(Solved): A \( 100-\mathrm{mm} \) by \( 150-\mathrm{mm} \) rectangular plate \( Q A B C \) is deformed into t ...

A \( 100-\mathrm{mm} \) by \( 150-\mathrm{mm} \) rectangular plate \( Q A B C \) is deformed into the shape shown by the dashed lines in Fig. P2.9. All dimensions shown in the figure are in millimeters. Determine at point \( Q \) (a) the strain components \( \varepsilon_{x}, \varepsilon_{y}, \gamma_{x y} \), and (b) the principal strains and the direction of the principal axes. Figure P2.9. (use finite difference method). Displacement-strain relations \( 6 . \) A displacement field in a body is given by \[ \begin{aligned} u &=c\left(x^{2}+10\right) \\ v &=2 c y z \\ w &=c\left(-x y+z^{2}\right) \end{aligned} \] where \( c=10^{-4} \). Determine the state of strain on an element positioned at \( (0,2,1) \)