What Is the Principle of Virtual Work? 仮想仕事の原理とは？

When I first encountered the principle of virtual work, I remember being confused—as if I were listening to a Zen riddle—and wondering what practical meaning it held. In contrast, the principle of stationary total potential energy seemed much more intuitive.
If we express the total potential energy Π as the difference between the elastic strain energy U and the work done by external forces W:

   Π = U – W

then the condition for stationarity, given by the first variation of Π, becomes:

   δΠ = δ(U – W) = 0
   ∴ δU = δW

This results in an expression that appears to be exactly the same as the principle of virtual work.
So why isn’t this explanation sufficient? I feel that very few textbooks provide a proper discussion of this question.Even in the nonlinear case, we still linearize it locally.

仮想仕事の原理をはじめて学んだ時，何だか禅問答を聞いているようでこれに何の意味があるのか困惑した覚えがある。一方，全ポテンシャルエネルギー停留の原理は分かりやすい。全ポテンシャルエネルギーΠを弾性歪みエネルギーUと外力仕事Wを用いて

   Π = U – W

と表すと，Πの停留条件である第１変分が0ということは，

   δΠ = δ(U – W) = 0
   ∴ δU = δW

となって，これは仮想仕事の原理と見た目上は全く同じ式になる。何でこの説明じゃだめなのか，ちゃんと解説している教科書はあまりない気がする。非線形の場合も，近傍で線形化するわけだし。