It seems complex collision and physics are mutually exclusive, as indicated by JamesG in (How to fix static mesh falling through floor? - World Creation - Unreal Engine Forums). According to him it is a design decision.
But what if I would want complex collision and physics? As a matter of fact, I am not using the engine for games, but misusing it for simulation. Is there a workaround to enable physics for complex collision objects?
“Complex collision” is called “triangle mesh” in PhysX and it’s not supported to be used in simulation. It’s allowed to be used only as kinematic body, preferable static one, for performance optimization reasons. So there is no workaround with triangle meshes, besides integrating different physics middleware which supports them.
But you can use multiple convex meshes (Convex Decomposition) as collision for your object to support physics simulation with it. UE4 has a build in tool too generate such convex meshes (although you don’t have much control over it). Normally you would make such convex meshes in a modelling package of your choice and import them together with visual mesh.