How to model an orthotropic plate so that it would have a smaller stiffness in one direction than in another?

You can create the orthotropic 2D material, which would have a different Young's Modulus in X and Y direction (hence different stiffness in both directions). To do so, please go to Materials page, then in the Material table on the right bottom corner select Orthotropic 2D tab and click Create button. In the opened window provide the required information and then assign this material to the plates.