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

Element and the coordinate systems

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

1. Is q Ufr

Umy Umx •

1. a) Derive the finite element shape (interpolation) functions at x=y=5 corn.
2. b) Verify that the shape functions obtained satisfy all the Lagrangian properties.