membrane_solution3.m

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