How to change only certain numbers in a matrices for a certain iteration?

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Robert Vandergriff
Robert Vandergriff 2022-2-15
编辑： Walter Roberson 2022-2-15
Hello, im struggling to understand a problem. I have solved a truss analysis by using the method of joints and turned it into a 10x10 matrix. I am solving using Ax=B form. I need to be able to find when the truss fails for a certain ultimate force at a certain m. therefore in the matrix B = [0;0;0;0;0;w;0;w;0;0]; w needs to increase from 2kg to m_max incrementing by .5 kg. This is what i have so far. I am extremely new to matlab.
A = [1 0 0 0 0 0 1 0 0 0;
0 0 0 0 0 0 0 1 0 0;
-1 0.707 0 0 -0.707 0 0 0 0 0;
0 -0.707 0 0 -0.707 -1 0 0 0 0;
0 -0.707 -1 0 0 0 0 0 0 0;
0 0.707 0 0 0 0 0 0 0 0;
0 0 1 -1 0 0 0 0 0 0;
0 0 0 0 0 1 0 0 0 0;
0 0 0 1 0.707 0 0 0 1 0;
0 0 0 0 0.707 0 0 0 0 1];
F_ult = 400
B = [0;0;0;0;0;w;0;w;0;0];
N = 100;
for w = 2:.5:N
F = A\B;
while F<<400
end

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回答（2 个）

KSSV
KSSV 2022-2-15
A = [1 0 0 0 0 0 1 0 0 0;
0 0 0 0 0 0 0 1 0 0;
-1 0.707 0 0 -0.707 0 0 0 0 0;
0 -0.707 0 0 -0.707 -1 0 0 0 0;
0 -0.707 -1 0 0 0 0 0 0 0;
0 0.707 0 0 0 0 0 0 0 0;
0 0 1 -1 0 0 0 0 0 0;
0 0 0 0 0 1 0 0 0 0;
0 0 0 1 0.707 0 0 0 1 0;
0 0 0 0 0.707 0 0 0 0 1];
F_ult = 400 ;
N = 100;
iter = 0 ;
x = zeros(10,[]) ; % save deformations for each iteration
for w = 2:.5:N
iter = iter+1 ;
B = [0;0;0;0;0;w;0;w;0;0];
x(:,iter) = A\B; % save deformations for each w
end
Walter Roberson
Walter Roberson 2022-2-15
编辑：Walter Roberson 2022-2-15
Ran in:
A = [1 0 0 0 0 0 1 0 0 0;
0 0 0 0 0 0 0 1 0 0;
-1 0.707 0 0 -0.707 0 0 0 0 0;
0 -0.707 0 0 -0.707 -1 0 0 0 0;
0 -0.707 -1 0 0 0 0 0 0 0;
0 0.707 0 0 0 0 0 0 0 0;
0 0 1 -1 0 0 0 0 0 0;
0 0 0 0 0 1 0 0 0 0;
0 0 0 1 0.707 0 0 0 1 0;
0 0 0 0 0.707 0 0 0 0 1];
F_ult = 400
F_ult = 400
syms w positive
B = [0;0;0;0;0;w;0;w;0;0];
F = A\B
F = 
maxF_ratio = max(abs(F/w))
maxF_ratio = 
3
breaking_w_exact = double(F_ult / maxF_ratio)
breaking_w_exact = 133.3333
breaking_w = ceil(breaking_w_exact / 0.5) * 0.5
breaking_w = 133.5000
That is, 133.0 would not be enough to break it, and you are incrementing by 0.5, so the number you are looking for is 133.5
I assumed here that a -400 force would also break the system.

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