比能

$$\begin{aligned} U_1 &= \frac{1}{2}(\sigma_x \varepsilon_x + \sigma_y \varepsilon_y + \tau_{xy} \gamma_{xy}) \\ &= \frac{E}{2(1-\mu^2)}\left[\varepsilon_x^2 + \varepsilon_y^2 + 2\mu\varepsilon_x \varepsilon_y + \frac{1-\mu}{2}\gamma_{xy}^2 \right] \\ &= \frac{E}{2(1-\mu^2)} \end{aligned}$$

位移变分方程

$$\begin{aligned} \delta U &= \iint_A(\sigma_x \delta\varepsilon_x + \sigma_y \delta\varepsilon_y + \tau_{xy}\delta\gamma_{xy}) dxdy \\ &= \iint_A(f_x \delta u + f_y \delta v)dxdy + \int_{s_{\sigma}}(\overline{f}_x \delta u + \overline{f}_y \delta v) ds \end{aligned}$$