Question

5.12 Figure (a) shows a four node quadrilateral Ω(e) in R2. Coordinates of the nodes are given. Figure (b) shows a map αξη) of Ω(e) in natural coordinate space ξη. (0,2) (2,2) (p. q) (0, 2) (0,0) (2,0) (0,0) (2,0) (a) e) in x, y space (b) Map Ω(En) of Ω(e) The coordinates of the nodes are also given in the two spaces in Figures (a) and (b) (a) Determine the equations describing the mapping of points in ry and ξη spaces for Ω(e) and Ωξη) 1.e. determine x = x(ξ, η), y y(ξ, η) Simplify the expressions till no further simplification is possible. (b) Determine the relationship between p and q (the Cartesian coordi- nates of node 3) for their admissibility in the geometric description of the geometry Ω(e) in the xy space. Simplify the final expression or equation.

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