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function [pw_se,w]=SE_diff(T,P,n)
E = 1e6;
v = .31;
t = .0003;
h = 10/(n+1);
w = membrane_solution(T,P,n);
z = zeros(n+2);
z(2:end-1,2:end-1) = reshape(w,[n n]);
nt = n + 1;
wn = zeros(nt);
for i = 1:nt
for j = 1:nt
wn(i,j) = mean([z(i,j),z(i+1,j),z(i,j+1),z(i+1,j+1)]);
end
end
pw = sum(sum(wn.*h^2.*P));
dwdx = zeros(nt);
dwdy = zeros(nt);
for i = 1:nt
for j = 1:nt
dwdx(i,j) = mean([z(i+1,j)-z(i,j),z(i+1,j+1)-z(i,j+1)]);
dwdy(i,j) = mean([z(i,j+1)-z(i,j),z(i+1,j+1)-z(i+1,j)]);
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;
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