SE_diff.m

function [pw_se,w]=SE_diff(T,P,n)
% SE_diff: difference between strain energy and work done by pressure in
% membrane
% [pw_se,w]=SE_diff(T,P,n)
% input:
% T = Tension (microNewton/micrometer)
% P = Pressure (MPa)
% n = number of rows and columns of interior nodes
% output:
% pw_se = difference between strain energy and work done by pressure in
% membrane
% w = vector of displacement of interior nodes

E = 1000000; %TPa Units may need to be changed
v = .31; %Poissons ratio
t = .0003; %um
h = 10/(n+1); %nm
w = membrane_solution(T,P,n);
z = zeros(n+2);
z(2:end-1,2:end-1) = reshape(w,[n n]);
num = n + 1;
wbar = zeros(num);
for i = 1:num
    for j = 1:num
        wbar(i,j) = mean([z(i,j),z(i+1,j),z(i,j+1),z(i+1,j+1)]);
    end
end
pw = sum(sum(wbar.*h^2.*P));
dwdx = zeros(num);
dwdy = zeros(num);
for i = 1:num
    for j = 1:num
        dwdx(i,j) = mean([z(i+1,j)-z(i,j),z(i+1,j+1)-z(i,j+1)])./h;
        dwdy(i,j) = mean([z(i,j+1)-z(i,j),z(i+1,j+1)-z(i+1,j)])./h;
    end
end
se = E*t*h^2/(2*(1-v^2))*sum(sum(0.25.*dwdx.^4+.25.*dwdy.^4+0.5.*(dwdx.*dwdy).^2));
pw_se = pw-se;