Problem 4.3
The Cartesian global coordinates of the corner nodes of a quadrilateral element
are given by (0,-1), (-2, 3),(2,4) and (5,3). Find the coordinate transformation
between the global and local (natural) coordinates. Using this determine the
Cartesian coordinates of the point defined by (r, s) = (0.5, 0.5) in the global
coordinate system.
SOLUTION
}= }
Where (xi, yi ) are the (x ,y) coordinates of node i(1,2,3,4)
Ni =1/4 (1+rri) (1+ssi) ;I =1,2,3,4
And (r1, s1) = (-1,-1)
(r2, s2) = (1,-1)
(r 3,s3)= (1, 1)
(r4, s4)= (-1, 1)
By substituting values of (xi, yi); i= 1,2,3,4 in equation 4.32, we obtain
X=N1x1+N2x2+N3x3+N4x4= 5N2+2N3-2N4
Y=N1y2+N2y2+N3y3+N4y4=N1+3N2+4N3+3N4
And N1=1/4(1-r) (1-s)
N2=1/4(1+r) (1-s)
N3=1/4(1+r) (1+s)
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