ひずみ
2 ∂ 2 ε 12 ∂ x 1 ∂ x 2 − ∂ 2 ε 11 ∂ x 2 2 − ∂ 2 ε 22 ∂ x 1 2 = 0 2 ∂ 2 ε 23 ∂ x 1 ∂ x 2 − ∂ 2 ε 22 ∂ x 3 2 − ∂ 2 ε 33 ∂ x 2 2 = 0 2 ∂ 2 ε 31 ∂ x 1 ∂ x 2 − ∂ 2 ε 33 ∂ x 1 2 − ∂ 2 ε 11 ∂ x 3 2 = 0 ∂ ∂ x 1 ( − ∂ ε 23 ∂ x 1 + ∂ ε 31 ∂ x 2 + ∂ ε 12 ∂ x 3 ) − ∂ 2 ε 11 ∂ x 2 ∂ x 3 = 0 ∂ ∂ x 2 ( ∂ ε 23 ∂ x 1 − ∂ ε 31 ∂ x 2 + ∂ ε 12 ∂ x 3 ) − ∂ 2 ε 22 ∂ x 3 ∂ x 1 = 0 ∂ ∂ x 3 ( ∂ ε 23 ∂ x 1 + ∂ ε 31 ∂ x 2 − ∂ ε 12 ∂ x 3 ) − ∂ 2 ε 33 ∂ x 1 ∂ x 2 = 0 {\displaystyle {\begin{aligned}&2{\frac {\partial ^{2}\epsilon _{12}}{\partial x_{1}\partial x_{2}}}-{\frac {\partial ^{2}\epsilon _{11}}{\partial x_{2}^{2}}}-{\frac {\partial ^{2}\epsilon _{22}}{\partial x_{1}^{2}}}=0\\&2{\frac {\partial ^{2}\epsilon _{23}}{\partial x_{1}\partial x_{2}}}-{\frac {\partial ^{2}\epsilon _{22}}{\partial x_{3}^{2}}}-{\frac {\partial ^{2}\epsilon _{33}}{\partial x_{2}^{2}}}=0\\&2{\frac {\partial ^{2}\epsilon _{31}}{\partial x_{1}\partial x_{2}}}-{\frac {\partial ^{2}\epsilon _{33}}{\partial x_{1}^{2}}}-{\frac {\partial ^{2}\epsilon _{11}}{\partial x_{3}^{2}}}=0\\&{\frac {\partial }{\partial x_{1}}}\left(-{\frac {\partial \epsilon _{23}}{\partial x_{1}}}+{\frac {\partial \epsilon _{31}}{\partial x_{2}}}+{\frac {\partial \epsilon _{12}}{\partial x_{3}}}\right)-{\frac {\partial ^{2}\epsilon _{11}}{\partial x_{2}\partial x_{3}}}=0\\&{\frac {\partial }{\partial x_{2}}}\left({\frac {\partial \epsilon _{23}}{\partial x_{1}}}-{\frac {\partial \epsilon _{31}}{\partial x_{2}}}+{\frac {\partial \epsilon _{12}}{\partial x_{3}}}\right)-{\frac {\partial ^{2}\epsilon _{22}}{\partial x_{3}\partial x_{1}}}=0\\&{\frac {\partial }{\partial x_{3}}}\left({\frac {\partial \epsilon _{23}}{\partial x_{1}}}+{\frac {\partial \epsilon _{31}}{\partial x_{2}}}-{\frac {\partial \epsilon _{12}}{\partial x_{3}}}\right)-{\frac {\partial ^{2}\epsilon _{33}}{\partial x_{1}\partial x_{2}}}=0\end{aligned}}}