The quadrilateral element shown in the figure has the nodal displacement of (left{u_{1}, v_{1}, u_{2}, v_{2} ight.),

The quadrilateral element shown in the figure has the nodal displacement of \(\left\{u_{1}, v_{1}, u_{2}, v_{2}\right.\), \(\left.u_{3}, v_{3}, u_{4}, v_{4}\right\}=\{-1,0,-1,0,0,1,0,1\}\).

a. Find the \((s, t)\) reference coordinates of point \(A(0.5,0)\) using the isoparametric mapping method.

b. Calculate the displacement at point \(B\) whose reference coordinate is \((s, t)=(0,-0.5)\)

c. Calculate the Jacobian matrix \([\mathbf{J}]\) at point \(B\).

Transcribed Image Text:

4 1 (3) A 3 B 1 -1 2 Physical element Reference element