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.
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).
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
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.
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.