6. (a) Obtain the Lagrangian and Eulerian forms of continuity equation. (4 marks) (b) The
deformation of a body is given by ul = (3M? +X). =(2.V_ee' - V3), and ५, = (4X3 ° + X]).
Compute the vector into which the vector | 0 -3 ( — passing through the point (| .1 .D
inthc reference configuration is deformed. (5 marks)

Parr ( ११०१४१८५ ۱۷ & VI) - Max marks:24

7. (a)From linear elastic constitutiue relation for isotropic materials, deduce the strain-
[[ v 5
_ _ & = -- ० = 700).
stressrelation എ “٢ ‏پر‎ ۸۸ ٢ (6 marks)
(b) Given an isotropic linear elastic material, whose elastic properties are E = 71
GPa, G = 26.6 GPa, find the strain tensor components and the strain energy

density at the point in which the stress state, in Cartesian basis is represented by

20-5
‏زه‎ = -4 0 10 3 (6 marks)
5 10 15

8. Determine the stresses and the angle of twist for a solid elliptical shaft of the
dimensions shown when subjected to end couples Mt. (12 marks)

a

ಸ್ಕಿ

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‎a ‏ب"‎ =

9. Consider a special stress function having the form (0 + Doqx3. Show that this stress
function may be adapted to solve for the stresses in an end-loaded cantilever beam

shown inthe sketch. Assume the body forces are zero for this problem, (12
marks)
x,
7

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