how to solve multiple iteration for multiple input?

Question

sivalogan satchithanandamoorthy 2017-7-27

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/350485-how-to-solve-multiple-iteration-for-multiple-input

回答： Abhi Sundararaman 2017-8-1

采纳的回答： Abhi Sundararaman

在 MATLAB Online 中打开

I want to solve this equation ∆ε=∆σ/E+2(∆σ/2k)^n for ∆σ using iteration. I have ε ranging from (0 to 2).

∆ε is elongation
∆σ is stress
E is modulus of elasticity
K and n are constant

x = 16; %x is ∆σ
x_old = 100;
iter = 0;
k=38.177;
n=7.22;
E=15.25;
% y=linspace(0,5,0.5);
for i=[0:.01:0.5]
  while abs(x_old-x) > 10^-3 && x ~= 0
      x_old = x;
      x = x - (2*(x/(2*k))^(n) + (x/(E))-i)/(2*n*(x/(2*k))^(n-1) + (1/(E)));
      iter = iter + 1;
      fprintf('Iteration %d: x=%.20f\n', iter, x);
      pause;
  end
end

I have script for Newton-Raphson Method for finding out ∆σ, but i don't know know how solve for multiple values. what i mean by multiple value is i have different ∆ε, ranging from 0 to 2. once i solved the iteration, i want to plot it as well. I think i could figure out ploting, but it would be helpful, if you could guide me on this. thank you very much!

sincerely siva

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Answer 1

Abhi Sundararaman 2017-8-1

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/350485-how-to-solve-multiple-iteration-for-multiple-input#answer_276392

在 MATLAB Online 中打开

You could create another for loop outside your "while" loop that changes epsilon during each iteration. Then you substitute this value of epsilon into your iteration equation inside your while loop. For example,after initializing your constants,

x = 16; %guess for x
Epsilon = 0:0.1:2
Sigma = zeros(size(Epsilon));
i = 1;
for Epsilon = 0:0.1:2
  x = 16; %reinitialize the guess for x
 while  abs(x_old - x) > 10^-3 && x ~= 0
    <insert your iteration equation here, with Epsilon included>
    <solve for sigma (x)>
 end
 Sigma(i) = x;
 i = i + 1;
end
plot( Epsilon, Sigma );