Quadrilateral finite elements. Figure 6.52 shows a two-dimensional, four-node element (quadrilateral element). Assume an approximation of the form ∅(x, y) = a+bx+cy+dxy
(a) Define the shape functions and their derivatives for a particular element with nodes at P1 (0, 0), P2(1, 0), P3(1, 1), and p4 (1, 1).
(b) Define the shape functions and their derivatives for the general element in Figure 6.52.
(c) Discuss the method and comment on its extension to more complex finite elements.
