Question

in copyable matlab code

The basic differential equation of the elastic curve for a cantilever beam as shown is given as: dx2 where E = the modulus of elasticity and I = the moment of inertia. Show how to use MATLAB ODE solvers to find the deflection of the beam. The following parameter values apply (make sure to do the conversion and use in as the Unit of Length in all calculations): E 30,000 ksi, 1 800 in4, P kips, L 10 ft 0

Answer 1

function dydx = odefun(x,y)

L = 10*12; %10 feet to in
E = 30000; I=800;P=1;

%converting 2nd order to two 1st order odes dy1dx and dy2dx
%let y1 = y and y2 = dy/dx
%differentiating y1 and y2 yields dy1dx = y2 and dy2dx = (-P/IE)(L-x)

dydx(1) = y(2); % dy1dx
dydx(2) = (-P/(E*I))*(L-x); % dy2dx

dydx = dydx'; %get transpose to return column vector
end

-------------------------------------------------------

clc
clear
close all

L = 10*12; %10 feet to in
xspan = 0:0.1:L;

y0 = [0 0]; %assuming y(0)=0 and y'(0)=0

model = ode45(@odefun,xspan,y0);

Y = model.y;
y = Y(1,:)'; %extract y1 which is the same as y
x = model.x;

plot(x,y)
grid on
xlabel('x')
ylabel('y')

0.005 -0.01 -0.015 -0.02 0.025 20 100 40 60 80 120

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