53212-mt----finite Element Analysis

NR

Code No: 53212/MT

M.Tech. – II Semester Regular Examinations, September, 2008 FINITE ELEMENT ANALYSIS (Advanced Manufacturing Systems) Time: 3hours

Max. Marks:60 Answer any FIVE questions All questions carry equal marks ---

1. a) Give a brief description on application of FEM in different fields of engineering. b) How FEM is different from Galerkin method? 2.a) Explain the importance of shape functions giving their characteristics. b) Write the basic equations of elasticity and strain displacement relations. 3. Consider the bar in the following figure.1 determine the nodal displacements, element stresses and support reactions. Solve this problem by hand calculation, adopting the elimination method for handling boundary conditions.

Figure.1 4.

For the two-dimensional loaded plate shown in the figure,.2 determine the displacements of nodes 1 and 2 and the elements stresses using plane stress conditions. Contd…2.,

Code No: 53212/MT

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5. For the ten – noded triangular element shown in figure.3 , determine shape functions Ni(r,s) for nodes 1, 2, 4, 5, 6 and 10.

Figure.3 Contd..3.,

Code No: 53212/MT

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6. A long bar of rectangular cross – section, having thermal conductivity of 1.5 W/m0C is subjected to the boundary conditions as shown in the Figure.4 Two opposite sides are maintained at a uniform temperature of 180 0C one side is insulated, and the remaining side is subjected to a convection process with T∞ = 250C, h= 50 w/m2 0C. Determine the temperature distribution in the bar.

Figure.4 7. Differentiate consistent mass matrix and lumped mass matrix and derive an expression for lumped mass for one dimensional bar element. 8. Write notes on the following:a) Non linear dynamic problems. b) Plane stress and plane strain problems. $$$