D&D 5E Divine Smite and grappling, shoving, and knocking prone

[Greenstone.Walker]

Grappling, shoving and knocking prone are all attacks. They just don't happen to include an attack roll. For example, they count for keeping Barbarian Rage going.

So, can a Paladin use Divine Smite to cause some damage with these attacks?

 

[Tormyr]

No, Divine Smite says you have to hit with a melee weapon attack.