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 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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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.