Derive the finite element shape functions at x=y=5 corn.Verify that the shape functions obtained satisfy all the Lagrangian properties.

1. Consider the element and the coordinate systems x and y in centimeters shown in figure below.
[(0,0), J(15,0), M(15,10), N(0,10) cm for coordinates.
Uix=Uiy = 0, Ujx= Ujy= Umx=Umy=.3 cm Unx=Uny=0 cm
U.1 cm
tuny Uri I
U. Is q Ufr
Umy Umx •

a) Derive the finite element shape (interpolation) functions at x=y=5 corn.

b) Verify that the shape functions obtained satisfy all the Lagrangian properties.

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