Exact microstructure-dependent Timoshenko beam element Academic Article

abstract

• 2016 Elsevier Ltd. All rights reserved. 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.

authors

• Reddy, Junuthula

published proceedings

• INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES

author list (cited authors)

• Karttunen, A. T., Romanoff, J., & Reddy, J. N.

citation count

• 25

complete list of authors

• Karttunen, Anssi T||Romanoff, Jani||Reddy, JN

publication date

• June 2016

publisher

• Elsevier  Publisher

published in

• International Journal of Mechanical Sciences  Journal

keywords

• Beam Finite Element
• Couple-stress
• General Solution
• Microstructure
• Timoshenko Beam

Digital Object Identifier (DOI)

• 10.1016/j.ijmecsci.2016.03.023

start page

• 35

end page

• 42

volume

• 111

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.ijmecsci.2016.03.023