Calculus of Variations and Geometric Measure Theory

E. Cabib - L. Freddi - A. Morassi - D. Percivale

Thin Notched Beams

created on 09 Feb 2001
modified on 12 Dec 2002


Published Paper

Inserted: 9 feb 2001
Last Updated: 12 dec 2002

Journal: J. Elasticity
Volume: 64
Pages: 157-178
Year: 2001


The three-dimensional elasticity energy for a notched rod under axial loads is shown to converge in a variational sense to a class of one-dimensional models with a localized compliance when the beam becomes very slender and when the ratio between the depth and the width of each notch vanishes in a suitable way. Also the case of notched thermal conductors is considered, in a parallel treatment, because it falls in a similar but simpler framework.

Keywords: dimension reduction, elasticity, variational convergence