An example of double forces taken from structural analysis

Citations of this article
Mendeley users who have this article in their library.


The classic Bernoulli-Euler beam is revisited in relation to the Timoshenko beam, using a T-type cross-section. A practical example of double forces is worked out, where the double forces appear due to the shearing of the horizontal flange of the T-section. It is shown that a non-local estimate of the mean value of the vertical deflection of the beam leads to a shear gradient that is energetically consistent with the double force. Therefore, an additional energy term that includes the derivative of the beam's curvature leads to a consistent non-local beam model, simple enough to be used in structural analysis. Such beam models are useful in micro- and nano-technology. Moreover, this simple example opens the discussion for the importance of non-local differentiation in the averaging theories of Mechanics. © 2005 Elsevier Ltd. All rights reserved.




Vardoulakis, I., & Giannakopoulos, A. E. (2006). An example of double forces taken from structural analysis. International Journal of Solids and Structures, 43(14–15), 4047–4062.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free