Homogenized behaviour of a beam with a multicellular cross section

Abstract

In this work we study the homogenized behaviour of a linearly elastic beam, with a multicellular cross section. Making use of homogenization techniques we give the limit behaviour of all the functions and constants showing up in a generalization of Saint Venant's and Timoshenko's beam theories obtained in Trabucho-Vianõ^1,2 via the asymptotic expansion method. In particular the warping and torsion problems are studied. We indicate the relationship between coefficients of the so obtained limit problems and those of the homogenized three dimensional elasticity model. We consider the homogenized behaviour of the shear and inplane stress fields taking into account the deformation of the cross section on its own plane

Keywords:

• Homogenization
• elasticity
• beams
• multicellular

AMS (MOS)::

• 73C40
• 73K05