Applied Mathematics and Mechanics

, Volume 40, Issue 4, pp 499–514 | Cite as

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

  • Jie Xu
  • Xuegang YuanEmail author
  • Hongwu Zhang
  • Zhentao Zhao
  • Wei Zhao


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.

Key words

incompressible thermo-hyperelastic cylinder fixed end axial load implicit analytical solution tensile instability 

Chinese Library Classification


2010 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Jie Xu
    • 1
  • Xuegang Yuan
    • 1
    • 2
    Email author
  • Hongwu Zhang
    • 1
  • Zhentao Zhao
    • 1
  • Wei Zhao
    • 2
  1. 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering MechanicsDalian University of TechnologyDalian, Liaoning ProvinceChina
  2. 2.School of ScienceDalian Minzu UniversityDalian, Liaoning ProvinceChina

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