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07_final_project/SE_diff.m
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function [pw_se,w] = SE_diff(T,P,n) | |
% Call function from part c to obtain vector w | |
w = membrane_solution(T,P,n); | |
% Create All Nodes Matrix (Interior & Exterior) | |
m = zeros(n+2); | |
c = vec2mat(w,n); % Vector w rearranged to n x n matrix. | |
m(2:n+1,2:n+1) = c; % insert matrix c into middle of m matrix | |
% m = symmetric matrix | |
h = 10/(n+1); % h = delta_x = delta_y (micron) | |
% Compute w bar | |
w_bar = zeros(n+1,n+1); | |
for i = 1:n+1 | |
for j = 1:n+1 | |
w_bar(i,j) = (m(i,j)+m(i,j+1)+m(i+1,j)+m(i+1,j+1))/4; | |
end | |
end | |
% Left side of the equation | |
left_side = zeros(n+1,n+1); | |
for i = 1:(n+1)^2 | |
left_side(i) = P * h^2*w_bar(i); | |
end | |
L = sum(sum(left_side)); | |
% Compute dw_dx | |
dx = zeros(n+2,n+1); | |
for i = 2:n+2 | |
dx(:,i-1)= (m(:,i)-m(:,i-1))/(h); | |
end | |
dw_dx = zeros(n+1,n+1); | |
for i = 1:n+1 % rows | |
for j = 1:n+1 % columns | |
dw_dx(i,j) = (dx(i,j)+dx(i+1,j))/2; | |
end | |
end | |
% Compute dw_dy | |
dy = zeros(n+1,n+2); | |
for i = 2:n+2 | |
dy(i-1,:)= (m(i-1,:)-m(i,:))/(h); | |
end | |
dw_dy = zeros(n+1,n+1); | |
for i = 1:n+1 % rows | |
for j = 1:n+1 % columns | |
dw_dy(i,j) = (dy(i,j)+dy(i,j+1))/2; | |
end | |
end | |
right_side = zeros(n+1,n+1); | |
for i = 1:(n+1)^2 | |
right_side(i) = (0.25*(dw_dx(i))^4+0.25*(dw_dy(i))^4+0.5*(dw_dx(i)*dw_dy(i))^2); | |
end | |
R = sum(sum(right_side)); | |
R = (1000*10^3*0.3*10^-3*h^2)/(2*(1-0.31^2))*R; | |
pw_se = R - L; | |
end |