Chapter 10.6, Problem 10.30P

For the case of plane stress, show that Hooke’s law can be written as

${\sigma }_x=\frac{E}{\left(1-v^2\right)}\left({\epsilon }_x+v{\epsilon }_y\right),{\sigma }_y=\frac{E}{\left(1-v^2\right)}\left({\epsilon }_y+v{\epsilon }_x\right)$