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、

$\displaystyle \frac{ \partial N }{ \partial \xi } _{(0)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \eta) (1 - \zeta) (1 + 2 \xi + \eta + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(1)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \eta) (1 - \zeta) (1 - 2 \xi + \eta + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(2)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \eta) (1 - \zeta) (1 - 2 \xi - \eta + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(3)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \eta) (1 - \zeta) (1 + 2 \xi - \eta + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(4)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \eta) (1 + \zeta) (1 + 2 \xi + \eta - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(5)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \eta) (1 + \zeta) (1 - 2 \xi + \eta - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(6)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \eta) (1 + \zeta) (1 - 2 \xi - \eta - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(7)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \eta) (1 + \zeta) (1 + 2 \xi - \eta - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(8)}$	$\textstyle =$	$\displaystyle -1/2 \xi (1 - \eta) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(9)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \eta^2) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(10)}$	$\textstyle =$	$\displaystyle -1/2 \xi (1 + \eta) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(11)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \eta^2) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(12)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \zeta^2) (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(13)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \zeta^2) (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(14)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \zeta^2) (1 + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(15)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \zeta^2) (1 + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(16)}$	$\textstyle =$	$\displaystyle -1/2 \xi (1 - \eta) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(17)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \eta^2) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(18)}$	$\textstyle =$	$\displaystyle -1/2 \xi (1 + \eta) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(19)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \eta^2) (1 + \zeta)$	(2.71)

$\displaystyle \frac{ \partial N }{ \partial \eta } _{(0)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \zeta) (1 - \xi) (1 + \xi + 2 \eta + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(1)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \zeta) (1 + \xi) (1 - \xi + 2 \eta + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(2)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \zeta) (1 + \xi) (1 - \xi - 2 \eta + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(3)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \zeta) (1 - \xi) (1 + \xi - 2 \eta + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(4)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \zeta) (1 - \xi) (1 + \xi + 2 \eta - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(5)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \zeta) (1 + \xi) (1 - \xi + 2 \eta - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(6)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \zeta) (1 + \xi) (1 - \xi - 2 \eta - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(7)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \zeta) (1 - \xi) (1 + \xi - 2 \eta - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(8)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \xi^2) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(9)}$	$\textstyle =$	$\displaystyle -1/2 \eta (1 - \zeta) (1 + \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(10)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \xi^2) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(11)}$	$\textstyle =$	$\displaystyle -1/2 \eta (1 - \zeta) (1 - \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(12)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \zeta^2) (1 - \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(13)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \zeta^2) (1 + \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(14)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \zeta^2) (1 + \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(15)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \zeta^2) (1 - \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(16)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \xi^2) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(17)}$	$\textstyle =$	$\displaystyle -1/2 \eta (1 + \zeta) (1 + \xi)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(18)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \xi^2) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(19)}$	$\textstyle =$	$\displaystyle -1/2 \eta (1 + \zeta) (1 - \xi)$	(2.72)

$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(0)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \xi) (1 - \eta) (1 + \xi + \eta + 2 \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(1)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \xi) (1 - \eta) (1 - \xi + \eta + 2 \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(2)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \xi) (1 + \eta) (1 - \xi - \eta + 2 \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(3)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \xi) (1 + \eta) (1 + \xi - \eta + 2 \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(4)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \xi) (1 - \eta) (1 + \xi + \eta - 2 \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(5)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \xi) (1 - \eta) (1 - \xi + \eta - 2 \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(6)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \xi) (1 + \eta) (1 - \xi - \eta - 2 \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(7)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \xi) (1 + \eta) (1 + \xi - \eta - 2 \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(8)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \xi^2) (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(9)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \eta^2) (1 + \xi)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(10)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \xi^2) (1 + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(11)}$	$\textstyle =$	$\displaystyle -1/4 (1 - \eta^2) (1 - \xi)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(12)}$	$\textstyle =$	$\displaystyle -1/2 \zeta (1 - \xi) (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(13)}$	$\textstyle =$	$\displaystyle -1/2 \zeta (1 + \xi) (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(14)}$	$\textstyle =$	$\displaystyle -1/2 \zeta (1 + \xi) (1 + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(15)}$	$\textstyle =$	$\displaystyle -1/2 \zeta (1 - \xi) (1 + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(16)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \xi^2) (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(17)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \eta^2) (1 + \xi)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(18)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \xi^2) (1 + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(19)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \eta^2) (1 - \xi)$	(2.73)