A Hierarchy of Approximated solutions in a Linear Elasticity Equibrium Problem

Here a problem in the framework of Linear Elasticity Theory is considered. Specifically, a plate equilibrium problem is studied, under the assumption that the displacement field can be represented in a suitable form to take into account the geometry which characterizes the body termed ``plate''. The exact equilibrium problem is written together with a hierarchy of approximate ones; the corresponding hierarchy of solutions is considered. Subsequently, the introduction of an appropriate ``energy'' norm (related to the elastic energy) allows to evaluate the energy distance between two successive approximate solutions. A convergence result is also shown in connection to the constructed hierarchy of approximate solutions.