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 $varepsilon$. 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 $varepsilon$ tends to zero. For different relative values of the powers of the parameter $varepsilon$, we show how the interplay between the plate and the stiffener affects the limit energy. We derive twenty-three limit problems.