Inserted: 9 feb 2001
Last Updated: 12 dec 2002
Journal: J. Elasticity
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