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Numerical analysis of static and dynamic stabilities of viscoelastic columns
Author(s) -
Haitian Yang,
Zhi Han,
Yiqian He
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3786
Subject(s) - discretization , viscoelasticity , mathematics , stability (learning theory) , numerical analysis , finite element method , dynamic problem , numerical stability , imperfect , mathematical analysis , algorithm , computer science , structural engineering , linguistics , philosophy , physics , machine learning , engineering , thermodynamics
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.