Title: A new modeling approach for planar beams: finite-element solutions based on mixed variational derivations
Language: English
Authors: Auricchio, Ferdinando
Balduzzi, Giuseppe
Lovadina, Carlo
Category: Research Article
Keywords: laminated linear elastic beam; analytical solution; finite element modeling; mixed variational formulation
Issue Date: 2010
Journal: Journal of Mechanic of Materials and Structures
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.
DOI: 10.2140/jomms.2010.5.771
Library ID: AC11362461
URN: urn:nbn:at:at-ubtuw:3-2995
ISSN: 1559-3959
Organisation: E202 - Institut für Mechanik der Werkstoffe und Strukturen 
Publication Type: Article
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