Accessing entries of symfun

I am trying to solve a structural mechanics problem for which I have defined

clear all
close all
clc

syms psi(x_1, x_2, x_3)
syms E nu

u_1 = diff(psi, x_1, 1);
u_2 = diff(psi, x_2, 1);
u_3 = diff(psi, x_3, 1);

epsilon_1 = diff(u_1, x_1, 1);
epsilon_2 = diff(u_2, x_2, 1);
epsilon_3 = diff(u_3, x_3, 1);
gamma_12 = diff(u_1, x_2, 1) + diff(u_2, x_1, 1);
gamma_13 = diff(u_1, x_3, 1) + diff(u_3, x_1, 1);
gamma_23 = diff(u_2, x_3, 1) + diff(u_3, x_2, 1);
epsilon = [epsilon_1; epsilon_2; epsilon_3; gamma_23; gamma_13; gamma_12];
C = E / ((1 + nu) * (1 - 2 * nu)) * [1 - nu nu nu 0 0 0; ...
    nu 1 - nu nu 0 0 0; ...
    nu nu 1 - nu 0 0 0; ...
    0 0 0 (1 - 2 * nu) / 2 0 0; ...
    0 0 0 0 (1 - 2 * nu) / 2 0; ...
    0 0 0 0 0 (1 - 2 * nu) / 2];

sigma = C * epsilon

Since the size of C is 6 x 6 and the size of epsilon is 6 x 1; the order of sigma should be 6 x 1. However when I use

size(sigma)

I get 1 x 1, which does not make sense to me. Also, I want to access individual entries of sigma. How can I do that?

Answer 1

[Setsuna Yuuki.]

you can try with formula():

clear all
close all
clc
syms psi(x_1, x_2, x_3)
syms E nu
u_1 = diff(psi, x_1, 1);
u_2 = diff(psi, x_2, 1);
u_3 = diff(psi, x_3, 1);
epsilon_1 = diff(u_1, x_1, 1);
epsilon_2 = diff(u_2, x_2, 1);
epsilon_3 = diff(u_3, x_3, 1);
gamma_12 = diff(u_1, x_2, 1) + diff(u_2, x_1, 1);
gamma_13 = diff(u_1, x_3, 1) + diff(u_3, x_1, 1);
gamma_23 = diff(u_2, x_3, 1) + diff(u_3, x_2, 1);
epsilon = [epsilon_1; epsilon_2; epsilon_3; gamma_23; gamma_13; gamma_12];
C = E / ((1 + nu) * (1 - 2 * nu)) * [1 - nu nu nu 0 0 0; ...
    nu 1 - nu nu 0 0 0; ...
    nu nu 1 - nu 0 0 0; ...
    0 0 0 (1 - 2 * nu) / 2 0 0; ...
    0 0 0 0 (1 - 2 * nu) / 2 0; ...
    0 0 0 0 0 (1 - 2 * nu) / 2];
sigma = C * epsilon;
sigma = formula(sigma) % -------- %

Answer 2

[Walter Roberson]

sigma is a function rather than an array. It is a 1x1 symfun object. It does not have individual entries: it is a formula.

You can invoke the function on symbolic arguments to get back the array that would be the result for those arguments.

Or you can use

feval(symengine, 'op', sigma)

Answer 3

[Ameer Hamza]

sigma is a symbolic function. You need to gives inputs to get a 6x1 matrix. For example, check

size(sigma(1,1,1))

For a general case, you can write

sigma = C * epsilon
Sigma = sigma(x_1, x_2, x_3)