11-06-2013, 01:00 PM
SEMESTER EXAMINATIONS FOR FINITE ELEMENT ANALYSIS
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Answer any five questions
All questions carry equal marks
1.a) What are the characteristics of a stiffness matrix of an element? Explain different types of elements along with their applications.
b) State and explain the Galerkin’s principle for solving the engineering problems.
2. A stepped bar is subjected to an axial load of 300 kN as shown in figure 1. Find the nodal displacements, element stresses and strains and reactions. Take E = 2 x 105 N/mm2.
3. Estimate the displacement vector, strains, stresses and reactions in the truss structure shown below in figure 2. Take A = 1000 mm2 and E = 200 GPa
4.a) Derive the strain displacement relation matrix for CST using weighted residual method.
b) Calculate the load vector for a triangular element subjected a variable traction load on the face 1-2 of 5 MPa and on the face 2-3 a variable load of 2MPa to 4 MPa. A point load of 400 kN acts at the node 3 with the inclination of 300 with horizontal axis.
5.a) Derive the strain displacement relation matrix for the four nodded quadrilateral element.
b) Estimate the temperature profile in a pin fin of diameter 30 mm, whose length is 500mm. The thermal conductivity of the fin material is 50 W/m K and heat transfer coefficient over the surface of the fin is 40 W/m2 K at 300C. The tip is insulated and the base is exposed to heat flux of 800 kW/m2.
6. Calculate the deflection at the center and slopes at the ends of a simply supported beam of 2 m length subjected to a UDL of 50 kN/m throughout the length and a bending moment of -5000 N-m at the centre. Take EI = 700 x 103 N-mm2.
7. Calculate natural frequency, displacements and mode shapes of the stepped bar shown in figure 3. Take E = 2 E 5 N/mm2 and ρ = 7200 kg/m3.