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Abstract
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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.
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Keywords
thin-walled beams, constrained
elasticity
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Milestones
Received: 26 May 2008
Accepted: 16 October 2008
Published: 12 April 2009
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