RTU Machenical engneering Advanced Machanics of Solids previous year questions 2012

The displacement field for a body is given by :

B.Tech, Advanced Machanics of Solids

 $$\begin{gathered} u = K(x^2+y)i+K(y+z)j+K(x^2+2z^2)K \\ Where K = {10}^3 \end{gathered}$$
At a point P(2,2,3), Cnsier two line segments PQ and PR having the following direction cosines before deformation.
$$\begin{gathered} PQ: n_{x1} = n_{y{1}_{}} = n_{z1} = \frac{1}{\sqrt{3}} \\ PR:\hspace{0.17em}{n}_{x2} = n_{y2} = \frac{1}{\sqrt{2}}, n_{z2} = 0 \end{gathered}$$
Determine the angle between the two segments before and after deformation.
2012

If the displacement field is given by.

B.Tech, Advanced Machanics of Solids

  $U_x=Kxy, U_y=Kxy, U_z=2K(x+y)z$
Where K is a constant small enough to ensure applicability of the small deformation theory.
1. Write down the stress matrix.
2. What is the strain in direction $n_x = n_y = n_z = \frac{1}{\sqrt{3}}$

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