I wanna ask a question that confuses me quite a long time. I saw many guys, in the context of computational mechanics, they seemed to choose the virtual functions or kinematics in a way that some kinematical quantities are kept/fixed zero, but they ask the remaining of them to act as roles during the derivation of a weak form equation. In the end, we can generally get a system of weak equations. I am all the time wondering whether we have a chance to change the nature of the original physical problem of a strong form. Who can shed lights on my doubts in a physcial or mathematical view?
Edit: Say, u=u1+u2+u3 for whatever reason. Its variation is delta u1+ delta u2 +delta u3. The weak form may be integral sigma(u): sym gradient(delta u1) =0, integral sigma(u): sym gradient(delta u2) =0, integral sigma(u): sym gradient(delta u3) =0.