Table $1-$ Design requirements, part $($a$)$

The maximum stress in the component is $\backslash$sigma $=($FL$)/($C$\_(1)$Z$)$ where C$\_(1)$ is a constant depending on the

load distribution and Z is the section modulus of the section $($m$^(3)).$

The bending stiffness is S$\_($B$)=($C$\_(2)$EI$)/($L$^(3))$ where C$\_(2)$ is a constant depending on the load

distribution, E is the modulus of elasticity, and I is the second moment of the area $($m$^(4)).$

Use the data in Table $2$ and select the best material for this component. In this problem

F$=50$N$,$S$^(*)=3\backslash$times $10^(7)($N$)/($m$),$L$=20$cm$,$H$=8$cm$,$C$\_(1)=12,$ and C$\_(2)=36.$

Table $2-$ List of available materials

$($b$)$ For the same design, our constraints and objectives changed as reported in

Table $3.$ Deri.e the penalty function $($Z$)$ and select the best material from Table $2$ for the

following exchange constants; $\backslash$alpha $=1,\backslash$alpha $=10,$ and $\backslash$alpha $=100.$

Table $3-$ Design requirements, part $($b$)$