelasticity theory, and the corresponding decomposition theorem is in extenso presented for the first time. It is shown that the stress state of thermoelastic plates with traction free faces can be uniquely decomposed into four parts: the plane-stress (P-S) state, the shear state, the Papkovich-Fadle (P-F) state, and the thermal state. In the proof course of the decomposition theorem, some basic mathematical methods are used only, so the proof is more convenient for being understood. Due to the corresponding relations of the P-S state and the biharmonic equation, of the shear state and the shear equation, and of the P-F state and the transcendental equation, this work practically proves the equivalence between the decomposition theorem and the refined theory of isothermal plates with free faces. More importantly, the thermal state is in agreement with the Solution P.

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Authors and Affiliations

  1. College of Science, China Agricultural University, P.O. Box 74, Beijing, 100083, People’s Republic of China

    Yang Gao

  2. School of Mechanical Engineering, University of Science and Technology Liaoning, Anshan, 114044, People’s Republic of China

    Bao-Sheng Zhao

  3. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering, Peking University, Beijing, 100871, People’s Republic of China

    Min-Zhong Wang

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  1. Yang Gao
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  2. Bao-Sheng Zhao
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  3. Min-Zhong Wang
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Correspondence to Yang Gao.

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Gao, Y., Zhao, BS. & Wang, MZ. Thermoelasticity theory and the decomposed form of thick plates for extensional deformation. Acta Mech 223, 755–764 (2012). https://doi.org/10.1007/s00707-011-0589-5

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  • DOI: https://doi.org/10.1007/s00707-011-0589-5

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