Calculus of Variations and Geometric Measure Theory

L. Della Longa - A. Londero

Thin walled beams with residual stress

created by freddi on 10 Jan 2008
modified on 16 Mar 2009


Accepted Paper

Inserted: 10 jan 2008
Last Updated: 16 mar 2009

Journal: Journal of Elasticity
Year: 2009


We present an asymptotic analysis of the three-dimensional problem for a thinwalled beam with rectangular cross section of side $\varepsilon$ and $\varepsilon^2$ for an anisotropic, inhomogeneous along the longitudinal axis, material with residual stress. We show that in the limit model bending, twisting and extensional problems are coupled. We also obtain the equations of equilibrium under the least symmetry group which uncouple them.

Keywords: $\Gamma$-convergence, dimension reduction, thin walled beams, residual stress