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ME_3255_Final_Project/membrane_solution3.m
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function [w] = membrane_solution3(T,P) | |
% Central finite difference approximation of gradient | |
% with 3x3 (um^2) interior nodes in terms of P & T. | |
% Input: | |
% T = tension per unit length (uN/um) | |
% P = pressure (MPa) | |
% Output: | |
% w = displacement vector for interior nodes | |
od = ones(8,1); | |
od(3:3:end) = 0; | |
k = -4 * diag(ones((3^2),1)) + diag(ones((3^2)-3,1),3) + diag(ones((3^2)-3,1),-3) + diag(od,1) + diag(od,-1); | |
y = -(10/4)^2*(P/T)*ones(9,1); | |
w = k\y; | |
% Find displacement vector w | |
% which represents 2D data set w(x,y) | |
[x,y] = meshgrid(0:10/4:10,0:10/4:10); | |
z = zeros(size(x)); | |
z(2:end-1,2:end-1) = reshape(w,[3 3]); | |
% Plot gradient of membrane displacement | |
surf(x,y,z) | |
title('Gradient of Membrane Displacement') | |
zlabel('Displacement [um] (micrometers)') | |
end |