In this paper, a new theoretical framework is presented for modeling non-locality in shear deformable beams. The driving idea is to represent non-local effects as long-range volume forces and moments, exchanged by non-adjacent beam segments as a result of their relative motion described in terms of pure deformation modes of the beam. The use of these generalized measures of relative motion allows constructing an equivalent mechanical model of non-local effects. Specifically, long-range volume forces and moments are associated with three spring-like connections acting in parallel between couples of non-adjacent beam segments, and separately accounting for pure axial, pure bending and pure shear deformation modes. The variational consistency of the proposed non-local beam model is demonstrated by minimization of an appropriate total potential energy functional. Numerical results concerning the static behavior for different boundary and loading conditions are presented. It is shown that the proposed non-local beam model is able to capture experimental data on the static deflection of micro-beams, available in the literature.

Failla, G., Sofi, A., Zingales, M. (2015). A new displacement-based framework for non-local Timoshenko beams. MECCANICA, 50(8), 2103-2122 [10.1007/s11012-015-0141-0].

A new displacement-based framework for non-local Timoshenko beams

ZINGALES, Massimiliano
2015-01-01

Abstract

In this paper, a new theoretical framework is presented for modeling non-locality in shear deformable beams. The driving idea is to represent non-local effects as long-range volume forces and moments, exchanged by non-adjacent beam segments as a result of their relative motion described in terms of pure deformation modes of the beam. The use of these generalized measures of relative motion allows constructing an equivalent mechanical model of non-local effects. Specifically, long-range volume forces and moments are associated with three spring-like connections acting in parallel between couples of non-adjacent beam segments, and separately accounting for pure axial, pure bending and pure shear deformation modes. The variational consistency of the proposed non-local beam model is demonstrated by minimization of an appropriate total potential energy functional. Numerical results concerning the static behavior for different boundary and loading conditions are presented. It is shown that the proposed non-local beam model is able to capture experimental data on the static deflection of micro-beams, available in the literature.
2015
Failla, G., Sofi, A., Zingales, M. (2015). A new displacement-based framework for non-local Timoshenko beams. MECCANICA, 50(8), 2103-2122 [10.1007/s11012-015-0141-0].
File in questo prodotto:
File Dimensione Formato  
meccanica2015.pdf

accesso aperto

Dimensione 1.29 MB
Formato Adobe PDF
1.29 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/215527
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 7
social impact