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Consider a body with displacement $(u,v,w)$, where $w$ is assumed to satisfy $w=w(x,y)$ (that is, the vertical displacement does not vary along the $z$ axis).

Why exactly should the virtual displacements $(\delta u, \delta v, \delta w)$ in the principle of virtual work also satisfy $\delta w=\delta w(x,y)$?

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  • $\begingroup$ What are $x$ and $y$ ? $\endgroup$
    – AJN
    Aug 31, 2023 at 11:15
  • $\begingroup$ @AJN Euclidean coordinates of the point whose displacement we are evaluating. $\endgroup$
    – Lilla
    Aug 31, 2023 at 12:08

1 Answer 1

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The virtual displacements should be such that they obey the kinematic constraints. In this case, you are constraining the $z$ displacement to not vary with $z$ coordinate, and the same would be followed by the virtual displacements.

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  • $\begingroup$ What's the motivation behind this? $\endgroup$
    – Lilla
    Aug 31, 2023 at 23:46
  • $\begingroup$ You mean motivation behind the virtual displacements having to follow kinematic boundary conditions? To understand this, one has to understand the need to introduce virtual displacements. Virtual displacements are a way of providing a 'test' displacement field, and an energy minimisation then tells which of the infinite possible virtual displacements gives equilibrium. Since virtual displacements are test candidates for the actual displacement field, they have to obey the characteristics of the actual displacement field, i.e boundary conditions and other constraints $\endgroup$
    – aaquib
    Sep 1, 2023 at 0:59

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