VTU Previous Year Question Papers BE ME Modelling and Finite Element Analysis December 2011

VTU Previous Year Question Papers BE ME Sixth Semester

Modelling and Finite Element Analysis December 2011

 

Note: Answer any FIVE full questions, selecting at least TWO questions from each part.

PART-A

1 a. Write the equilibrium equation for 3-D state of stress and state the terms involved. (04 Marks)

b.  Solve the following system of equations by Gaussian elimination method :

X1 + X2 + X3 = 6

X1-x2 + 2x3 = 5

X1 + 2x2 – X3 = 2.

c. Determine the displacements of holes of the spring system shown in the figure using principle of minimum potential energy.                                                                          (08 Marks)

2 a. Explain the discretization process of a given domain based on element shapes number and size.

b.  Explain basic steps involved in FEM with the help of an example involving a structural member subjected to axial loads.

C . Why FEA is widely accepted in engineering? List various applications of FEA in engineering.

 

3 a.  Derive interpolation model for 2-D simplex element in global co – ordinate system.

b.  What is an interpolation function? Write the interpolation functions for:

i) 1 – D linear element ; ii)1 — Dquadistie element,

iii) 2-D linear element ; iv) 2-D quadratic element.

v) 3-D linear element.

c.   Explain “complete” and “conforming” elements.

 

4       a Derive shape function for 1 – D quadratic bar element in neutral co-ordinate, system.

b.   Derive shape functions for CST element in NCS.

c.   What are shape functions and write their properties, (any two).

 

PART-B

5  a. Derive the body force load vector for 1 – D linear bar element.

b.   Derive the Jacobian matrix for CST element starting from shape function.

c.   Derive stiffness matrix for a beam element starting from shape function.

 

6 a. Explain the various boundary conditions in steady state heat transfer problems with simple sketches.

b.  Derive stiffness matrix for 1 – D heat conduction problem using either functional approach or Galerkin’s approach.

c.   For the composite wall shown in the figure, derive the global stiffness matrix.

Take Ai = Aa = A3 = A

1

7    a. The structured member shown in figure consists of two bars. An axial load of P = 200 fcN is loaded as shown. Determine the following:

i) Element stiffness matricies.

ii) Global stiffness matrix.

iii) Global load vector.

iv) Nodal displacements.

 

i)  Steel Ai = 1000 mm Ei = 200 GPa

ii)   Bronze A2 = 2000 mm2 E2 = 83 GPa.

b.  For the truss system shown, determine the nodal displacements. Assume E – 210 GPa and A = 600 mm for both elements.

2

 

8  a. Determine the temperature distribution in 1 – D rectangular cross – section fin as shown in 3w figure. Assume that convection heat loss occurs from the end of the fin. Take k =Cm C0 Iw-, T= 20°C. Consider two elementsh=-Cm2°C

b.  For the cantilever beam subjected to UDL as shown in determine the deflections of the free end. Consider one element.

 

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