Synthax Question for Equation

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]')

[Walter Roberson]

I do not know what that syntax is intended to mean, with {} and upper and lower modififiers. Upper and lower modifiers like that would most often be used for limits of integration or limits of summation or limits of product, but are not exclusively used for that -- upper and lower modifiers are sometimes used for combinatorics or for some functions related to hypergeometric or Bessel functions.

[ ] around an expression that has another apparent set of brackets around it, can sometimes denote taking the integer part -- though more typical for that would be if the | was missing either the upper or lower _ mark, in which case the notation tells you whether you are taking floor or ceiling.

[Briana Canet]

{} is just another type of parentheses in this case. Same goes for the brackets.

[Briana Canet]

My question is more with respect to I am not sure how to put the periods/dots that I know are used in MATLAB when writing equations.

[Walter Roberson]

{} is not just another type of parentheses here. Parentheses do not have tailing subscripts.

does not mean the same thing as

Answer 1

[Walter Roberson]

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.