Linear Models of a Stiffened Plate via Gamma-Convergence

We consider a family of three-dimensional stiffened plates whose dimensions are scaled through different powers of a small parameter epsilon. The plate and the stiffener are assumed to be linearly elastic, isotropic, and homogeneous. By means of Gamma-convergence, we study the asymptotic behavior of the three-dimensional problems as the parameter e tends to zero. For different relative values of the powers of the parameter epsilon, we show how the interplay between the plate and the stiffener affects the limit energy. We derive twenty-three limit problems.