広告
・内挿関数N3の微分
3角形1次要素 の内挿関数N3の微分値を示します。
x微分
\[
\begin{aligned}
\frac{\partial N_3}{\partial x}
&=\frac{\partial L_3}{\partial x}
=\frac{\partial(S_3/S)}{\partial x}
=\frac{1}{S}\frac{\partial S_3}{\partial x}\\[6pt]
&=\frac{1}{S}\frac{\partial}{\partial x}\frac{1}{2}
(x_2y-y_2x-x_1y+x_1y_2+y_1x-y_1x_2)\\[6pt]
&=\frac{1}{2S}(-y_2+y_1)
\end{aligned}
\]
y微分
\[
\begin{aligned}
\frac{\partial N_3}{\partial y}
&=\frac{\partial L_3}{\partial y}
=\frac{\partial(S_3/S)}{\partial y}
=\frac{1}{S}\frac{\partial S_3}{\partial y}\\[6pt]
&=\frac{1}{S}\frac{\partial}{\partial x}\frac{1}{2}
(x_2y-y_2x-x_1y+x_1y_2+y_1x-y_1x_2)\\[6pt]
&=\frac{1}{2S}(x_2-x_1)
\end{aligned}
\]
| prev | | | up | | | next |
