expanded matrix wont be bigger than 8 by 8

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Olivier
Olivier 2024-6-14
回答： Swastik Sarkar 2024-10-14
Ran in:
why wont K_global be bigger than 8 by 8?
this is my code:
clc; clear; clear all;
% Topology and element matrix
topologydegree = [1 2 3 4; 3 4 5 6; 5 6 7 8;
7 8 9 10; 9 10 11 12; 11 12 13 14;
13 14 15 16; 1 2 15 16; 3 4 15 16;
3 4 13 14; 5 6 13 14; 7 8 13 14; 7 8 11 12]
topologydegree = 13×4
1 2 3 4 3 4 5 6 5 6 7 8 7 8 9 10 9 10 11 12 11 12 13 14 13 14 15 16 1 2 15 16 3 4 15 16 3 4 13 14
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element = [1 2; 2 3; 3 4; 4 5; 5 6; 6 7; 7 8;
1 8; 2 8; 2 7; 3 7; 4 7; 4 6]
element = 13×2
1 2 2 3 3 4 4 5 5 6 6 7 7 8 1 8 2 8 2 7
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% Number of nodes
unique_elements = unique(element);
nodemax = numel(unique_elements)
nodemax = 8
% Number of elements
n = size(topologydegree, 1);
% Given variables
E = 24.17;
A = 1;
L = [300*sqrt(2); 300; 300; 300*sqrt(2);
300; 300; 300; 300; 300; 300*sqrt(2);
300; 300*sqrt(2); 300]
L = 13×1
424.2641 300.0000 300.0000 424.2641 300.0000 300.0000 300.0000 300.0000 300.0000 424.2641
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co = [0, 0; 300, 300; 600, 300;
900, 300; 1200, 0; 900, 0; 600, 0; 300, 0]
co = 8×2
0 0 300 300 600 300 900 300 1200 0 900 0 600 0 300 0
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% Initialize the global stiffness matrix
K_global = zeros(nodemax, nodemax);
for i = 1:n
% Stiffness matrix for the current element
Ke(:,:,i) = (E * A) / L(i) * [1, -1; -1, 1]
% Calculate nxx and nyx
x1 = co(element(i,1), 1);
x2 = co(element(i,2), 1);
y1 = co(element(i,1), 2);
y2 = co(element(i,2), 2);
nxx = (x2 - x1) / L(i);
nyx = (y2 - y1) / L(i);
% Geometry matrix for the current element
G(:,:,i) = [nxx, nyx, 0, 0; 0, 0, nxx, nyx];
G_(:,:,i) = G(:,:,i)';
% Stiffness matrix in global coordinates
Kea(:,:,i) = G_(:,:,i) * Ke(:,:,i) * G(:,:,i)
% Assemble the global stiffness matrix
for ii = 1:size(topologydegree, 2)
for jj = 1:size(topologydegree, 2)
row = topologydegree(i, ii);
col = topologydegree(i, jj);
K_global(row, col) = K_global(row, col) + Kea(ii, jj);
end
end
end
Ke = 2×2
0.0570 -0.0570 -0.0570 0.0570
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Kea = 4×4
0.0285 0.0285 -0.0285 -0.0285 0.0285 0.0285 -0.0285 -0.0285 -0.0285 -0.0285 0.0285 0.0285 -0.0285 -0.0285 0.0285 0.0285
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Ke =
Ke(:,:,1) = 0.0570 -0.0570 -0.0570 0.0570 Ke(:,:,2) = 0.0806 -0.0806 -0.0806 0.0806
Kea =
Kea(:,:,1) = 0.0285 0.0285 -0.0285 -0.0285 0.0285 0.0285 -0.0285 -0.0285 -0.0285 -0.0285 0.0285 0.0285 -0.0285 -0.0285 0.0285 0.0285 Kea(:,:,2) = 0.0806 0 -0.0806 0 0 0 0 0 -0.0806 0 0.0806 0 0 0 0 0
Ke =
Ke(:,:,1) = 0.0570 -0.0570 -0.0570 0.0570 Ke(:,:,2) = 0.0806 -0.0806 -0.0806 0.0806 Ke(:,:,3) = 0.0806 -0.0806 -0.0806 0.0806
Kea =
Kea(:,:,1) = 0.0285 0.0285 -0.0285 -0.0285 0.0285 0.0285 -0.0285 -0.0285 -0.0285 -0.0285 0.0285 0.0285 -0.0285 -0.0285 0.0285 0.0285 Kea(:,:,2) = 0.0806 0 -0.0806 0 0 0 0 0 -0.0806 0 0.0806 0 0 0 0 0 Kea(:,:,3) = 0.0806 0 -0.0806 0 0 0 0 0 -0.0806 0 0.0806 0 0 0 0 0
Ke =
Ke(:,:,1) = 0.0570 -0.0570 -0.0570 0.0570 Ke(:,:,2) = 0.0806 -0.0806 -0.0806 0.0806 Ke(:,:,3) = 0.0806 -0.0806 -0.0806 0.0806 Ke(:,:,4) = 0.0570 -0.0570 -0.0570 0.0570
Kea =
Kea(:,:,1) = 0.0285 0.0285 -0.0285 -0.0285 0.0285 0.0285 -0.0285 -0.0285 -0.0285 -0.0285 0.0285 0.0285 -0.0285 -0.0285 0.0285 0.0285 Kea(:,:,2) = 0.0806 0 -0.0806 0 0 0 0 0 -0.0806 0 0.0806 0 0 0 0 0 Kea(:,:,3) = 0.0806 0 -0.0806 0 0 0 0 0 -0.0806 0 0.0806 0 0 0 0 0 Kea(:,:,4) = 0.0285 -0.0285 -0.0285 0.0285 -0.0285 0.0285 0.0285 -0.0285 -0.0285 0.0285 0.0285 -0.0285 0.0285 -0.0285 -0.0285 0.0285
Index in position 2 exceeds array bounds. Index must not exceed 8.
disp('Global Stiffness Matrix K:')
disp(K_global)

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回答（2 个）

Walter Roberson
Walter Roberson 2024-10-14
unique_elements = unique(element);
nodemax = numel(unique_elements)
nodemax is 8.
K_global = zeros(nodemax, nodemax);
You initialize K_global as 8 x 8
row = topologydegree(i, ii);
col = topologydegree(i, jj);
K_global(row, col) = K_global(row, col) + Kea(ii, jj);
Although row and col can each be larger than 8, you are adding a value to K_global(row,col) which is a problem when row or col exceeds 8 as K_global does not exist for row or col greater than 8.
Swastik Sarkar
Swastik Sarkar 2024-10-14
Hi @Olivier,
In the provided code, K_global is being initialized to zeros based on the maximum of unique values from the element array, as seen in the following lines:
% Number of nodes
unique_elements = unique(element);
nodemax = numel(unique_elements)
K_global = zeros(nodemax, nodemax);
However, K_global is accessed using values from topologydegree instead of element:
row = topologydegree(i, ii);
col = topologydegree(i, jj);
K_global(row, col) = K_global(row, col) + Kea(ii, jj);
To align with the requirements, nodemax should be set to max(topologydegree) instead. This adjustment ensures that K_global is sized appropriately for the indices used.
Hope this helps.

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