Vol. 5, No. 5, 2010

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ISSN: 1559-3959
A new modeling approach for planar beams: finite-element solutions based on mixed variational derivations

Ferdinando Auricchio, Giuseppe Balduzzi and Carlo Lovadina

Vol. 5 (2010), No. 5, 771–794
Abstract

This paper illustrates a new modeling approach for planar linear elastic beams. Referring to existing models, we first introduce the variational principles that could be adopted for the beam model derivation, discussing their relative advantages and disadvantages. Then, starting from the Hellinger–Reissner functional we derive some homogeneous and multilayered beam models, discussing some properties of their analytical solutions. Finally, we develop a planar beam finite element, following an innovative approach that could be seen as the imposition of equilibrium in the cross-section and compatibility along the axis. The homogeneous model is capable of reproducing the behavior of the Timoshenko beam, with the advantage that the shear correction factor appears naturally from the variational derivation; the multilayered beam is capable of capturing the local effects produced by boundary constraints and load distributions; the finite element is capable of predicting the cross-section stress distribution with high accuracy, and more generally the behavior of planar structural elements.

Keywords
laminated linear elastic beam, analytical solution, finite element modeling, mixed variational formulation
Milestones
Received: 3 December 2009
Revised: 1 June 2010
Accepted: 16 June 2010
Published: 3 December 2010
Authors
Ferdinando Auricchio
Dipartimento di Meccanica Strutturale
Università degli Studi di Pavia
Via Ferrata 1
27100 Pavia
Italy
http://www.unipv.it/auricchio/
Giuseppe Balduzzi
Dipartimento di Meccanica Strutturale / Dipartimento di Matematica
Università degli Studi di Pavia
Via Ferrata 1
27100 Pavia
Italy
http://www-2.unipv.it/compmech/members/giuseppebalduzzi.html
Carlo Lovadina
Dipartimento di Matematica
Università degli Studi di Pavia
Via Ferrata 1
27100 Pavia
Italy
http://www-dimat.unipv.it/lovadina/