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- Finite Element Methods - FEM
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Registration no: Total Number of Pages: 02 B.Tech PCAE4306 6th Semester Regular / Back Examination 2016-17 FINITE ELEMENT METHOD BRANCH: AERO Time: 3 Hours Max Marks: 70 Q.CODE: Z180 Answer Question No.1 which is compulsory and any five from the rest. The figures in the right hand margin indicate marks. Q1 Answer the following questions: a) Distinguish between essential boondary conditions and natural boundary conditions. b) Write down the expression of shape function N and displacement u for 1-D bar (2 x 10) element. c) Write down the expression of stiffness matrix for a truss element. d) Find out the natural frequency of a fixed free bar with one element discretization. e) What is a isoparametric element? Give example. f) Name the weighted residual techniques? g) Define shape function. h) Give two examples of plane strain problems. i) Name any four FEA softwares? j) What is the importance of Pascal’s triangle in FE analysis? Q2 A simply supported beam of length L and constant section is subjected to a uniformly distributed load of intensity q 0. Determine the maximum deflection and maximum bending moment using the basic Galkerin method. (10) Q3 A brass bar of length 3m is subjected to loads as shown in the figure. The cross section of the bar is a circle. The segment AB is of length 0.5m and the diameter is 50 mm. The length of BC is 1.0 m and the diameter is 20 mm. The length of CD is 1.5m and diameter is 30mm. Given E=100 GPa, Compute the stress in the three segments of the bar. (10) 40 KN 1 3 B Q4 20 KN C Compute the stress developed in the members of the truss shown in the figure, E=200GPa. Area of the member AB is 20 cm2 and its length is 5 m. Members BC and AC have the same area and is equal to 25 cm2. D (10) 1 2 Page 100 KN

6 KN C 5 KN 600 300 A Q5 B Derive the shape function, strain displacement relation matrix [B] and element (10) stiffness matrix for a 3-noded triangular element. (CST) Q6 a) The Cartesian coordinates of the corner nodes 1,2 and 3 of a tringular element (5) are given by (1,1), (3,1) and (2,3) respectively. Determine the shape functions N1, N2 and N3 at a interior point P(2,2). b) The Cartesian coordinates of the corner nodes of an isoparametric quadrilateral element are given by (1,1), (5,2),(4,5) and (2,4). find its Jacobian matrix. Q7 a) For the composite wall shown in the figure, derive global stiffness matrix. (5) (5) A 1 = A2 = A 3 = A K1 L1 b) K2 L2 K3 L3 Calculate the stiffness matrix for the elements shown in the figure. Assume plane starin conditions. Take poisson's ratio =0.25, thickness t=15 mm and E=210 GPa. The coordinates are shown in units of milimeters. (5) 3 (0,500) 2 (750,500) 1 (0,0) Write short answer on any TWO: a) Advantages and disadvantages of FEM. (5 x 2) b) Difference between FEM and FDM. d) Preprocessing and Postprocesing in FEM. 2 c) Basic Steps involved in FEM. Page Q8

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