Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (11): 1441-1448.doi: https://doi.org/10.1007/s10483-015-1994-7

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Mathematical and numerical modelling of large creep deformations for annular rotating disks

K. SZUWALSKI, A. USTRZYCKA   

  1. Faculty of Mechanical Engineering, Institute of Applied Mechanics, Cracow University of Technology, Cracow 31-864, Poland
  • 收稿日期:2014-11-13 修回日期:2015-05-22 出版日期:2015-11-01 发布日期:2015-11-01
  • 通讯作者: A. USTRZYCKA E-mail:anetaustrzycka@mech.pk.edu.pl

Mathematical and numerical modelling of large creep deformations for annular rotating disks

K. SZUWALSKI, A. USTRZYCKA   

  1. Faculty of Mechanical Engineering, Institute of Applied Mechanics, Cracow University of Technology, Cracow 31-864, Poland
  • Received:2014-11-13 Revised:2015-05-22 Online:2015-11-01 Published:2015-11-01
  • Contact: A. USTRZYCKA E-mail:anetaustrzycka@mech.pk.edu.pl

摘要: A simulation model is presented for the creep process of the rotating disks under the radial pressure in the presence of body forces. The finite strain theory is applied. The material is described by the Norton-Bailey law generalized for true stresses and logarithmic strains. A mathematical model is formulated in the form of a set of four partial differential equations with respect to the radial coordinate and time. Necessary initial and boundary conditions are also given. To make the model complete, a numerical procedure is proposed. The given example shows the effectiveness of this procedure. The results show that the classical finite element method cannot be used here because both the geometry and the loading (body forces) change with the time in the creep process, and the finite elements need to be redefined at each time step.

关键词: creep process, finite strain theory, simulation model, rotating disk

Abstract: A simulation model is presented for the creep process of the rotating disks under the radial pressure in the presence of body forces. The finite strain theory is applied. The material is described by the Norton-Bailey law generalized for true stresses and logarithmic strains. A mathematical model is formulated in the form of a set of four partial differential equations with respect to the radial coordinate and time. Necessary initial and boundary conditions are also given. To make the model complete, a numerical procedure is proposed. The given example shows the effectiveness of this procedure. The results show that the classical finite element method cannot be used here because both the geometry and the loading (body forces) change with the time in the creep process, and the finite elements need to be redefined at each time step.

Key words: simulation model, rotating disk, finite strain theory, creep process

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