11.6 Deformable body

11.6.1 Principle of Virtual Work for Deformable Bodies

\[\begin{equation*} \delta W = \delta W_e + \delta W_i = 0 \end{equation*}\]

  • Where:
    • \(\delta W_i =\) virtual work of internal forces
      • \(\delta W_i = - \displaystyle\int_V {\left[\displaystyle\sum_i \displaystyle\sum_j {\sigma_{ij}}\cdot \delta {\varepsilon_{ij}}\right]\;} dV\)
      • \(i,j = x,y,z\)
    • \(\delta W_e =\) virtual work of external forces, including body forces
  • Notes:
    • Reactions at restrained supports do not do work.
    • The principle is not limited to any constitutive equation.