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Reg. No. :

M.E. DEGREE EXAMINATION, APRIL/MAY 2011

Second Semester

Engineering Design

ED 9221 FINITE ELEMENT METHODS IN MECHANICAL DESIGN

(Common to M.E. Computer Aided Design and M.E. Product Design and

Development)

Time : Three hours Maximum : 100 marks

Answer ALL questions

PART A (10 2 = 20 marks)

1. What is the essence of finite element method?2. What is the need to perform a patch test? How is it done?3. Mention the basic steps of Galerkins method.4. Distinguish between one dimensional and two dimensional elements.5. Specify the Jacobian matrix for CST element.6. What is a Mindlin plate element?7. Specify the mass matrix for a truss element having four degrees of freedom.8. State the required condition for solving dynamic problems as specified by

characteristic polynomial method.

9. Mention two examples for contact non-linearity.10. State the essential difference between nonlinear elastic material and elastic-

plastic material.

Question Paper Code :77708

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PART B (5 16 = 80 marks)

11. (a) Using direct method, formulate the stiffness matrix for a simple planebeam element.

Or

(b) A horizontal rod (E = l, A = 1, L = l) fixed at both ends is subjected to an

axially varying body force, f = x3 N/m. Using a quadratic displacement

field, determine the displacement u(x) and stress (x) in the rod.

(All the quantities have units which must be taken suitably).

12. (a) Describe Galerkins method of formulation for solving a one dimensionalstructural problem with an illustrative example.

Or

(b) Establish the shape functions for the eight node quadrilateral element

belonging to serendipity family.

13. (a) A rectangular element is defined by nodal coordinates (in m) as 1(0,0),2(2,0), 3(2,2) and 4(0,2). The nodal displacement vector is given by

q = [0,0,0.002,0.003,0.006,0.0032,0,0]T.

Evaluate the stress at the centroid of the element, assuming plane stress

condition. Take Youngs modulus and Poissons ratio as 30 106 N/m2

and 0.3 respectively.

Or

(b) For a one dimensional composite bar shown in Fig. 1, determine the

interface temperatures. For element 1, let Kxx= 200W/mC; for element

2, let Kxx = 100 W/mC; and for element 3, let Kxx = 50W//mC;

Let A = 0.1m2. The left end has a constant temperature of 100C and the

right end has a constant temperature of 300C.

Fig. 1

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14. (a) A pin jointed truss defined by coordinates P (0,0), Q(1000,0) andR(500, 1700) is fixed at P and Q. The links are of 8 mm diameter and

made of steel (E = 2 105 N/mm2, density = 7800 kg/m3). Using the

lumped mass matrix, determine the natural frequencies of the truss.

Or

(b) Explain the central difference method for determining the transient

dynamic response of a structure.

15. (a) Explain, with examples, the solution algorithms for performingnon-linear analysis.

Or

(b) Explain stress stiffening and its use in linear buckling analysis and

non-linear analysis.

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