Numerical analysis of static and dynamic stabilities of viscoelastic columns

• Published in: Mathematical methods in the applied sciences Vol. 39; no. 14; pp. 3932 - 3946
• Main Authors: Haitian, Yang, Zhi, Han, Yiqian, He
• Format: Journal Article
• Language: English
• Published: Freiburg Blackwell Publishing Ltd 30.09.2016; Wiley Subscription Services, Inc
• Subjects: adaptive algorithm; column; Descriptions; Dynamic stability; Dynamical systems; Exact solutions; Mathematical analysis; Mathematical models; Static stability; static/dynamic stability; Viscoelasticity
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.3786

This paper presents a new numerical approach for the static and dynamic stabilities analysis of viscoelastic columns. By expanding all variables in a discretized time interval, a time and space coupled integral‐differential equation system is converted into a series of recursive spatial problems that are solved via FEM. A temporally piecewised adaptive algorithm is developed to maintain computing accuracy. Consequently, the descriptions of static stability of imperfect viscoelastic columns and dynamic stability of perfect viscoelastic columns are realized, respectively. Numerical examples are presented to verify the proposed approach. Additionally, two analytical expressions are derived for the dynamic stability analysis of linear and Burgers models, respectively. Copyright © 2016 John Wiley & Sons, Ltd.