Nonlinear finite elements/Homework 6/Solutions/Problem 1/Part 14

Problem 1: Part 14

Apply the plane stress condition and solve for $D_{yy}$.

The plane stress condition requires that $\sigma _{yy}=0$ in the laminar coordinate system. We assume that the rate of $\sigma _{yy}$ is also zero. In that case, we get

$0={\cfrac {D}{Dt}}(\sigma _{yy})=C_{13}~D_{xx}+C_{11}~D{yy}$

or,

$D_{yy}=-{\cfrac {C_{13}}{C_{11}}}~D_{xx}~.$

Plugging in the values we get

$D_{yy}=-\left({\cfrac {60}{10}}\right)~(2.4837)=-14.902~.$

Nonlinear finite elements/Homework 6/Solutions/Problem 1