How to generate an nxn matrix using n number of 2x2 matrices?

Question

Monique Embury 2019-1-22

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/440965-how-to-generate-an-nxn-matrix-using-n-number-of-2x2-matrices

评论： Monique Embury 2019-1-29

Hi,

I am having trouble generating a code in the exisiting loop to create a global stiffness matrix from each element stiffness matrix. I am trying to program matlab to do something similar to this.

I have written the code and loop to generate the connectivity matrix and each element stiffness matrix. I am hoping to use the same loop to generate the global stiffness matrix.

e = %connectivity table
     1     1     2
     2     2     3
     3     3     4
     4     4     5
     5     5     6
     6     6     7
%element stiffness matricies
ke(:,:,1) =
    1.5708   -1.5708
   -1.5708    1.5708
ke(:,:,2) =
    0.8836   -0.8836
   -0.8836    0.8836
ke(:,:,3) =
    0.6981   -0.6981
   -0.6981    0.6981
ke(:,:,4) =
    0.6136   -0.6136
   -0.6136    0.6136
ke(:,:,5) =
    0.5655   -0.5655
   -0.5655    0.5655
ke(:,:,6) =
    0.5345   -0.5345
   -0.5345    0.5345
>> 

Can anyone help me?

Thank you!

%Element connectivity Table
n=6; %creates 6 elements 
e=[]; %creates empty connectivity matrix 
k=[1 -1;-1 1]; %standard format of K
ke=[]; %creates empty element stiffness matrix
Ae=[]; %creates empty element area amatrix
ks=zeros(n,n);
E=1; 
L=2;
R1=1;
R2=0.5;
i=1;
for m=1:n; %goes through each element
    i=i;
    j=i+1;
    x=L/m;%thickness of each slice of the beam
    A1=pi()/L^2*(R2*L+(R1-R2)*x)^2;%area of each slice of the beam 
    Ae(:,m)=[A1];%stores each area in a matrix
    e(m,:)= [m i j];%stores results in matrix 
    ke(:,:,m)=E*Ae(:,m)/L*k; %stores each element stiffness matrix
end

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Guillaume 2019-1-23

I'm also not sure what the question is. Furthermore, as far as I can tell you explain how to form a matrix for two springs in series but not when they're in parallel. I don't know anything about stiffness matrices, but I would assume the result is not the same for parallel springs.

I can see several possible question with what you have described. Given a connectivity table, the first task would probably be to find which springs are in parallel and which are in series. Once that is done you would then have to assemble the matrices according to the relevant formula. It's not clear which part of this you need help with.

Monique Embury 2019-1-23

In my problem, the springs are in series.

The image posted is an example of what I am trying to do. In the example, 2 2x2 matrices are combined to make a 3x3 matrix.

I am trying to combine 6 2x2 matrices to create a 6x6 matrix in a similar fashion. I am not sure how to program this. That is what I am seeking help on.

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Answer 1

Guillaume 2019-1-24

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/440965-how-to-generate-an-nxn-matrix-using-n-number-of-2x2-matrices#answer_357811

在 MATLAB Online 中打开

"I am trying to combine 6 2x2 matrices to create a 6x6 matrix in a similar fashion"

According to your algorithm the stiffness matrix will be 7x7 not 6x6. It is trivial to achieve

% inputs:
% ke: a 2x2xN matrix
stiffness_matrix = zeros(size(ke, 3) + 1);  %create a (N+1)x(N+1) matrix of 0s
for idx = 1:size(ke, 3)
    stiffness_matrix(idx:idx+1, idx:idx+1) = stiffness_matrix(idx:idx+1, idx:idx+1) + ke(:, :, idx);
end

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Monique Embury 2019-1-28

编辑：Monique Embury 2019-1-28

在 MATLAB Online 中打开

I now have another problem silimar to the other. My element matrices are now 4x4 with 11 of them. I would like to add all the element matricies to make a global one. The problem this time, the elements and nodes are not in numerical order. Can you help with the KG matrix?

E=1.9E6; % lb/in^2 modulus of elasticity
A2=21.5; % in^2 area of cross section
EA2=E*A2;
node=[1 0 0; 2 8.7*12 0; 3 6*12 2.2*12; 4 12*12 4.4*12; 5 15.3*12 0; 6 18*12 2.2*12; 7 24*12 0]%node, x, y 
e2=[1 1 3; 2 1 2; 3 2 3; 4 3 4; 5 2 4; 6 2 5; 7 4 5; 8 4 6; 9 5 6; 10 5 7; 11 6 7] %element, node1, node2
d=11; %11 elements 
KE=zeros(4,4); %empty matrix to store element stiffness maxtrix
for c=1:d;
    I=e2(c,2);
    J=e2(c,3);
    xI=node(I,2);
    yI=node(I,3);
    xJ=node(J,2);
    yJ=node(J,3);
    L=sqrt((xJ-xI)^2+(yJ-yI)^2);
    l=(xJ-xI)/L;
    m=(yJ-yI)/L;
    KE(:,:,c)=EA2/L*[l^2 l*m -l^2 -l*m; l*m m^2 -l*m -m^2; -l^2 -l*m l^2 l*m;  -l*m -m^2 l*m m^2]
    for n=1:2; %number of nodes in each element 
        for o=1:2;
            I=e2(c,n);
            J=e2(c,o);
            for p=1:2; %DOF for each element 
                for t=1:2;
                    KG((I-1)*2+p, (J-1)*2+t)=KG((I-1)*2+p, (J-1)*2+t)+KE((n-1)*2+p, (o-1)*2+t);
                end 
            end
        end 
    end 
end

Thank you!

Monique Embury 2019-1-29

在 MATLAB Online 中打开

With this code:

E=1.9E6; % lb/in^2 modulus of elasticity
A2=21.5; % in^2 area of cross section
EA2=E*A2;
node=[1 0 0; 2 8.7*12 0; 3 6*12 2.2*12; 4 12*12 4.4*12; 5 15.3*12 0; 6 18*12 2.2*12; 7 24*12 0]%node, x, y 
e2=[1 1 3; 2 1 2; 3 2 3; 4 3 4; 5 2 4; 6 2 5; 7 4 5; 8 4 6; 9 5 6; 10 5 7; 11 6 7] %element, node1, node2
d=11; %11 elements 
KE=zeros(4,4); %empty matrix to store element stiffness maxtrix
KG=[];
for c=1:d;
    I=e2(c,2);
    J=e2(c,3);
    xI=node(I,2);
    yI=node(I,3);
    xJ=node(J,2);
    yJ=node(J,3);
    L=sqrt((xJ-xI)^2+(yJ-yI)^2);
    l=(xJ-xI)/L;
    m=(yJ-yI)/L;
    KE(:,:,c)=EA2/L*[l^2 l*m -l^2 -l*m; l*m m^2 -l*m -m^2; -l^2 -l*m l^2 l*m;  -l*m -m^2 l*m m^2]
    stiffness_matrix = zeros(2*max([e2(:, 2); e2(:, 3)]));
        for idx = 1 : size(e2, 1)
            indices = 2 * e2(idx, 2:3) - [1;0];  %creates a 2x2 matrix of indices [2i-1, 2j-1; 2i, 2j]
            stiffness_matrix(indices, indices) = stiffness_matrix(indices, indices) + KE(:, :, idx);
        end
end

I get this error:

Index in position 3 exceeds array bounds (must not exceed 1).
Error in MECH532_Project1_Embury (line 98)
            stiffness_matrix(indices, indices) = stiffness_matrix(indices, indices) + KE(:, :, idx);

Any Ideas on how to fix it?

Thank you!

Guillaume 2019-1-29

The construction of the stiffness matrix can only happen after KE has been fully constructed, not during the construction, so move that code after the c loop.

Monique Embury 2019-1-29

You are amazing and thank you so very much for your help!

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Answer 2

jahanzaib ahmad 2019-1-22

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/440965-how-to-generate-an-nxn-matrix-using-n-number-of-2x2-matrices#answer_357557

编辑：Guillaume 2019-1-23

u just want to add stiffness matrix of each element to get n x n stiffness matrix

423601-assemble-global-stiffness-matrix

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jahanzaib ahmad 2019-1-22

编辑：jahanzaib ahmad 2019-1-22

else share code and explain bit more about problem please

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How to generate an nxn matrix using n number of 2x2 matrices?

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