Finite Element Methods - Dec 2014

Mechanical Engg. (Semester 6)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks. 1 (a) Obtain an equilibrium equation of a 3-D elastic body subjected to a body force.(8 marks) 1 (c) Explain the general description of finite element method.(6 marks) 1(b) Discuss the types of elements based on geometry.(6 marks) 2 (a) Derive an expression for Total potential energy of an elastic body subjected to body force, traction force and a point force(8 marks) 2 (b) Using Raleigh's Ritz method find a deflection of a simply supported beam of length L subjected to a uniformly distributed load of P₀ N/m.(12 marks) 3 (a) Write an interpolation polynomial for liner quadratic and cubine element.(6 marks) 3 (b) Obtain an expression for a strain displacement matrix of a rectangular element.(14 marks) 4 (a) Determine the nodal displacements, reactions and stresses for the Fig. Q4 (a) using penalty approach. Take E =210GPa, Area=250mm². (12 marks) 4 (b) Find the nodal displacement stress and strain of the system shown in fig Q4(b).Take E=70GPa, Area -1m². (8 marks) 5 (a) Find the shape functions of a 2-D quadrilateral quadratic (9 noded) element.(14 marks) 5 (b) With a sketch define ISO, Sub and super parametric elements(6 marks) 6 (a) Obtain an expression for stiffness matrix of a truss element.(8 marks) 6 (b) Find the nodal displacement, stress and reaction of truss element shown in fig Q6(b). take E=70GPa, Area =200mm². (12 marks) 7 (a) Derive the Hermine shape function of a n beam element(8 marks) 7 (b) For the beam and loading shown in fig Q7(b) determine the slopes at 2 and 3 and the vertical deflection at the midpoints of the distributed load. Take E=200 Gpa, I=4×10⁶ mm⁴. (12 marks) 8 (a) Discuss the derivation of one dimensional heat transfer in thin films(8 marks) 8 (b) A composite wall consists of 3 material shown in fig Q8(b). the outer temperature is T₀=20°C, determine the temperature distribution in the wall. Convection heat transfer takes place at inner surface with T_&infty;=800°C. Take h=25 w/m²°C area=1m². (12 marks)