Hi, the error you are encountering, "valid indices for 'K' are restricted in parfor," occurs because the 'parfor' loop in MATLAB requires specific conditions to be met in order to execute in parallel. One of these conditions is that the loop indices must be known at the start of the loop, which is not the case when you are updating K and F inside the nested loops.
To resolve this issue, you can use temporary variables to accumulate the values in each iteration of the 'parfor' loop and then update K and F outside the loop. Here's an updated version of your code that should work:
%% Bar Problem
% E - Young's Modulus; l - length of the bar; A - Cross-sectional area
% k local stiffness matrix; and K - Global stiffness matrix
clear();
clc();
tic();
syms x;
l = 300; % mm
E = 210*10^3; % MPa
A = 100; % sqmm
p = 100; % N/mm
ne = 3;
nn = 4;
n_dof = 1;
ne_dof = 2;
nd = nn * n_dof;
le = l / ne;
N = [(le - x) / le, x / le];
Nx = diff(N, x);
k = double(int(E * A * Nx.' * Nx, x, 0, le));
f = double(int(p * N.', x, 0, le));
% Initialize global stiffness matrix and force vector to zero
K = zeros(nd);
F = zeros(nd, 1);
% Connectivity matrix
c = [1, 2; 2, 3; 3, 4; 4, 5; 5, 6];
% Temporary matrices for accumulation
temp_K = zeros(nd);
temp_F = zeros(nd, 1);
parfor e = 1:ne
temp_K_e = zeros(nd);
temp_F_e = zeros(nd, 1);
for i = 1:ne_dof
for j = 1:ne_dof
temp_K_e(c(e, i), c(e, j)) = temp_K_e(c(e, i), c(e, j)) + k(i, j);
end
temp_F_e(c(e, i)) = temp_F_e(c(e, i)) + f(i);
end
% Accumulate values in temporary matrices
temp_K = temp_K + temp_K_e;
temp_F = temp_F + temp_F_e;
end
% Update K and F outside the parfor loop
K = temp_K;
F = temp_F;
% Apply boundary conditions
K1 = K(2:end, 2:end);
F1 = F(2:end);
X = linsolve(K1, F1);
toc();
By using temporary variables, you avoid the issue of updating K and F inside the 'parfor' loop, allowing the code to execute in parallel without any indexing errors.
