ROF$-002$

You are tasked with analyzing the thermal stress in a complex mechanical component subjected to high temperatures. The component is made of a material with nonlinear thermal expansion behavior. As the component is heated up$,$ you need to determine the critical temperature at which the component will experience a sudden change in stress. The thermal stress in the component can be calculated using the following equation:

$=(\frac{E}{1-v})[(T-T_0)-(T-T_0{)}^2],$ for $T{T}_{\text{c}\text{r}\text{i}\text{t}}$

where:

$=$ thermal stress in the component at temperature $T$

$E=2e11\frac{(N)}{m^2}=$ Young's modulus of the material

$v=0\mathrm{.}3=$ Poisson ratio

$(,)=(1\mathrm{.}2{10}^{-5}\frac{1}{C},2\mathrm{.}8{10}^{-9}\frac{1}{C^2})=$ material$-$specific coefficients

$T_0=25C=$ reference temperature.

a$)$ Given $T=200C,$ calculate the thermal stress. Assume $T_{\text{c}\text{r}\text{i}\text{t}}>200C.$

b$)$ Implement the Bisection Method to find the critical temperature $(T_{\text{c}\text{r}\text{i}\text{t}}),$ the temperature at which the stress is closest to ${}_{limit}=75{10}^7\frac{(N)}{m^2}.$ Iterate until the absolute error falls below $0\mathrm{.}001.$

c$)$ Plot the thermal stress as a function of temperature. Indicate the critical temperature and stress limit on the plot.

Write this in MATLAB please!