Synthax Question for Equation

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Briana Canet
Briana Canet on 17 Mar 2022
Answered: Walter Roberson on 17 Mar 2022
I am trying to code out this equation: K_traction
I am not sure if I am expressing it correctly synthax wise in order to plot.
% Part A for COMP1
E_m = 70000; % Elastic modulus of matrix, MPa
v_m = .33; % Poisson ratio of matrix
E_i = 250000; % Elastic modulus of inclusion, MPa
v_i = .2; % Poisson ratio of inclusion
% Fiber volume fraction
f_i = 0:0.01:1;
% 0 is 0% fiber and 1 is 100% fiber content
% points to be plotted
K_m = (E_m)/(3*(1-2*(v_m))); % Bulk modulus of matrix, MPa
K_i = (E_i)/(3*(1-2*(v_i))); % Bulk modulus of inclusion, MPa
s1 = (1+v_m)/(3*(1+v_m));
K_traction = K_m*((1+(f_i*(((K_m)/(K_m-K_i))-s1).^-1).^-1));
K_disp = K_m*((1-(f_i*(((K_m)/(K_m-K_i))-s1)^-1).^-1));
% Plotting
plot(f_i,K_traction, 'Color', 'red', 'LineWidth', 2.5);
grid off;
title('Bulk Modulus vs. Inclusion Volume Fraction')
xlabel('Inclusion Volume Fraction, f_i')
ylabel('Bulk Modulus, K [MPa]')
  4 Comments
Walter Roberson
Walter Roberson on 17 Mar 2022
{} is not just another type of parentheses here. Parentheses do not have tailing subscripts.
does not mean the same thing as

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Answers (1)

Walter Roberson
Walter Roberson on 17 Mar 2022
Rules for dots:
  • The dotted versions of the operators are generally different operators than the non-dotted versions. The dotted versions are for element-by-element calculations. When using the dotted operations, the arrays must be "compatible" sizes. Arrays are "compatible" sizes if they are the same length in every non-singular dimension but dimensions that are size 1 in one of the arrays can be non-1 in the corresponding position in the other. For example a 3 x 2 can be .^ with a 1 x 2 and the 1 x 2 will be replicated to be 3 x 2 before the 3 x 2 is .^ with the (expanded to) 3 x 2.
  • In all cases, when the two operands are both scalars, the dotted operations and the non-dotted operations are the same. So 3*5 and 3.*5 are the same
  • If one of the two operands are scalar then the .* and * operations are the same. This does not generally hold true for the ^ or / or \ operations.
  • When the left operand is scalar, then the \ and .\ operations are the same. 3\[5 7] and 3.\[5 7] for example
  • When the right operand is scalar, then the / and ./ operations are the same. [5 7]/3 and [5 7]./3 for example
  • The ^ and .^ operations are never the same if either operand is non-scalar
So:
You can use constant*array or array*constant or array/constant or constant\array instead of using constant.*array or array.*constant or array./constant or constant.\array if you want.
But constant^array and constant.^array are different, and constant/array and constant./array are different, and array^constant and array.^constant are different.
array^array is never permitted for non-scalar arrays.
array*array and array/array and array\array have size constraints and are only the same as the corresponding dotted operator under some conditions.

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