形状関数

形状関数 $N_{(In)}$ を自然座標 $\{ \xi \}$ で表現すると、以下のようになる。

$\displaystyle N_{(0)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \xi) (1 - \eta) (1 - \zeta) (2 + \xi + \eta + \zeta)$
$\displaystyle N_{(1)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \xi) (1 - \eta) (1 - \zeta) (2 - \xi + \eta + \zeta)$
$\displaystyle N_{(2)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \xi) (1 + \eta) (1 - \zeta) (2 - \xi - \eta + \zeta)$
$\displaystyle N_{(3)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \xi) (1 + \eta) (1 - \zeta) (2 + \xi - \eta + \zeta)$
$\displaystyle N_{(4)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \xi) (1 - \eta) (1 + \zeta) (2 + \xi + \eta - \zeta)$
$\displaystyle N_{(5)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \xi) (1 - \eta) (1 + \zeta) (2 - \xi + \eta - \zeta)$
$\displaystyle N_{(6)}$	$\textstyle =$	$\displaystyle -1/8 (1 + \xi) (1 + \eta) (1 + \zeta) (2 - \xi - \eta - \zeta)$
$\displaystyle N_{(7)}$	$\textstyle =$	$\displaystyle -1/8 (1 - \xi) (1 + \eta) (1 + \zeta) (2 + \xi - \eta - \zeta)$
$\displaystyle N_{(8)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \xi^2) (1 - \eta) (1 - \zeta)$
$\displaystyle N_{(9)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \eta^2) (1 - \zeta) (1 + \xi)$
$\displaystyle N_{(10)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \xi^2) (1 + \eta) (1 - \zeta)$
$\displaystyle N_{(11)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \eta^2) (1 - \zeta) (1 - \xi)$
$\displaystyle N_{(12)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \zeta^2) (1 - \xi) (1 - \eta)$
$\displaystyle N_{(13)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \zeta^2) (1 + \xi) (1 - \eta)$
$\displaystyle N_{(14)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \zeta^2) (1 + \xi) (1 + \eta)$
$\displaystyle N_{(15)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \zeta^2) (1 - \xi) (1 + \eta)$
$\displaystyle N_{(16)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \xi^2) (1 - \eta) (1 + \zeta)$
$\displaystyle N_{(17)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \eta^2) (1 + \zeta) (1 + \xi)$
$\displaystyle N_{(18)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \xi^2) (1 + \eta) (1 + \zeta)$
$\displaystyle N_{(19)}$	$\textstyle =$	$\displaystyle 1/4 (1 - \eta^2) (1 + \zeta) (1 - \xi)$	(2.70)