Finite Element Analysis - May 2012

Mechanical Engineering (Semester 6)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks. 2(b) Solve the following differential equation using Rayleigh-Ritz method $$3\dfrac{d^{2}y}{dx^{2}}-\dfrac{dy}{dx}+8=0\ \cdots\ 0≤x≤1$$ with boundary condition y(0) =1 and y(1) =2.assume cubic Polynomial for trial solution. Find the value at y(2,3) and y(0,8)(10 marks) 3(a) Evaluate the following integral using Gauss Quadrature. Compare your answer with exact
$$I=\int_{-1}^{1} \int_{-1}^{1}(r^{3}-1)(s-1)^{2}dr ds$$

4(a) For the bar truss shown in figure, determine the nodal displacement, stresses in each element and reaction at support. Take $$E =2\times 10^{5} \dfrac{N}{mm^{2}}, A= 200mm^{2}$$
(15 marks)

5(a) Using Direct Stiffness method,determine the nodal displacements of stepped bar shown in
  (12 marks)

6(b) The nodal co-ordinates of a triangular element are as shown in figure.The x co-ordinate of interior point P is 3.3 and shape function N₁=0.3.Determine N₂ N₃ and y co-ordinates of point P
  (8 marks)