Considering the following integral
$$ \delta U = \frac{1}{2}\int_{\Omega} \sigma_{ij}\left( \delta \frac{\partial u_i}{\partial x_j} + \delta \frac{\partial u_j}{\partial x_i} \right) \text{d}\Omega \tag{1}$$
According to the book (Mechanical Vibrations - Michel Géradin and Daniel J. Rixen) that I'm reading, applying the Divergence Theorem on (1) yields
$$ \delta U = \int_{\Gamma} n_j \sigma_{ij} \delta u_i\ \text{d}\Gamma - \int_{\Omega}\left(\frac{\partial \sigma_{ij}}{\partial x_j}\delta u_i \right) \text{d}\Omega \tag{2} $$
I cannot get it by applying the Divergente Theorem, as the authors said in the book.
Does someone know how I get (2) by applying Divergence Theorem on (1)?
NOTES
- $\sigma_{ij}$ is a symmetric tensor;
- $\delta$ is the variation from Calculus of Variations;
- $\Gamma$ is the boundary surface of $\Omega$.