The Finite Element Method - Mechanics of Structures: Variational and Computational Methods - page 387

FIGURE 6.33
Tetrahedral element.

1111
x 1

. For i

x 2 x 3 x 4

1
6

α β γ δ = = =

where

i , i , i , i ,i

1 , 2 , 3 , 4 are constants and V 1 ,

y 1 y 2 y 3 y 4

z 1 z 2 z 3 z 4

x 2 x 3 x 4 111

y 2 α 1 = y 2 y 3 y 4 β 1 =− y 3 y 4

z 2 z 3 z 4 z 2 z 3 z 4

111
x 2

111
x 2 γ = x 3 x 4 δ =− x 3 x 4

1 1

z 2 z 3 z 4 y 2 y 3 y 4

and the constants for other values of i are obtained by cyclic permutation of the subscripts
i . For example,

x 3 x 4 x 1

α 2 = y 3 y 4 y 1

z 3 z 4 z 1