Question

Task 4 The material chosen for the body panels of an automobile will be subjected to cyclic loading (alternating positive and negative forces or stresses) during use. To test the material's behaviour in the laboratory under such cyclic loading, the force acting on the material is measured over time. A computer precisely determines when the material sample fractures. The equation describing the loading is: df dt F, sin(at) + F, cos(200) where F1 34 kN, F2 -18 kN and 33 rad/s. The material was observed to fracture after 3 hours, 15 minutes and 5 seconds. Write an M-file that uses ode45 and a step size of 0.01 seconds to determine what the force acting on the material was at the instant it fractures.

Answer 1

Code: func.m

function df = func(t, f)
global F1 F2 w
df = F1.*sin(w.*t) + F2.*cos(2.*w.*t);
  
end

Code: ForceODE.m

clc
clear
global F1 F2 w
F1 = 34; %kN
F2 = -18; %kN
w = 33; %rad/s
f0 = 0;

t = 0:0.01:(3*3600 + 15*60 + 5);
[t,f] = ode45(@func, t, f0);
% The force is negative when material fractures
disp("Force at instant material fractures = " + num2str(f(end))+"kN");

Output:

Scrap. Command Window Force at Instant material fractures =-0.27|63kN fy >