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Roll No.
Total No. of Questions : 08
M.Tech (ME) (2017 Batch) (Sem.-1)
FINITE ELEMENT ANALYSIS
Subject Code : MTME-102
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M.Code: 74716
Time: 3 Hrs.
Max. Marks : 100
INSTRUCTIONS TO CANDIDATES :
- Attempt any FIVE questions in all.
- Each question carries TWENTY marks.
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- Discuss the general procedure for finite element analysis of physical problems. How does FEA differ from exact solutions approach for solving boundary value problems in engineering?
- Derive relation for expressing strain energy as product of strain energy density and total volume of deformed material for a fixed bar element subjected to load. Using the work- strain energy relation, obtain the governing equations for the bar element using Castigliano's theorem.
- A structure consisting of two bars is shown in 1. An axial load P = 200 kN is applied as shown. Determine the (a) element stiffness matrix (b) global stiffness matrix (c) global load vector (d) stress in each bar and (e) reaction forces.
W 1 2 P 200 mm + -100 mm Steel A1 = 1000 mm² E1 = 200 Gpa Bronze A1 = 2000 mm² E1 = 83 Gpa FIG. 1 - Analyze a simply supported beam subjected to a uniformly distributed load throughout using Rayleigh Ritz method. Adopt one-parameter trigonometric function. Evaluate the maximum deflection and bending moment and compare with the exact solution.
- The differential equation for a phenomenon is given by (d²y/dx²) + 500x² = 0; 0 = x = 5. The boundary conditions are y(0) = 0 and y(5) = 0. Find the approximate solution using any classical technique. Start with minimal possible approximate solution.
- Develop a one-dimensional finite element model of heat transfer including both conduction and convection for a solid cylindrical body surrounded by a fluid medium. Assume boundary conditions.
- A fin having rectangular cross-section 4 cm wide and 1 cm thick is 8 cm long. The fixed end of the fin is exposed to a temperature of 100°C. Determine the temperature distribution along the length of the fin, assuming that convection heat loss occurs from the fin. Given k = 3 W/cm°C, h = 0.1 W/cm² °C and surrounding fluid temperature is 20°C.
- Discuss the use of stream functions and velocity potential functions in solving two- dimensional, incompressible flow problems.
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