Permalink
Cannot retrieve contributors at this time
Name already in use
A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
ME3255_Final_Project/README.md
Go to fileThis commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
197 lines (176 sloc)
4.51 KB
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
# ME3255_Final_Project | |
# Part A | |
```matlab | |
function [w] = membrane_solution3(T,P) | |
% T = Tension (microNewton/micrometer) | |
% P = Pressure (MPa) | |
od = ones(8,1); | |
od(3:3:end) = 0; | |
k = -4*diag(ones(9,1))+diag(ones(9-3,1),3)+diag(ones(9-3,1),-3)+diag(od,1)+diag(od,-1); | |
y = -(10/4)^2*(P/T)*ones(9,1); | |
w = k\y; | |
% Solves for displacement (micrometers) | |
% Output w is a vector | |
% Solution represents a 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]); | |
surf(x,y,z) | |
title('Membrane Displacement') | |
zlabel('Displacement (micrometer)') | |
% Membrane displacement is shown on chart | |
end | |
``` | |
# Part B | |
```matlab | |
% Part B Script | |
[w] = membrane_solution3(0.006,0.001); | |
``` | |
![](https://github.uconn.edu/ltd13002/ME3255_Final_Project/blob/master/Part%20B/PartBFigure.png) | |
# Part C | |
```matlab | |
function [w] = membrane_solution(T,P,n) | |
% T = Tension (microNewton/micrometer) | |
% P = Pressure (MPa) | |
% n = # of interior nodes | |
od = ones(n^2-1,1); | |
od(n:n:end) = 0; | |
k = -4*diag(ones(n^2,1))+diag(ones((n^2)-n,1),n)+diag(ones((n^2)-n,1),-n)+diag(od,1)+diag(od,-1); | |
y = -(10/(n+1))^2*(P/T)*ones(n^2,1); | |
w = k\y; | |
% Solves for displacement (micrometers) | |
% Output w is a vector | |
% Solution represents a 2D data set w(x,y) | |
[x,y] = meshgrid(0:10/(n+1):10,0:10/(n+1):10); | |
z = zeros(size(x)); | |
z(2:end-1,2:end-1) = reshape(w,[n n]); | |
surf(x,y,z) | |
title('Membrane Displacement') | |
zlabel('Displacement (micrometer)') | |
% Membrane displacement is shown on chart | |
end | |
``` | |
# Part D | |
```matlab | |
% Part D Script | |
[w] = membrane_solution(0.006,0.001,10) | |
``` | |
![](https://github.uconn.edu/ltd13002/ME3255_Final_Project/blob/master/Part%20D/PartDFigure.png) | |
# Part E | |
```matlab | |
function [pw_se,w]=SE_diff(T,P,n) | |
E = 1; %TPa Units may need to be changed | |
v = .31; %Poissons ratio | |
t = .3; %nm | |
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)]); | |
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; | |
``` | |
# Part F | |
```matlab | |
n=[3,20:5:40]; | |
P=0.001; %MPa | |
T = zeros(1,length(n)); | |
ea = zeros(1,length(n)); | |
for i = 1:length(n) | |
[T(i), ea(i)] = tension_sol(P,n(i)); | |
end | |
``` | |
```matlab | |
function [T,ea] = tension_sol(P,n) | |
y =@(T) SE_diff(T,P,n); | |
[T,fx,ea,iter]=bisect(y,.01,1); | |
``` | |
```matlab | |
function [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,varargin) | |
% bisect: root location zeroes | |
% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...): | |
% uses bisection method to find the root of func | |
% input: | |
% func = name of function | |
% xl, xu = lower and upper guesses | |
% es = desired relative error (default = 0.0001%) | |
% maxit = maximum allowable iterations (default = 50) | |
% p1,p2,... = additional parameters used by func | |
% output: | |
% root = real root | |
% fx = function value at root | |
% ea = approximate relative error (%) | |
% iter = number of iterations | |
if nargin<3,error('at least 3 input arguments required'),end | |
test = func(xl,varargin{:})*func(xu,varargin{:}); | |
if test>0,error('no sign change'),end | |
if nargin<4||isempty(es), es=0.0001;end | |
if nargin<5||isempty(maxit), maxit=50;end | |
iter = 0; xr = xl; ea = 100; | |
while (1) | |
xrold = xr; | |
xr = (xl + xu)/2; | |
iter = iter + 1; | |
if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end | |
test = func(xl,varargin{:})*func(xr,varargin{:}); | |
if test < 0 | |
xu = xr; | |
elseif test > 0 | |
xl = xr; | |
else | |
ea = 0; | |
end | |
if ea <= es || iter >= maxit,break,end | |
end | |
root = xr; fx = func(xr, varargin{:}); | |
``` | |
```matlab | |
function re = Rel_error (T) | |
re = zeros(1,length(T)-1); | |
for i = 2:length(T) | |
re(i-1)= abs(T(i)-T(i-1))/T(i-1); | |
end | |
``` | |
|number of nodes|Tension (uN/um)| rel. error| | |
|---|---|---| | |
|3 |0.0489 |n/a| | |
|20|0.0599|22.6%| | |
|25|0.0601|0.27%| | |
|30|0.0602|0.15%| | |
|35|0.0602|0.09%| | |
|40|0.0603|0.06%| | |
# Part G | |
```matlab | |
P = linspace(.001,.01,10); | |
n = 20; | |
T = zeros(1,length(P)); | |
wmax = zeros(1,length(P)); | |
for i = 1:length(P) | |
T(i) = tension_sol(P(i),n); | |
w = membrane_solution(T(i),P(i),n); | |
wmax(i) = max(w); | |
end | |
clf | |
setDefaults | |
x = wmax'; | |
y = P'; | |
Z=x.^3; | |
a=Z\y; | |
x_fcn=linspace(min(x),max(x)); | |
plot(x,y,'o',x_fcn,a*x_fcn.^3) | |
``` |