Hi, my loop function is not working and giving me index error in my member stiffens matrix. any idea what is the issue? thank you

%define coordinates of each nodes%
Coord_nodes = [0 0; 10 0; 10 10; 0 10];
% define connection of each element%
Connect_elements = [1 2; 1 3; 1 4; 4 3; 4 2; 2 3];
%define degree of Freedom of each nodes
Deg_free=[1 2; 6 5; 7 8; 3 4];
% define number of reactions at supports
Nr= 3;
%define number of members
Nm= 6;
%define number of nodes
Nn= 4;
%define EA
EA= 1;
%define Lenght of each member
L=zeros(Nm,1);
L= [10; 14.14 ;10 ;10 ; 14.14 ;10]

L = 6×1

10.0000 14.1400 10.0000 10.0000 14.1400 10.0000

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% creation of ID Array
ID = zeros(Nm,4);
for k = 1:Nm
    i = Connect_elements(k,1);
    j = Connect_elements(k,2);
    ID(k,1:2)=Deg_free(i,1:2);
    ID(k,3:4)=Deg_free(j,1:2);
end

% assemble Global Stiffness matrix
Kg=zeros(8,8);
for k = 1:Nm
    i = Connect_elements(k,1);
    j = Connect_elements(k,2);
    Lamda_x= (Coord_nodes(j,1)- Coord_nodes(i,1))/L(k)
    Lamda_y= (Coord_nodes(j,2)- Coord_nodes(i,2))/L(k)
end

Lamda_x = 1

Lamda_y = 0

Lamda_x = 0.7072

Lamda_y = 0.7072

Lamda_x = 0

Lamda_y = 1

Lamda_x = 1

Lamda_y = 0

Lamda_x = 0.7072

Lamda_y = -0.7072

Lamda_x = 0

Lamda_y = 1

%member Stiffness matrix
for k = 1:Nm
    
    k11(k)= (Lamda_x(k)^2/L(k));
    k12(k)= (Lamda_x(k)*Lamda_y(k))/L(k);
    k13(k)= -k11(k);
    k14(k)= (-Lamda_x(k)*Lamda_y(k))/L(k);
    k21(k)= k12(k);
    k22(k)= (Lamda_y(k))^2/L(k);
    k23(k)= -k12(k);
    k24(k)= -k22(k);
    k31(k)= -k11(k);
    k32(k)= k23(k);
    k33(k)= k11(k);
    k34(k)= k12(k);
    
    k41(k)= k14(k);
    k42(k)= k24(k);
    k43(k)= k12(k);
    k44(k)= k22(k);
    k_elem(:,:,k)= [k11(k) k21(k) k31(k) k41(k);
        k12(k) k22(k) k32(k) k42(k);
        k13(k) k23(k) k33(k) k43(k);
        k14(k) k24(k) k34(k) k44(k)]
end

k_elem = 4×4

0 0 0 0 0 0.1000 0 -0.1000 0 0 0 0 0 -0.1000 0 0.1000

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Index exceeds the number of array elements. Index must not exceed 1.

Answer 1

[Stephen23]

% define coordinates of each nodes
Coord_nodes = [0,0; 10,0; 10,10; 0,10];
% define connection of each element
Connect_elements = [1,2; 1,3; 1,4; 4,3; 4,2; 2,3];
% define degree of Freedom of each nodes
Deg_free = [1,2; 6,5; 7,8; 3,4]; % [x-direction DOF, y-direction DOF]
% define number of reactions at supports
Nr = 3;
% define number of members
Nm = size(Connect_elements,1);
% define number of nodes
Nn = 4;
% define EA
EA = 1;
% creation of ID Array
ID = zeros(Nm,4);
for k = 1:Nm
	i = Connect_elements(k,1);
	j = Connect_elements(k,2);
	ID(k,1:2) = Deg_free(i,1:2);
	ID(k,3:4) = Deg_free(j,1:2);
end
% assemble Global Stiffness matrix
k_elem = nan(4,4,Nm);
for k = 1:Nm
	i = Connect_elements(k,1);
	j = Connect_elements(k,2);
	dx = Coord_nodes(j,1) - Coord_nodes(i,1);
	dy = Coord_nodes(j,2) - Coord_nodes(i,2);
	L = norm([dx,dy]);
	Lambda_x = dx/L;
	Lambda_y = dy/L;
	%
	k11 = Lambda_x^2/L;
	k12 = (Lambda_x*Lambda_y)/L;
	k13 = -k11;
	k14 = -k12; % not (-Lambda_x*Lambda_y)/L;
	k21 = k12;
	k22 = Lambda_y^2/L;
	k23 = -k12;
	k24 = -k22;
	k31 = -k11;
	k32 = k23;
	k33 = k11;
	k34 = k12;
	k41 = k14;
	k42 = k24;
	k43 = k12;
	k44 = k22;
	k_elem(:,:,k) = EA * [...
		k11, k21, k31, k41;...
		k12, k22, k32, k42;...
		k13, k23, k33, k43;...
		k14, k24, k34, k44];
end
%
% Get total number of DOFs
Nd = max(Deg_free(:));
% Initialize global stiffness matrix
GSM = zeros(Nd,Nd);
% Assemble global stiffness matrix
for k = 1:Nm
	for i = 1:4
		for j = 1:4
			GSM(ID(k,i), ID(k,j)) = GSM(ID(k,i), ID(k,j)) + k_elem(i,j,k);
		end
	end
end

Giving

display(GSM)

GSM = 8×8

0.1354 0.0354 0 0 0 -0.1000 -0.0354 -0.0354 0.0354 0.1354 0 -0.1000 0 0 -0.0354 -0.0354 0 0 0.1354 -0.0354 0.0354 -0.0354 -0.1000 0 0 -0.1000 -0.0354 0.1354 -0.0354 0.0354 0 0 0 0 0.0354 -0.0354 0.1354 -0.0354 0 -0.1000 -0.1000 0 -0.0354 0.0354 -0.0354 0.1354 0 0 -0.0354 -0.0354 -0.1000 0 0 0 0.1354 0.0354 -0.0354 -0.0354 0 0 -0.1000 0 0.0354 0.1354

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[Federico III]

thank you... I need to study and familiarizes all this codes..