Use plain old FEA? Never! Instead you should use isogeometric analysis because it's needlessly more complex by using B-splines for everything! :)

Sometimes I think mathematicians get bored of easy solutions so they invent much harder solutions.

Hey neat! I didn't know about isogeometric analysis. Dunno if I'll ever actually use it but it looks like fun reading. 

Maybe mathematicians use different definitions of "easy" and "hard".  

It's only useful if you are using NURBS to define your structure. NURBS were once seen as the possible path toward better 3d objects because they are based on trigonometric functions and therefore have infinite precision. However, NURBS has mostly fallen by the wayside due to the computational complexity of doing basic things like collision detection. The infinite precision of NURBS may be great in niche situations where computational power is not a factor but it's mostly a dead technology.