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How can I solve this question? And the ODE equation made me confused.

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Hi, I have a problem regarding my assignment using MATLAB. This is my first time using this MATLAB. Can anybody help me with this problem ?
A simply supported beam of length is loaded by a distributed load and a tensile axial force as shown in the figure. The deflection of the beam, is determined from the solution of the following ODE:
(d^2 y)/(dx^2 )=1/EI [1+(dy/dx)^2 ]^(3/2) [1/6 q_0 (Lx-x^3/L)+Ty]
with the boundary conditions y(0)=0 and y(L)=0 .
EI=1.2×(10)^7 Nm^2 is the flexural rigidity, q_0= 30x(10)^3 N/m, and T=20x(10)^3 N .

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Accepted Answer

Ameer Hamza
Ameer Hamza on 29 Jun 2020
Edited: Ameer Hamza on 29 Jun 2020
See bvp4c() for boundary condition problems. Something like this
EI = 1.3e7;
q0 = 30e3;
T = 20e3;
L = 4;
xmesh = linspace(0, L, 100);
odeFun = @(x, y) [y(2);
1./EI*(1+y(2).^2).^(3/2)*(1/6*q0*(L*x-x.^3/L)+T*y(1))];
bcFun = @(yl, yr) [yl(1)-0; % y(0) = 0
yr(1)-0]; % y(L) = 0;
guess = bvpinit(xmesh, [0; 0]);
y_sol = bvp4c(odeFun, bcFun, guess);
plot(y_sol.x, y_sol.y);
legend({'$y$', '$\dot{y}$'}, 'Location', 'best', 'FontSize', 16, 'Interpreter', 'latex');

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