ASSIGNMENT 5

NOTE

Q 1 to Q 3 = 20 MARK

Q 4 to Q 8 = 60 MARK (each question 12 mark)

Q.1. What are serendipity elements? Derive and graphically represent interpolation functions for eight noded rectangular element.

Q.2.Write short note on nine-noded quadrilateral element.

Q 3. Write short note on generalized Jacobi method.

Q.4. Using serendipity concept, find the shape function for the element shown in the fig.

ή

4 3

ε

1 5 6 2

(-1/3,-1) (1/3,-1)

Q.5. find the natural frequency of axial vibration of a bar of uniform c/s of 20 mm2 and length 1 m. take e=2 x105

n/mm2 and ρ= 8000 kg/m3 . take two linear elements.

Q.6.find the two natural frequencies of transverse vibration of a beam fixed at both ends as show in fig. Use consistent mass matrix .EI = 106 units ρ A = 106

units

(NOTE : Both the end are fixed)

Q 7 Consider the governing differential equation for unsteady heat transfer in a fin.

k∂2T∂ t 2

+q = pAh (T−T ∞ ) + ρc ∂T

∂ t

Where T: Temperature, x: Spatial coordinate

t:Time, T∞: Temerature of the ambient air,

k, q, P, A, h, ρ, and c are known constants.

Derive the element matrix equation for a linear element (two noded), using galerkins method on the weak form of the weighted residual statement for the above differential equation.

1 unit

Q 8.find the two natural frequencies of transverse vibration of a beam fixed at both ends as show in fig. Use Lumped mass matrix . EI = 106 units and ρ A = 106

units

(NOTE : Both the end are fixed)

1 unit