Reg. No.: Question Paper Code : 11419 B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2011 Sixth Semester Mechanical Engineering ME 2353 — FINITE ELEMENT ANALYSIS (Common to Automobile Engineering) (Regulation 2008) Time : Three hours PART A — (10 × 2 = 20 marks) 1. 2. 3. What should be considered during piecewise trial functions? Mention the basic steps of Rayleigh-Ritz method. Why are polynomial terms preferred for shape functions in finite element method? 4. 5. 6. 7. 8. 9. When do we resort to 1 D quadratic spar elements? What are higher order elements and why are they preferred? Give four applications where axisymmetric elements can be used. Sketch two 3D elements exhibiting linear strain behavior. What is the influence of element distortion on the analysis results? Define the stream function for a one-dimensional incompressible flow. 4 10. Mention two natural boundary conditions as applied to thermal problems. 21 4 21 Answer ALL questions 4 21 Maximum : 100 marks 1. Or (b) du dx 75 cm 12. E= 70Gpa. 3. Fig. x =L x 11419 .3. A = 24 cm2 20 kN 75 cm 60 cm Fig. y 3 21 80 cm 4 4 0 21 A = 15 cm2 10 kN Find the nodal displacement and elemental stresses for the bar shown in Fig. ② ① 60 cm 30o P = 50 kN Fig.cross-sectional area A = 2cm2 for all truss members.PART B — (5 × 16 = 80 marks) 11. The deformation of the bar is governed by the differential equation given below. 2 4 21 = 0. (a) Calculate nodal displacement and elemental stresses for the truss shown in Fig. qo AE d 2u + q0 = 0 dx 2 with the boundary conditions u (0 ) = 0 . 2. (a) A uniform rod subjected to a uniform axial load is illustrated in Fig. Determine the displacement using weighted residual method. 1.2. 1) j = 2 (5.1) 14. determine the nodal displacements and element stress using plane strain condition considering body force. Or (b) Derive element force vector when linearly varying pressure acts on the side joining nodes jk of a triangular element shown in Fig. Or the system given below using modal (b) Find the response of superposition method.5 and body force of 25N/mm2 acts downwards. Thickness = 5mm. For the two-dimensional loaded plate shown in Fig. Consider lumped mass matrix approach. 21 k=3 (3. 3 4 21 11419 . (a) Establish the shape functions of an eight node quadrilateral element and represent them graphically. Fig.3 and density as 7800 kg/m3. 4. 5. (a) 4 21 Determine the natural frequencies and mode shapes of transverse vibration for a beam fixed at both ends. each of length L and cross-sectional area A. Take Young’s modulus as 200 GPa. Poisson’s ration as 0. Pl 4 i = 1 (1.Or (b) 13.4.7) Pl Fig. The beam may be modeled by two elements. q1 = 0 .T ∞ = 20°C. . Take h = 3W/cm° C. Or 4 1m 1 A1 = 3 m 2 21 2 A2 = 2 m 2 1m (b) For the smooth pipe of variable cross-section shown in Fig.1 W(cm2° C. q2 = 1 15.The fin has rectangular cross-section and is 8cm long 4cm wide and 1cm thick. the velocities in each pipe. 21 4 ————––––—— 4 4 21 A3 = 1 m2 4 1m &2 = 1 q 11419 . Fig.6. 6.The permeability coefficient is 1 m/sec. Assume that convection heat loss occurs from the end of the fin.&&1 + 2 kq 1 − kq 2 = 0 2m q &&2 + 2 kq 2 − kq 1 = 0 mq With the initial conditions at t = 0 . 100o C Fig. The potentials at the left end is 10 m and that at the right end is 2m. (a) Determine the temperature distribution in one dimensional rectangular cross-section as shown in Fig. q1 = 0. 7. h = 0. 7 determine the potentials at the junctions.