形状関数の微分

形状関数の自然座標 $\{ \xi \}$ に関する微分 $\frac{ \partial N }{ \partial \{ \xi \} } _{(In)}$ は、

$\displaystyle \frac{ \partial N }{ \partial \xi } _{(0)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \eta) (2 \xi + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(1)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \eta) (2 \xi - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(2)}$	$\textstyle =$	$\displaystyle 1/4 (1 + \eta) (2 \xi + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(3)}$	$\textstyle =$	$\displaystyle 1/4 (1 + \eta) (2 \xi - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(4)}$	$\textstyle =$	$\displaystyle -\xi (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(5)}$	$\textstyle =$	$\displaystyle 1/2 (1 - \eta^2)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(6)}$	$\textstyle =$	$\displaystyle -\xi (1 + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(7)}$	$\textstyle =$	$\displaystyle -1/2 (1 - \eta^2)$	(2.36)

$\displaystyle \frac{ \partial N }{ \partial \eta } _{(0)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \xi) (2 \eta + \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(1)}$	$\textstyle =$	$\displaystyle 1/4 (1 + \xi) (2 \eta - \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(2)}$	$\textstyle =$	$\displaystyle 1/4 (1 + \xi) (2 \eta + \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(3)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \xi) (2 \eta - \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(4)}$	$\textstyle =$	$\displaystyle -1/2 (1 - \xi^2)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(5)}$	$\textstyle =$	$\displaystyle -\eta (1 + \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(6)}$	$\textstyle =$	$\displaystyle 1/2 (1 - \xi^2)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(7)}$	$\textstyle =$	$\displaystyle -\eta (1 - \xi)$	(2.37)