  For two different scenarios regarding thin elastic structures, described by
2d-F\"oppl-von K\'arm\'an plate models, we obtain energy scaling laws. Firstly,
assuming the reference geometry being that of a singular excess-cone, we obtain
fairly optimal upper- and lower energy bounds and we highlight how those bounds
scale wrt. the thickness-parameter $h.$ Secondly, we consider the half sphere,
while being indented by a thin object at the top and perpendicular to its
surface. In this situation we provide an energy-scaling law, for radial
symmetric admissible maps, this time, depending on $h$ and the indentation
depth $d.$
