広告
・内挿関数N1の微分
3角形1次要素 の内挿関数N1の微分値を示します。
x微分
\[
\begin{aligned}
\frac{\partial N_1}{\partial x}
&=\frac{\partial L_1}{\partial x}
=\frac{\partial(S_1/S)}{\partial x}
=\frac{1}{S}\frac{\partial S_1}{\partial x}\\[6pt]
&=\frac{1}{S}\frac{\partial}{\partial x}\frac{1}{2}
(x_2y_3-y_2x_3-xy_3+xy_2+yx_3-yx_2)\\[6pt]
&=\frac{1}{2S}(-y_3+y_2)
\end{aligned}
\]
y微分
\[
\begin{aligned}
\frac{\partial N_1}{\partial y}
&=\frac{\partial L_1}{\partial y}
=\frac{\partial(S_1/S)}{\partial y}
=\frac{1}{S}\frac{\partial S_1}{\partial y}\\[6pt]
&=\frac{1}{S}\frac{\partial}{\partial y}\frac{1}{2}
(x_2y_3-y_2x_3-xy_3+xy_2+yx_3-yx_2)\\[6pt]
&=\frac{1}{2S}(x_3-x_2)
\end{aligned}
\]
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