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Combined effects of axial load and temperature on finite deformation of incompressible thermo-hyperelastic cylinder

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Abstract

A finite deformation problem is examined for a cylinder composed of a class of incompressible thermo-hyperelastic Mooney-Rivlin materials under an equal axial load at its two fixed ends and a temperature field at its lateral boundary. Firstly, a thermo-mechanical coupling term is taken into account in the strain energy density function, and a governing equation of the problem is obtained. Secondly, an implicit analytical solution is derived by using the incompressibility and the boundary conditions. Significantly, numerical examples show that the middle portion of the cylinder undergoes almost a uniform radial deformation. However, the deformation near the two ends varies remarkably along the axial direction for relatively large axial loads. In addition, the rising temperature can increase the deformation of structures, and its influence is linear approximately. Specially, in the case of tensile load, the jump increase of the axial deformation may occur.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning Province, 116024, China

    Jie Xu, Xuegang Yuan, Hongwu Zhang & Zhentao Zhao

  2. School of Science, Dalian Minzu University, Dalian, Liaoning Province, 116600, China

    Xuegang Yuan & Wei Zhao

Authors
  1. Jie Xu
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  2. Xuegang Yuan
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  3. Hongwu Zhang
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  4. Zhentao Zhao
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  5. Wei Zhao
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Correspondence to Xuegang Yuan.

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Citation: XU, J., YUAN, X. G., ZHANG, H. W., ZHAO, Z. T., and ZHAO, W. Combined effects of axial load and temperature on finite deformation of incompressible thermo-hyperelastic cylinder. Applied Mathematics and Mechanics (English Edition), 40(4), 499–514 (2019) https://doi.org/10.1007/s10483-019-2466-8

Project supported by the National Natural Science Foundation of China (Nos. 11672069, 11702059, 11232003, and 11672062), the Ph.D Programs Foundation of Ministry of Education of China (No. 20130041110050), the Natural Science Foundation of Liaoning Province of China (Nos. 20170540199 and 2014020137), and the Programme of Introducing Talents of Discipline to Universities (No. B08014)

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Xu, J., Yuan, X., Zhang, H. et al. Combined effects of axial load and temperature on finite deformation of incompressible thermo-hyperelastic cylinder. Appl. Math. Mech.-Engl. Ed. 40, 499–514 (2019). https://doi.org/10.1007/s10483-019-2466-8

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  • DOI: https://doi.org/10.1007/s10483-019-2466-8

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