$(25$ points$)$ Conduct finite element analysis to verify the stress concentration factor

for a plate with a hole in it$.$ Use the last digit in your ID

as the a$/$b ratio. Make appropriate assumptions

about material properties and symmetry.

For an infinite plate, the solution is:

${}_{\text{m}\text{a}\text{x}}=(1+2\frac{a}{b}){}_{\text{n}\text{o}\text{m}}$

$($Where $$ represents stress, a and b are

dimensions of the hole$)$

For a plate with finite width $D,$ the solution Is:

Roarks Equation for Elliptical Hole Stress Concentration Factor

$K=Cl+C2*(\frac{2*a}{D})+C3*(\frac{2*a}{D}{)}^2+C4*(\frac{2*a}{D}{)}^3$

$Cl=1\mathrm{.}00+2\mathrm{.}00*(\frac{a}{b})$

$C2=-0\mathrm{.}351-0\mathrm{.}021*\sqrt[\phantom{2}]{(\frac{a}{b})}-2\mathrm{.}483*(\frac{a}{b})$

$C3=3\mathrm{.}621-5\mathrm{.}183*\sqrt[\phantom{2}]{(\frac{a}{b})}+4\mathrm{.}494*(\frac{a}{b})$

$C4=-2\mathrm{.}270+5\mathrm{.}204*\sqrt[\phantom{2}]{(\frac{a}{b})}-4\mathrm{.}011*(\frac{a}{b})$

Note: The stress concentration factor calculation for the first problem has a small detail that

may result in a higher value for stress concentration than the analytical solution. The

definition of the stress concentration factor is the ratio of stress at a geometrical

discontinuity to the nominal stress at the location if stress concentration did not exist. Now,

for an infinite$-$width plate, this will not be a problem as the nominal stress will be the stress

that you are applying far away from the stress location. So you can use the nominal stress as

the stress that you applied in the FEM.