Determine the Jacobian matrix [J] and its determinant for the elements shown in Figure P10-11. Show that the determinant of [J] for rectangular and parallelogram shaped elements is equal to A / 4, where A is the physical area of the element and 4 actually represents the area of the rectangle of sides 2 × 2 when b = 1 and h = 1 in Figure 6-20.

Figure P10-20

(2, 3) (4, 3) (-2, 1) (2, 1) (-2, 1) , (2, 1) > (2, 1) (-2, 1) (-2, -1) (2,-1) (0, 0) (2, 0) (c) (a) (b) Figure P10-11 2. 3. 2. (0, 2) 3 (4, 2) (Coordinates in inch units) (4, 0) (0, 0) 1 2