広告
・内挿関数Nの微分まとめ
4面体1次要素 の内挿関数Niの微分値のまとめを示します。
内挿関数N1の微分値
\[
\frac{\partial N_1}{\partial x}
=\frac{\partial L_1}{\partial x}
=\frac{c_{1x}}{6V}
=\frac{1}{6V}\left(-y_3z_4+z_3y_4+y_2z_4-y_2z_3-z_2y_4+z_2y_3\right)
\]
\[
\frac{\partial N_1}{\partial y}
=\frac{\partial L_1}{\partial y}
=\frac{c_{1y}}{6V}
=\frac{1}{6V}\left(x_3z_4-z_3x_4-x_2z_4+x_2z_3+z_2x_4-z_2x_3\right)
\]
\[
\frac{\partial N_1}{\partial z}
=\frac{\partial L_1}{\partial z}
=\frac{c_{1z}}{6V}
=\frac{1}{6V}\left(-x_3y_4+y_3x_4+x_2y_4-x_2y_3-y_2x_4+y_2x_3\right)
\]
内挿関数N2の微分値
\[
\frac{\partial N_2}{\partial x}
=\frac{\partial L_2}{\partial x}
=\frac{c_{2x}}{6V}
=\frac{1}{6V}\left(y_3z_4-z_3y_4-y_1z_4+y_1z_3+z_1y_4-z_1y_3\right)
\]
\[
\frac{\partial N_2}{\partial y}
=\frac{\partial L_2}{\partial y}
=\frac{c_{2y}}{6V}
=\frac{1}{6V}\left(-x_3z_4+z_3x_4+x_1z_4-x_1z_3-z_1x_4+z_1x_3\right)
\]
\[
\frac{\partial N_2}{\partial z}
=\frac{\partial L_2}{\partial z}
=\frac{c_{2z}}{6V}
=\frac{1}{6V}\left(x_3y_4-y_3x_4-x_1y_4+x_1y_3+y_1x_4-y_1x_3\right)
\]
内挿関数N3の微分値
\[
\frac{\partial N_3}{\partial x}
=\frac{\partial L_3}{\partial x}
=\frac{c_{3x}}{6V}
=\frac{1}{6V}\left(-y_2z_4+z_2y_4+y_1z_4-y_1z_2-z_1y_4+z_1y_2\right)
\]
\[
\frac{\partial N_3}{\partial y}
=\frac{\partial L_3}{\partial y}
=\frac{c_{3y}}{6V}
=\frac{1}{6V}\left(x_2z_4-z_2x_4-x_1z_4+x_1z_2+z_1x_4-z_1x_2\right)
\]
\[
\frac{\partial N_3}{\partial z}
=\frac{\partial L_3}{\partial z}
=\frac{c_{3z}}{6V}
=\frac{1}{6V}\left(-x_2y_4+y_2x_4+x_1y_4-x_1y_2-y_1x_4+y_1x_2\right)
\]
内挿関数N4の微分値
\[
\frac{\partial N_4}{\partial x}
=\frac{\partial L_4}{\partial x}
=\frac{c_{4x}}{6V}
=\frac{1}{6V}\left(y_2z_3-z_2y_3-y_1z_3+y_1z_2+z_1y_3-z_1y_2\right)
\]
\[
\frac{\partial N_4}{\partial y}
=\frac{\partial L_4}{\partial y}
=\frac{c_{4y}}{6V}
=\frac{1}{6V}\left(-x_2z_3+z_2x_3+x_1z_3-x_1z_2-z_1x_3+z_1x_2\right)
\]
\[
\frac{\partial N_4}{\partial z}
=\frac{\partial L_4}{\partial z}
=\frac{c_{4z}}{6V}
=\frac{1}{6V}\left(x_2y_3-y_2x_3-x_1y_3+x_1y_2+y_1x_3-y_1x_2\right)
\]
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