Express the explicit shape functions N2 through N8, similar to N1 given by Eq. (11.3.4), for the linear hexahedral element shown in Figure 11-5 on page 548.

Figure P11-5

Figure 11-5 Linear hexahedral element

(a) In a global-coordinate system and

(b) Element mapped into a cube of two unit sides placed symmetrically with natural or intrinsic coordinates s, t, and z'

(a)

(b)

(x3, y3, z3) (X7, y7, 2) (xg, ys, Z) (x4, Y4, za) 6. (x2, Ya, 2) (Xs, Ys, z3) (X1, y, z1) (-1, 1, 1) 3. (1, 1, -1) (1, 1,1) (-1, 1, 1) 4. (-1, -1, -1) 6. (1, -1, -1) (-1, 1, 1) 3(1, 1, 1)