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、

$\displaystyle \frac{ \partial N }{ \partial \xi } _{(0)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \eta) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(1)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \eta) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(2)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \eta) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(3)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \eta) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(4)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \eta) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(5)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \eta) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(6)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \eta) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \xi } _{(7)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \eta) (1 + \zeta)$

$\displaystyle \frac{ \partial N }{ \partial \eta } _{(0)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \xi) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(1)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \xi) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(2)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \xi) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(3)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \xi) (1 - \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(4)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \xi) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(5)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \xi) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(6)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \xi) (1 + \zeta)$
$\displaystyle \frac{ \partial N }{ \partial \eta } _{(7)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \xi) (1 + \zeta)$	(2.68)

$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(0)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \xi) (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(1)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \xi) (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(2)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \xi) (1 + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(3)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \xi) (1 + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(4)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \xi) (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(5)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \xi) (1 - \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(6)}$	$\textstyle =$	$\displaystyle 1/8 (1 + \xi) (1 + \eta)$
$\displaystyle \frac{ \partial N }{ \partial \zeta } _{(7)}$	$\textstyle =$	$\displaystyle 1/8 (1 - \xi) (1 + \eta)$	(2.69)