Exact microstructure-dependent Timoshenko beam element

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2016-06-01
Major/Subject
Mcode
Degree programme
Language
en
Pages
8
35-42
Series
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, Volume 111-112
Abstract
In this study, we develop an exact microstructure-dependent Timoshenko beam finite element. First, a Timoshenko beam model based on the modified couple-stress theory is reviewed briefly. The general closed-form solution to the equilibrium equations of the beam is derived. The two-dimensional in-plane stress distributions along the beam in terms of load resultants are obtained. In addition, the general solution can be used to model any distributed load which can be expressed as a Maclaurin series. Then, the solution is presented in terms of discrete finite element (FE) degrees of freedom. This representation yields the exact shape functions for the beam element. Finally, the exact beam finite element equations are obtained by writing the generalized forces at the beam ends using the FE degrees of freedom. Three calculation examples which have applications in micron systems and sandwich structures are presented.
Description
Keywords
Beam finite element, Couple-stress, General solution, Microstructure, Timoshenko beam
Other note
Citation
Karttunen , A T , Romanoff , J & Reddy , J N 2016 , ' Exact microstructure-dependent Timoshenko beam element ' , International Journal of Mechanical Sciences , vol. 111-112 , pp. 35-42 . https://doi.org/10.1016/j.ijmecsci.2016.03.023