Can someone help me make a function for determining a global stiffness matrix for a truss?

Question

Benjamin Campbell 2016-2-3

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/266522-can-someone-help-me-make-a-function-for-determining-a-global-stiffness-matrix-for-a-truss

回答： Nagulavancha Sai Preetham 2022-6-18

I am confused on where to start and I can't get function command to not have errors.

2 个评论
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Geoff Hayes 2016-2-4

Benjamin - please clarify what you mean by I can't get function command to not have errors. If you have coded a function then please post it with the errors that you are observing so that we can try to help you understand where the problem is.

KSSV 2016-2-4

Are you using Finite element Method to get stiffness matrix of truss? You will not get a function inbuilt in MATLAB to get stiffness, you have to go through the equations and write you code depending on the numerical technique you are following.

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Answer 1

Nagulavancha Sai Preetham 2022-6-18

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/266522-can-someone-help-me-make-a-function-for-determining-a-global-stiffness-matrix-for-a-truss#answer_988110

在 MATLAB Online 中打开

clear
ne = input("No Of Elements : ");
n = input("No Of Nodes : ");
A = input("Enter A in m^2 : ");
E = input("Enter E kN/m^2 : ");
K(2*n, 2*n) = 0;
XY(n,2)=0;
for i = 1 : n
    XY(i,1) = input("X Coordinates of Node " + i + " : ");
    XY(i,2) = input("Y Coordinates of Node " + i + " : ");
end
Ele(ne, 4) = 0;
for i = 1 : ne
    Ele(i,1) = input("Start Node of Element " + i + " : ");
    Ele(i,2) = input("End Node of Element " + i + " : ");
    Ele(i,3) = ((XY(Ele(i,1),1)-XY(Ele(i,2),1))^2 + (XY(Ele(i,1),2)-XY(Ele(i,2),2))^2 )^(1/2);
    Ele(i,4) = atan((XY(Ele(i,1),2)-XY(Ele(i,2),2))/(XY(Ele(i,1),1)-XY(Ele(i,2),1)));
end
for i = 1 : ne
    K(Ele(i,1)*2-1,Ele(i,1)*2-1) = K(Ele(i,1)*2-1,Ele(i,1)*2-1) + cos(Ele(i,4))^2*(A*E/Ele(i,3));
    K(Ele(i,1)*2-1,Ele(i,1)*2) = K(Ele(i,1)*2-1,Ele(i,1)*2) + cos(Ele(i,4))*sin(Ele(i,4))*(A*E/Ele(i,3));
    K(Ele(i,1)*2-1,Ele(i,2)*2-1) = K(Ele(i,1)*2-1,Ele(i,2)*2-1) - cos(Ele(i,4))^2*(A*E/Ele(i,3));
    K(Ele(i,1)*2-1,Ele(i,2)*2) = K(Ele(i,1)*2-1,Ele(i,2)*2) - cos(Ele(i,4))*sin(Ele(i,4))*(A*E/Ele(i,3));
    
    K(Ele(i,1)*2,Ele(i,1)*2-1) = K(Ele(i,1)*2,Ele(i,1)*2-1) + cos(Ele(i,4))*sin(Ele(i,4))*(A*E/Ele(i,3));
    K(Ele(i,1)*2,Ele(i,1)*2) = K(Ele(i,1)*2,Ele(i,1)*2) + sin(Ele(i,4))^2*(A*E/Ele(i,3));
    K(Ele(i,1)*2,Ele(i,2)*2-1) = K(Ele(i,1)*2,Ele(i,2)*2-1) - cos(Ele(i,4))*sin(Ele(i,4))*(A*E/Ele(i,3));
    K(Ele(i,1)*2,Ele(i,2)*2) = K(Ele(i,1)*2,Ele(i,2)*2) - sin(Ele(i,4))^2*(A*E/Ele(i,3));
    
    K(Ele(i,2)*2-1,Ele(i,1)*2-1) = K(Ele(i,2)*2-1,Ele(i,1)*2-1) - cos(Ele(i,4))^2*(A*E/Ele(i,3));
    K(Ele(i,2)*2-1,Ele(i,1)*2) = K(Ele(i,2)*2-1,Ele(i,1)*2) - cos(Ele(i,4))*sin(Ele(i,4))*(A*E/Ele(i,3));
    K(Ele(i,2)*2-1,Ele(i,2)*2-1) = K(Ele(i,2)*2-1,Ele(i,2)*2-1) + cos(Ele(i,4))^2*(A*E/Ele(i,3));
    K(Ele(i,2)*2-1,Ele(i,2)*2) = K(Ele(i,2)*2-1,Ele(i,2)*2) + cos(Ele(i,4))*sin(Ele(i,4))*(A*E/Ele(i,3));
    
    K(Ele(i,2)*2,Ele(i,1)*2-1) = K(Ele(i,2)*2,Ele(i,1)*2-1) - cos(Ele(i,4))*sin(Ele(i,4))*(A*E/Ele(i,3));
    K(Ele(i,2)*2,Ele(i,1)*2) = K(Ele(i,2)*2,Ele(i,1)*2) - sin(Ele(i,4))^2*(A*E/Ele(i,3));
    K(Ele(i,2)*2,Ele(i,2)*2-1) = K(Ele(i,2)*2,Ele(i,2)*2-1) + cos(Ele(i,4))*sin(Ele(i,4))*(A*E/Ele(i,3));
    K(Ele(i,2)*2,Ele(i,2)*2) = K(Ele(i,2)*2,Ele(i,2)*2) + sin(Ele(i,4))^2*(A*E/Ele(i,3));
end
k = input("Enter Number of Q known : ");
Qk(k,1) = 0;
Dk(2*n-k,1) = 0;
Qu(2*n-k,1) = 0;
Du(k,1) = 0;
for i = 1 : k
    Qk(i,1) = input("Enter known Q " + i + " in kN/m^2 : " );
end
for i = k+1 : 1 : 2*n
    Dk(i,1) = input("Enter known D " + i + " in m : " );
end
k1 = K(1:k,1:k);
k2 = K(k+1:2*n,1:k);
Du = (k1^-1)*Qk;
Qu = k2*Du;
disp("ELement Information");
disp(Ele);
disp("Stiffness Matrix of System");
disp(K);
disp("D unknown in mm");
disp(1000*Du);
disp("Q unknown");
disp(Qu);

K is the Global Stiffness Matrix. Just make sure you number the nodes and members beforehand and enter the values in the right order. The code also returns the reaction forces and displacements aswell.