error in matrix multiplication and integration

%%
clc;
clear;
syms x;
%pi = 180.;
% syms y_x;
% syms y_x_das; 
L = 100.; 
E = 29000. ; 
c = 0.1*L;
d_0 = 5.; 
d_1 = 2.*d_0;
d_x = 2.*d_0*(x/(2.*L));
b = 2.; 
I_z = (b*d_x.^3)/12.;
G = 11000.;
A_x = b*d_x; 
As = 5/6*A_x;
y_x = c*sin(2*pi*x/L);
y_x_das = diff(y_x);
theta_2 = atan(y_x_das);
Q_a = [-cos(theta_2) -sin(theta_2) 0];
Q_s = [-sin(theta_2) -cos(theta_2) 0];
Q_b = [-c*sin((2*pi*x)/L) x -1];
%%
%flexibility matrix
d1= sqrt(1 + y_x_das.^2).*((Q_a'.*Q_a)./(A_x*E));
d1_int = integral(@(x) d1(), 0, 100., 'ArrayValued', 1);

Error using superiorfloat
Inputs must be floats, namely single or double.

Error in integralCalc/iterateArrayValued (line 159)
outcls = superiorfloat(x,fxj);

Error in integralCalc/vadapt (line 130)
[q,errbnd] = iterateArrayValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 87)
Q = integralCalc(fun,a,b,opstruct);

[Star Strider]

I got this to run, although the integral may not exist.

When I went to plot ‘d1’ to see what the function looked like (thinking that perhaps the singularities would show themselves), I got a matrix size incompatibility error.

Using arrayfun to see what the matrices look like, they all appear to be NaN(3) for every value of ‘yv’.

That needs to be investigated —

%%
clc;
clear;
% syms x;
%pi = 180.;
% syms y_x;
% syms y_x_das; 
L = 100.; 
E = 29000. ; 
c = 0.1*L;
d_0 = 5.; 
d_1 = 2.*d_0;
d_x = @(x) 2.*d_0*(x/(2.*L));
b = 2.; 
I_z = @(x) (b*d_x(x).^3)/12.;
G = 11000.;
A_x = @(x) b*d_x(x); 
As = @(x) 5/6*A_x(x);
y_x = @(x) c*sin(2*pi*x/L);
y_x_das = @(x) gradient(y_x(x))./gradient(x);
theta_2 = @(x) atan(y_x_das(x));
Q_a = @(x) [-cos(theta_2(x)) -sin(theta_2(x)) 0];
Q_s = @(x) [-sin(theta_2(x)) -cos(theta_2(x)) 0];
Q_b = @(x) [-c*sin((2*pi*x)/L) x -1];
%%
%flexibility matrix
d1 = @(x) sqrt(1 + y_x_das(x).^2).*((Q_a(x)'.*Q_a(x))./(A_x(x)*E));
d1_int = integral(@(x)d1(x), 1E-8, 100., 'ArrayValued', 1)

Warning: Inf or NaN value encountered.

d1_int = 3×3

NaN NaN NaN NaN NaN NaN NaN NaN NaN

xv = linspace(0, 100);
yv = arrayfun(d1, xv, 'Unif',0);

yv{1}

ans = 3×3

NaN NaN NaN NaN NaN NaN NaN NaN NaN

yv{end}

ans = 3×3

NaN NaN NaN NaN NaN NaN NaN NaN NaN

.

[Walter Roberson]

Pi = sym(pi);
syms x real

L = 100.; 
E = 29000. ; 
c = 0.1*L;
d_0 = 5.; 
d_1 = 2.*d_0;
d_x = @(x) 2.*d_0*(x/(2.*L));
b = 2.; 
I_z = @(x) (b*d_x(x).^3)/12.;
G = 11000.;
A_x = @(x) b*d_x(x); 
As = @(x) 5/6*A_x(x);
y_x = @(x) c*sin(2*Pi*x/L);
y_x_das = @(x) gradient(y_x(x))./gradient(x);
theta_2 = @(x) atan(y_x_das(x));
Q_a = @(x) [-cos(theta_2(x)) -sin(theta_2(x)) 0];
Q_s = @(x) [-sin(theta_2(x)) -cos(theta_2(x)) 0];
Q_b = @(x) [-c*sin((2*Pi*x)/L) x -1];
%%
%flexibility matrix
d1 = @(x) sqrt(1 + y_x_das(x).^2).*((Q_a(x)'.*Q_a(x))./(A_x(x)*E));

d1_x = d1(x)

d1_x = 

%d1_int = integral(@(x)d1(x), 1E-8, 100., 'ArrayValued', 1)
d1_int = int(d1_x, 1e-8, 100)

d1_int = 

vpa(d1_int)

ans = 

[Torsten]

@Milan comment moved here:

Thanks alot, this works now!

[Torsten]

@Milan question moved here:

Hello,

I got a 6*6 matrix in this format, how do I get this as a one single matrix?

[ 626.35, -97.77, -4756.45, -626.35, 97.77, -5020.31]

[ -97.77, 35.79, 2115.79, 97.77, -35.79, 1462.95]

[-4756.45, 2115.79, 142701.95, 4756.45, -2115.79, 68877.21]

[ -626.35, 97.77, 4756.45, 626.35, -97.77, 5020.31]

[ 97.77, -35.79, -2115.79, -97.77, 35.79, -1462.95]

[-5020.31, 1462.95, 68877.21, 5020.31, -1462.95, 77418.13]

[Torsten]

The output might be written in this format - internally, it's a usual matrix.

[Torsten]

@Milan comment moved here

But I want to present with in one bracket

[Torsten]

Could you include the code that gave this output for the matrix ?

And please don't use the answer button because you only make comments.

[Milan]

%unit inch, ksi, 
clc;
clear;
close;
Pi = sym(pi);
syms x real
L = 100.; 
E = 29000. ; 
c = 0.1*L;
d_0 = 5.; 
b = 2.;
d_1 = b*d_0;
d_x = @(x) 2.*d_0*(1-(x/(2.*L)));
b = 2.; 
I_z = @(x) (b*d_x(x).^3)/12.;
G = 11000.;
A_x = @(x) b*d_x(x); 
As = @(x) 5/6*A_x(x);
y_x = @(x) c*sin(2*Pi*x/L);
y_x_das = @(x) gradient(y_x(x))./gradient(x);
theta_2 = @(x) atan(y_x_das(x));
Q_a = @(x) [-cos(theta_2(x)) -sin(theta_2(x)) 0];
Q_s = @(x) [sin(theta_2(x)) -cos(theta_2(x)) 0];
Q_b = @(x) [-c*sin((2*Pi*x)/L) x -1];
%%
%flexibility matrix
d1 = @(x) sqrt(1 + y_x_das(x).^2).*((Q_a(x)'.*Q_a(x))./(A_x(x)*E));
d1_x = d1(x);
d1_int = int(d1_x, 1e-8, L);
d_11 = vpa(d1_int);
d2 = @(x) sqrt(1 + y_x_das(x).^2).*(Q_s(x)'.*Q_s(x))./(G*As(x));
d2_x = d2(x);
d2_int = int(d2_x, 1e-8, L);
d_22 = vpa(d2_int);
%no shear consideration
% G_noshear = Inf;
% d2_noshear = @(x) sqrt(1 + y_x_das(x).^2).*(Q_s(x)'.*Q_s(x))./(G_noshear*As(x));
% d2_x_noshear = d2_noshear(x);
% d2_int_noshear = int(d2_x, 1e-8, L);
% d_22_noshear = vpa(d2_int);
d_22_noshear = 0;
d3 = @(x) sqrt(1 + y_x_das(x).^2).*(Q_b(x)'.*Q_b(x)) ./(E*I_z(x));
d3_x = d3(x);
d3_int = int(d3_x, 1e-8, L);
d_33 = vpa(d3_int);
d = d_11+d_22+d_33; %flexibility matrix
d_noshear =  d_11+d_33;
% equllibrium matrix
phi = [-1 0 0; 0 -1 0; 0 L -1];
%Siffness matrix 
Kff = inv(d);
Kfs = inv(d)*phi'; 
Ksf = phi*inv(d);
Kss = phi*inv(d)*phi';
K = round([Kff Kfs; Ksf Kss], 2);
%no shear stiffness matrix
Kff_ns = inv(d_noshear);
Kfs_ns = inv(d_noshear)*phi'; 
Ksf_ns = phi*inv(d_noshear);
Kss_ns = phi*inv(d_noshear)*phi';
K_noshear = round([Kff_ns Kfs_ns; Ksf_ns Kss_ns], 2)

K_noshear = 

% K = [inv(d) inv(d).*phi';
%      phi.*inv(d) phi.*inv(d).*phi'];
sdof = ([1, 2, 5]);
fdof = ([3,4,6]);
K_ff = K(fdof, fdof);
f_f = [300 100 0]';
delta_f = inv(K_ff)*f_f;
theta_z1 = round(delta_f(1,:),5);

[Walter Roberson]

mat2str() will show it with just one []

Note: mat2str() may lose the bottom bit of numbers. format long g loses the bottom bit of numbers. If you need to be able to exactly reproduce the array then you will need to create your own function to convert it.