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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.

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  • $\begingroup$ Ps: We can do whatever we want with maths. However, sometimes I almost lose the physical insights . $\endgroup$ Jan 2, 2018 at 12:14
  • $\begingroup$ Not sure what you're asking. Are you asking 'why do we use weak formulations'? Or 'Why do we need virtual functions'? $\endgroup$ Jan 2, 2018 at 14:30
  • $\begingroup$ Neither.For example, u=u1+u2. When formulating the weak form, one can set delta u1=0, but delta u2 arbitrarily, where delta means variation operation. $\endgroup$ Jan 2, 2018 at 14:34
  • $\begingroup$ Your clarification seems more confusing to me :S $\endgroup$
    – nicoguaro
    Jan 2, 2018 at 14:43
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    $\begingroup$ Or is it d'Alemberts principle of virtual work you're talking about here? I think this is really more a physics question then.. $\endgroup$ Jan 2, 2018 at 14:45

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