Error in sum of matrixes

Dear Community,

I need to create a script where I obtain a matrix as an output. In addition, such matrix is a resultant matrix of the sum of 8 other matrixes. Unfortunately when I create the for loop it saves only the 8th matrix in the variable that I created to fulfill such requirement. Could you pelase help me?

clc

close all

clear all

m = 5;

Z = randi(20,1,10);

n = size(Z,2);

Z_out = [Z;zeros(m-1,n)];

for ii=2:m

Z_out(ii,:) = Z_out(ii-1,:) + randi(5,1,n);

end

%% Copiando el sistema

Nplies = 8;

thetadt = [90; -45; 45; 0; 0; 45; -45; 90];

t = 0.125; %SI unit, milimeters

h = Nplies*t;

% Ply engineering properties (UD-Laminat)

E1 = 240000; % N/mm^2

nu12 = .3133 ;

E2 = 7500 ; % N/mm^2

G12 = 5150 ; % N/mm^2

nu21 = .3133 ; %nu12 * E2 / E1

a1 = -0.38e-7 ; % coefficients of thermal expansion [1/°C]

a2 = 1e-5 ;

deltaT = 0;

% Q matrix (material coordinates)- reduced stiffness matrix

denom = 1 - nu12 * nu21 ;

Q11 = E1 / denom ; %reduced stiffness coefficients

Q12 = nu12 * E1 / denom ;

Q21 = nu12 * E2 / denom ;%reduced stiffness coefficients

Q22 = E2 / denom ; %reduced stiffness coefficients

Q66 = G12 ; %reduced stiffness coefficients

m = 3;

Ai = [1,0,0;0,1,0;0,0,1];

Aii = zeros(3,3);

Qbari = zeros(3,3);

R = [1,0,0;0,1,0;0,0,2];

Q = [ E1/denom nu12*E1/denom 0; nu12* E2/denom E2/denom 0; 0 0 G12]; %Reduced stiffness matrix

AA=[];

for i = 1:Nplies

theta = thetadt(i) * pi / 180;% ply i angle in radians, from bottom

c = cos(theta);

s = sin(theta);

T = [ c^2 s^2 -2*c*s; s^2 c^2 2*c*s; c*s -c*s (c^2 - s^2)];

T_inv = [c^2 s^2 c*s; s^2 c^2 -c*s; -2*c*s 2*c*s (c^2 - s^2)];

Qbar = Qbari + T * Q * T_inv %transformed reduced stiffness matrix

A{i,1,1} = Aii + Qbar*t

end

Af = A{1,1,1} + A{2,1,1} + A{3,1,1} + A{4,1,1} + A{5,1,1} + A{6,1,1} + A{7,1,1} + A{8,1,1}

%% another approach

res=0;

for k=1:5

M=rand(4);

res=bsxfun(@plus,res,M);

end

%%

%if ii<2

% A=0;

% else

%transformed reduced stiffness matrix

% A = Aii + Qbar*(ii-1)*t

% end

[Image Analyst]

To format your code, in MATLAB, type control-a, control-i to fix the indenting. Then control-c to copy. Then back here, paste it in, and highlight it, then click the Code icon on the toolbox. Which of these matrices do you consider to be the "resultant matrix"?

[Marcelo Boldt]

A Matrix is the resultant matrix and should be 3x3. The problem I am facing is that I get the different Ai submatrixes but I can't obtain the resultant matrix which is the sum of the 8 Ai matrixes

[Image Analyst]

Did you try the answer below? And why didn't you format your code like I suggested?

[Marcelo Boldt]

Yes I tried and it works but not as planed. Here are the modifications/editing

Answer 1

[Rafael Hernandez-Walls]

try this

Nplies = 8;
thetadt = [90; -45; 45; 0; 0; 45; -45; 90];
t = 0.125; %SI unit, milimeters
h = Nplies*t;
% Ply engineering properties (UD-Laminat)
E1   =  240000; % N/mm^2
nu12 = .3133 ;
E2   = 7500  ; % N/mm^2
G12  = 5150  ; % N/mm^2
nu21 = .3133 ; %nu12 * E2 / E1
a1 = -0.38e-7 ; % coefficients of thermal expansion [1/°C]
a2 = 1e-5 ;
deltaT = 0;
% Q matrix (material coordinates)- reduced stiffness matrix
 denom = 1 - nu12 * nu21 ;
Q11 = E1 / denom        ; %reduced stiffness coefficients
Q12 = nu12 * E1 / denom ;
Q21 = nu12 * E2 / denom ;%reduced stiffness coefficients
Q22 = E2 / denom        ; %reduced stiffness coefficients
Q66 = G12             ; %reduced stiffness coefficients
m = 3;
Ai = [1,0,0;0,1,0;0,0,1];
Aii = zeros(3,3);
R = [1,0,0;0,1,0;0,0,2];
Q = [ E1/denom nu12*E1/denom 0; nu12* E2/denom E2/denom 0; 0 0 G12]; %Reduced stiffness matrix
AA=[];
for i = 1:Nplies
    
    theta = thetadt(i) * pi / 180;% ply i angle in radians, from bottom
  
        c = cos(theta) 
  
        s = sin(theta)  
  
        T = [ c^2 s^2 -2*c*s; s^2 c^2 2*c*s; c*s -c*s (c^2 - s^2)]
  
        T_inv = [c^2 s^2 c*s; s^2 c^2 -c*s; -2*c*s 2*c*s (c^2 - s^2)]
        Qbar = T * Q * T_inv;
        
        for ii=2
            
        
        
        %transformed reduced stiffness matrix
        
        A = Aii + Qbar*(ii-1)*t;
        AA = [AA; sum(A,1)]
        end 
        
end

[Marcelo Boldt]

Hi, thanks for your help. I tried the problem but unfortunately I cant obtain what I need to. the matrix A is what I am trying to calculate. This matrix is a 3x3 but the problem that I am facing is that after my most recent update I am getting a 8x1 array where in each row I have a 3x3 matrix inside and I cant usa that data for further plots or anything like that.

Nplies = 8; % number of plies

thetadt = [90; -45; 45; 0; 0; 45; -45; 90];

t = 0.125; % thickness [SI unit], milimeters

h = Nplies*t;

% Ply engineering properties (UD-Laminat)

E1 = 131900; % N/mm^2

nu12 = .3 ;

E2 = 9700 ; % N/mm^2

G12 = 5200 ; % N/mm^2

nu21 = .022 ; %nu12 * E2 / E1

a1 = 4e-7 ; % coefficients of thermal expansion [1/°C]

a2 = 3e-5 ; % coefficients of thermal expansion [1/°C]

a = [a1 a2 0]'; % coefficients of thermal expansion vector [1/°C]

deltaT = 30;

% Q matrix (material coordinates)- reduced stiffness matrix

denom = 1 - nu12 * nu21 ;

Q11 = E1 / denom ; %reduced stiffness coefficients

Q12 = nu21 * E1 / denom ;

Q21 = nu12 * E2 / denom ;%reduced stiffness coefficients

Q22 = E2 / denom ; %reduced stiffness coefficients

Q66 = G12 ; %reduced stiffness coefficients

% Classical laminar theory

% m = 3; To use it in case I need HIBEF

Ai = zeros(3,3);

Bi = zeros(3,3);

Di = zeros(3,3);

NTi = zeros(3,1);

MTi = zeros(3,1);

Qbari = zeros(3,3);

NT_plot =[];

nt_plot = zeros(3,1);

R = [1,0,0;0,1,0;0,0,2];

Q = [ E1/denom nu21*E1/denom 0; nu12* E2/denom E2/denom 0; 0 0 G12]; %Reduced stiffness matrix

for i = 1:Nplies

zbar(i) = -(h + t)/2 + i*t;

theta = thetadt(i) * pi / 180;% ply i angle in radians, from bottom

c = cos(theta);

s = sin(theta);

T = [ c^2 s^2 -2*c*s; s^2 c^2 2*c*s; c*s -c*s (c^2 - s^2)];

T_inv = [c^2 s^2 c*s; s^2 c^2 -c*s; -2*c*s 2*c*s (c^2 - s^2)];

Qbar = T * Q * T_inv; %transformed reduced stiffness matrix

Qbar2 {i,1,1} = Qbari + T * Q * T_inv;

A{i,1} = Ai + Qbar*t;

end