1. First test of the course work in PhD Programme, June 2015
Course I - Advanced Finite Element Analysis
I a) State and explain the principle of virtual work 5
b) Find the stresses and compression in each section of the composite
member shown in Fig 1. The first member from the fixed support is made
up of steel with a diameter of 200mm, the middle member is made of
copper with a diameter of 150mm and the last member is made of brass
with a diameter of 100mm . The length of each member being 150mm.
Use Es=2x105 MPa, Ecu=1x105 MPa, Ebr= 1.14x105 MPa and the
minimum number of linear elements. The force towards right is 10 kN and
the force towards left is 5kN.
Fig 1 15
OR
II a) State and explain the principle of minimum potential energy 5
b) Using virtual displacement principle, determine the forces developed in
three bars of the truss shown in Fig 2. AE= constant
Fig 2 15
III a) Distinguish between higher and lower order elements 5
b) Using Lagrange interpolation formula, write down the trial solution for a
three node quadratic element with nodes and displacements given below
x 0 3 8
u 4 3 -1
Also, plot the shape function and variation of u(x) 15
OR
IV a) Explain C-continuity 5
b) Determine the shape function of two noded bar element in
i. Cartesian coordinate system
ii. Local coordinate system ranging from 1 to zero.
iii. Local coordinate system with range -1 to +1. 15
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Duration : 2 hours Max. Marks: 40
2m
60°
20kN