A quadrilateral element in the figure is mapped into the parent element.

a. A point \(P\) has a coordinate \((x, y)=(1 / 2, y)\) in the physical element and \((s, t)=(-1 / 2, t)\) in the parent element. Find the \(y\) and \(t\) coordinates of the point using isoparametric mapping.

b. Calculate the Jacobian matrix at the center of the element.

c. Is the mapping valid? Explain your answer.

Transcribed Image Text:

y 3 (0,2) (1,1) (4)(-1,1) At 3 (1,1) 4 (0,0) (1,0) (1) (-1,-1) 2 (1,-1)