Question

2. Use MATLAB (ode45) to solve the second-order Euler-Cauchy ODE given in the thick-walled tube elasticity problem handout for the case:

?_r(1) = 0.1, du_r(1)/dr = −0.02

Have your MATLAB code print out the values for the constants you determined in the general solution; i.e. “C1 = ... , C2 = ...” make a comparison plot showing your exact solution and the numerical MATLAB result on the same axes.

Answer 1

Here is the solution. Please do upvote thank you.

Code:

clear all

close all

clc

r=[1:0.5:25];

u0=[0.1-0.02];

[r,u]=ode45(@(r,u) Euler_Cauchy(r, u), r, u0) ;

plot(r, u(:, 1))

axis([1,25 min(u(:, 1)) max(u:, 1))])

xlabel('r');

ylabel('u(r)');

Code 2:

function [udot]=Euler_Cauchy(r, u) ;

udot(1)=u(2);

udot(2)=-(u(2).r+2*u(1).r/.^2);

udot=udot'

end