Vol. 4, No. 2, 2009

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ISSN: 1559-3959
Anisotropic thin-walled beam models: A rational deduction from three-dimensional elasticity

Franco Maceri and Giuseppe Vairo

Vol. 4 (2009), No. 2, 371–394
Abstract

In this paper anisotropic thin-walled beam models are rationally deduced from three-dimensional elasticity by means of a constrained approach. Consistent frictionless internal constraints on both stress and strain dual fields are enforced through a modified Hu–Washizu functional obtained by a nonstandard application of Lagrange multipliers. Beam theories accounting for different shear refinement levels are justified, showing that this variational approach enables the development of new refined models, including high-order nonconventional effects and enhancing standard treatments of shear deformation effects. In agreement with the constrained problem, a locally equilibrated approximation of the stress field acting on beam cross-section is recovered in closed form. Finally, cases of laminated thin-walled beams as well as of unilateral conewise constitutive behavior (with special reference to bimodular materials) are investigated.

Keywords
thin-walled beams, constrained elasticity
Milestones
Received: 26 May 2008
Accepted: 16 October 2008
Published: 12 April 2009
Authors
Franco Maceri
Università degli Studi di Roma “Tor Vergata”
Dipartimento di Ingegneria Civile
via del Politecnico 1
00133 Roma
Italy
Giuseppe Vairo
Università degli Studi di Roma “Tor Vergata”
Dipartimento di Ingegneria Civile
via del Politecnico 1
00133 Roma
Italy