index exceeds the number of array elements

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Mostafa Moradi
Mostafa Moradi 2021-3-29
评论： Cris LaPierre 2021-3-29
I try to plot the deflection of a simply supported beam using rk4 with the following initial conditions
y(0)=0 and y (L)=0
L= length of beam
close all
clear all
clc
%constants
E=20*10^9;
w=0.05;
h=0.1;
I= w*h^3/12;
L=5;
q=1500*L;
% converting 2nd ODE into two 1st ODE
% y''=(-q/2.*(x.^2-L.*x))/EI
% let y'=d , y(0)=0;
% define function handles
%y=(x, d) <= y(1,:)=y y(2,:)=d
Y= @(x,y) [ ...
y(2);
(-q/2.*(x.^2-L.*x))/(E*I)];
%stepsize
Length=5;
h=0.0001;
n=Length/h;
% initial conditions
% at position x=0 and x=L, position is fixed and thus y(1,1)
x(1)=0;
y(1,1)=0;
y(1,n)=0;
%loop
for i= 1:n
%timeloop
x(i+1)= x(i)+h;
%rk loop
k1= Y(x(i) ,y(:,i) );
k2= Y(x(i)+0.5.*h,y(:,i)+0.5.*k1.*h);
k3= Y(x(i)+0.5.*h,y(:,i)+0.5.*k2.*h);
k4= Y(x(i)+ h,y(:,i)+ k3.*h);
y(:,i+1)= y(:,i)+h.*(k1+2*k2+2*k3+k4)/6;
end
figure
plot (x, y(1,:))
title('question6')
hold on
plot (x, y(2,:))
hold on
a1=plot (x, y(1,:)) ; M1="distance vs position";
a2=plot (x, y(2,:)) ; M2="distance vs deflection";
legend([a1, a2],[M1, M2])
hold off

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回答（1 个）

Cris LaPierre
Cris LaPierre 2021-3-29
Ran in:
The error message is telling you the issue. Somewhere in your code, you are indexing an array using an index value greater than the length of the array.
A=1:5;
% This works
a=A(5)
a = 5
% This does not
b=A(8)
Index exceeds the number of array elements (5).
  6 个评论
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Mostafa Moradi
Mostafa Moradi 2021-3-29
I'm still not sure if this method (rk4) is appropriate to simulate the deflection of a simply supported beam
which has this deflection formula d2y/dx2=(-q/2*(x^2-L*x))/(2*E*I)
I do know that centered finited difference method (CFD) works well for this problem but I don't know how to use CFD to reduce the problem in matrixes and obtain the solution.
Cris LaPierre
Cris LaPierre 2021-3-29
I suspect the issue is with your implementation of the runge-kutta method. That is a different question than the one asked here. You could search this forum to find hundreds of answers on implementing it.

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