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The mixed finite element method for the quasi‐static and dynamic analysis of viscoelastic timoshenko beams
Author(s) -
Aköz Yalçin,
Kadioǧlu Fethi
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990430)44:12<1909::aid-nme573>3.0.co;2-p
Subject(s) - viscoelasticity , laplace transform , finite element method , timoshenko beam theory , inverse laplace transform , mathematical analysis , mathematics , fourier transform , structural engineering , materials science , engineering , composite material
The quasi‐static and dynamic responses of a linear viscoelastic Timoshenko beam on Winkler foundation are studied numerically by using the hybrid Laplace–Carson and finite element method. In this analysis the field equation for viscoelastic material is used. In the transformed Laplace–Carson space two new functionals have been constructed for viscoelastic Timoshenko beams through a systematic procedure based on the Gâteaux differential. These functionals have six and two independent variables respectively. Two mixed finite element formulations are obtained; TB12 and TB4. For the inverse transform Schapery and Fourier methods are used. The numerical results for quasi‐static and dynamic responses of several visco‐elastic models are presented. Copyright © 1999 John Wiley & Sons, Ltd.