From be6584617408235eb82a253aaa2f129d45fede5a Mon Sep 17 00:00:00 2001 From: Matthew Maliniak Date: Thu, 14 Dec 2017 19:55:16 -0500 Subject: [PATCH 01/13] Update README.md --- README.md | 52 ++++++++++++++++++++++++++++++++++++++++++++++------ 1 file changed, 46 insertions(+), 6 deletions(-) diff --git a/README.md b/README.md index 13f48c4..822ba54 100644 --- a/README.md +++ b/README.md @@ -3,8 +3,14 @@ # Part A ```matlab function [w] = membrane_solution3(T,P) - % T = Tension (microNewton/micrometer) - % P = Pressure (MPa) +% membrane_solution3: dispalacement of node for membrane with 3x3 interior +% nodes +% [w] = membrane_solution3(T,P) +% input: +% T = Tension (microNewton/micrometer) +% P = Pressure (MPa) +% output: +% w = vector of displacement of interior nodes od = ones(8,1); od(3:3:end) = 0; @@ -40,9 +46,14 @@ end # Part C ```matlab function [w] = membrane_solution(T,P,n) - % T = Tension (microNewton/micrometer) - % P = Pressure (MPa) - % n = # of interior nodes +% membrane_solution: dispalacement of node for membrane with nxn interior nodes +% [w] = membrane_solution(T,P,n) +% input: +% T = Tension (microNewton/micrometer) +% P = Pressure (MPa) +% n = number of rows and columns of interior nodes +% output: +% w = vector of displacement of interior nodes od = ones(n^2-1,1); od(n:n:end) = 0; @@ -76,6 +87,18 @@ end # Part E ```matlab function [pw_se,w]=SE_diff(T,P,n) +% SE_diff: calculates 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 = 1; %TPa Units may need to be changed v = .31; %Poissons ratio t = .3; %nm @@ -115,7 +138,17 @@ pw_se = pw-se; end ``` ```matlab - function [T,ea] = tension_sol(P,n) +function [T,ea] = tension_sol(P,n) +% tension_sol: outputs tension of a membrane given the pressure and number +% of nodes +% [T,ea] = tension_sol(P,n) +% input: +% P = Pressure (MPa) +% n = number of rows and columns of interior nodes +% output: +% T = Tension (microNewton/micrometer) +% ea = approximate relative error (%) + y =@(T) SE_diff(T,P,n); [T,fx,ea,iter]=bisect(y,.01,1); ``` @@ -160,6 +193,13 @@ root = xr; fx = func(xr, varargin{:}); ``` ```matlab function re = Rel_error (T) + Rel_error: calculates relative error of a vector +% re = Rel_error (T) +% input: +% T = vector of numbers +% output: +% re = relative error of vector + re = zeros(1,length(T)-1); for i = 2:length(T) re(i-1)= abs(T(i)-T(i-1))/T(i-1); From 3217bec2baefdb9797b60fd7e29f12b838227cd0 Mon Sep 17 00:00:00 2001 From: Matthew Maliniak Date: Thu, 14 Dec 2017 20:13:47 -0500 Subject: [PATCH 02/13] Update README.md --- README.md | 16 +++++++++++++++- 1 file changed, 15 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index 822ba54..0c9f8c6 100644 --- a/README.md +++ b/README.md @@ -125,6 +125,12 @@ 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; ``` +### Approach +- Using the membrane_solution function, a vector of the displacements is formed +- Next, the average displacement for each element is calculated. For each elements, the dispalcement at all four courners is taken and then averaged +- Using these values, the work done by pressure can be calculated +- For the change in dispalcement over the x and y coordinate system, the values of the change on the left and right (y-axis) or top and bottom (x-axis) are taken and averaged +- Using these values, the strain enegery can be calculated # Part F ```matlab @@ -214,7 +220,9 @@ end |35|0.0602|0.09%| |40|0.0603|0.06%| - +### Approach +- This problem uses the bisect method for locating roots and the SE_diff function for calculating the difference in work and strain energy of the membrane +- The script runs through all iterations of different amounts of nodes, zeroing the SE_diff function output and saving the values for tension in the T variable as a vector # Part G ```matlab P = linspace(.001,.01,10); @@ -240,3 +248,9 @@ ylabel('Pressure (MPa)') print('Part g','-dpng') ``` ![](https://github.uconn.edu/ltd13002/ME3255_Final_Project/blob/master/Part%20G/Part%20g.png) + +### Approach +- This script uses the tension_sol function as described in the part above, running though all iterations of pressure +- Additionally, the max deflection for each pressure and tension is calculated at each iteration +- From there, a general linear regression is calculated with the formula P(x) = A*w^3 +- The results are plotted From 1667a4e785666adfe2a7281031bdd5e912f1aa60 Mon Sep 17 00:00:00 2001 From: Lucas Dombroski Date: Thu, 14 Dec 2017 20:18:19 -0500 Subject: [PATCH 03/13] . --- Part A/membrane_solution3.m | 6 ++++-- Part B/PartBFigure.png | Bin 66833 -> 71894 bytes Part B/membrane_solution3.m | 25 +++++++++++++++++++++++++ Part D/PartDFigure.png | Bin 90563 -> 95144 bytes Part D/membrane_solution.m | 25 +++++++++++++++++++++++++ 5 files changed, 54 insertions(+), 2 deletions(-) create mode 100644 Part B/membrane_solution3.m create mode 100644 Part D/membrane_solution.m diff --git a/Part A/membrane_solution3.m b/Part A/membrane_solution3.m index ec29f9b..d495083 100644 --- a/Part A/membrane_solution3.m +++ b/Part A/membrane_solution3.m @@ -16,8 +16,10 @@ function [w] = membrane_solution3(T,P) 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)') + title('Membrane Displacement (3 x 3)') + zlabel('Z Position (micron)') + ylabel('Y Position (micron)') + xlabel('X Position (micron)') % Membrane displacement is shown on chart end \ No newline at end of file diff --git a/Part B/PartBFigure.png b/Part B/PartBFigure.png index 4699760408420410eb20b55df053a6534e1cca7b..32dd6f3fff69c301e11b81363cc3efcd15483c25 100644 GIT binary patch literal 71894 zcmdSBg}TYK|&E!8YHDdKlv27|5D<_CNomR7 zEPcOkzx#LWe_(Swk8rGet^2;NxhBpzXJ)-oR+PDpO^S^`Ag;^FN~$6dSBww{G+9hk zc;)JSTo(9+^+HzL5rM#MMgETx%YsXWyyhhLSnBHBwHqiH7+g6=>hKbsla!W|nw`0m ztFeO_;<328g17`LmHIO?s>jAo&z{&hSUIv%$=RB)3u#Rg!~1EF?|z=?p9{6t$rH&ebphCz=imSg&*_d|oRR8wp__v9<1nMhR zVybtyQJ)ihP|lI`VNOy;4^UQMbw>X;l=bb@HqDU&oR_2XK}Vx z^ykXmyhV)cC}pqEuF+9{Rp{J~cwIf7nB3KCYQ9y=oqj~w*j(6A>$;V)lCmPSl2cX1 zg96J%;L)^iU?BhSWyXAm{QdI^Djo7S-zx+b^0y+D7*cG$xBmZsxo+Y*>;%6kGgBPX zxO!?~VWH1f9#8W7B`$)Op|Y|vaT)_L=JIDLzD|$*oUQtYLr(&y$&Wjl1_s_o)2?;X z#}Phf4+HK5_AGrq+wEDJ6?Wf$xmCN;YZIaEeL6ME!^`V2bLZBrkzD!soSYmSj`|lr zYU~@_4}R^eaWw2lP2U;gX7ct$ z9M!6hjt(Ka9-r+GzG};dk|hJ8muFG(?1_B#^VPH7>)Vdoa66C&7Ijh6#mUxmT@P8h z+j63Ixp`$p#Y>Tk*Ed9t4~l(k_@YTvy&tUY_HYbzcH&7C8a7>|y3Sx3vY_~*quliU z>BvW(?tSv%f-t_P(yWKDeDXEI)XePdR7I0q zsal9g$?x7AcTl6CYb05h=pWv{zn7aDC|in?3bNy12qXe&)On8m{QA0*Y`oa8xMA|a zxL)>jqx-@0O_%e97AjwQFF5c?eM-+AaXwufs!^>LY^rA)E~iKpI=!CEV>3K(FD5p& zOB5FDKI691aB;G3V9>GT5E~myA>h<$UVgq|Axg&YkP~tJeNoZHPRor5N>LG`FTVJ+ z(yQB(wT>(Ose-yXI-miIE>Apg$@xmmdg4qv!gF(S!a!^2^A?znmY0`#XI?(U zK=V_Sk5bZoxw?kNM(>U9rQ1!H-XYa7;d?HY20f4*TzdtXqH%x9l

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z(2:end-1,2:end-1) = reshape(w,[3 3]); + surf(x,y,z) + title('Membrane Displacement (3 x 3)') + zlabel('Z Position (micron)') + ylabel('Y Position (micron)') + xlabel('X Position (micron)') + % Membrane displacement is shown on chart + +end \ No newline at end of file diff --git a/Part D/PartDFigure.png b/Part D/PartDFigure.png index ca69c450f0f61c91a2c7d43fb419cdbf175150b0..f367cda84c3c29086b61f856833dfbdf8754a31b 100644 GIT binary patch literal 95144 zcmd43go*DCb8T)4jj%GI2 zjOu1q&k!EITX&ur-Qwlu5oF}$7U32a;pMg!w5&l8MnvI`l)7vD%9w|%dSB()<}+TV z^Q_^i5&o>k%)4rL=8~mV%+9}fjNX*)o_V23ko=_H@7VIo<6txrp(#eubwiq*K(CWf zFY`eV75WnHy#_<9B4x(&SVja2jAXnD-aZ`KW9_#bCJIc)a~m5?WBxQJeiT0{7;y2~ zzq`7+iZKVmcqe2W2lI=strQybj_)>sJm%lF^jPOHuk9?1SnyKghRcfir%;$LF6MRN zQaI*iQVg3E^BOPr|MQDGQukq)zCZZ{1PGZF*&a$u`;8m%AQY5OIVg*Yi~oq9L#Cef zrmG6XDS5P2?vIOF4sw^5uZ~xG{Pe?f);j&$;X@p73yEtJFz>zQCM+!ccP?7L-$l&* zZ_?RchOEA2S1(0H#WdxFGN(Tul9GISlmvA>Hyh|Aj^7H7bAOaBQ&F1G3L_PWTkXww 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zY;0`MFoqqEjwTlrRNwgpYymp)1xrfL7vWMN@b~Ng81U^iG*=(1uP-RDgI;-2-0C{C zuS(GC+5c>=vP%18<23@F;|iP~R&x*?)d0E+-vS-J&hqhX4~^~W=<72=X$*8L=QFA^ zSf7@l`u8K%b0E`w=1l@C8COj;1cKqj^ zmonSq$KjlXhlI4Xw?{j})OF;(%AV>W1Yy~iz0#l>r#Albg4{5ki~Fw%352bV5dQ<9 zJY;moNJ)b}Y>m=(w8+9Te?XU6_O@Y#o$=aC52{!M#YvMQoH?`!Sa Date: Thu, 14 Dec 2017 20:20:03 -0500 Subject: [PATCH 04/13] Update README.md --- README.md | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 0c9f8c6..a68a116 100644 --- a/README.md +++ b/README.md @@ -33,7 +33,11 @@ function [w] = membrane_solution3(T,P) end ``` - +### Approach +- A matrix is set up using finite element analysis of the interior nodes of a 5x5 matrix +- A vector for the y direction is then set up for the membrane +- Using linear algebra, a vector for the displacement of the nodes is created +- The vector can then be transformed to represent the actual surface as a matrix # Part B ```matlab @@ -74,7 +78,9 @@ function [w] = membrane_solution(T,P,n) % Membrane displacement is shown on chart end ``` - +### Approach +- This problem uses the same steps as with the membrane_solution3 function, except it allows for the user to change the number of interior nodes +- This required alterations of the all the indexing and sizing in the function along with a few calculations # Part D ```matlab From 0a2c0f177cc239b2aba60156cb47154c43113719 Mon Sep 17 00:00:00 2001 From: Matthew Maliniak Date: Thu, 14 Dec 2017 20:21:42 -0500 Subject: [PATCH 05/13] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index a68a116..1ef15b3 100644 --- a/README.md +++ b/README.md @@ -136,7 +136,7 @@ pw_se = pw-se; - Next, the average displacement for each element is calculated. For each elements, the dispalcement at all four courners is taken and then averaged - Using these values, the work done by pressure can be calculated - For the change in dispalcement over the x and y coordinate system, the values of the change on the left and right (y-axis) or top and bottom (x-axis) are taken and averaged -- Using these values, the strain enegery can be calculated +- Using these values, the strain energy can be calculated # Part F ```matlab From 0221c79916d476138347397a333e2031894945e8 Mon Sep 17 00:00:00 2001 From: Lucas T Dombroski Date: Thu, 14 Dec 2017 20:29:10 -0500 Subject: [PATCH 06/13] Update membrane_solution3.m --- Part A/membrane_solution3.m | 31 +++++++++++-------------------- 1 file changed, 11 insertions(+), 20 deletions(-) diff --git a/Part A/membrane_solution3.m b/Part A/membrane_solution3.m index 91e2d25..bbd0c09 100644 --- a/Part A/membrane_solution3.m +++ b/Part A/membrane_solution3.m @@ -8,19 +8,6 @@ function [w] = membrane_solution3(T,P) % output: % w = vector of displacement of interior nodes -<<<<<<< HEAD - [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 (3 x 3)') - zlabel('Z Position (micron)') - ylabel('Y Position (micron)') - xlabel('X Position (micron)') - % Membrane displacement is shown on chart - -end -======= 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); @@ -32,14 +19,18 @@ w = k\y; % Solves for displacement (micrometers) % 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)') + + [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 (3 x 3)') + zlabel('Z Position (micron)') + ylabel('Y Position (micron)') + xlabel('X Position (micron)') + % Membrane displacement is shown on chart % Membrane displacement is shown on chart end ->>>>>>> 3217bec2baefdb9797b60fd7e29f12b838227cd0 + From af2c716c50f0c7a05abc037a8994a0bce4837187 Mon Sep 17 00:00:00 2001 From: Lucas T Dombroski Date: Thu, 14 Dec 2017 20:31:00 -0500 Subject: [PATCH 07/13] Update README.md --- README.md | 33 ++++++++++++++++++++------------- 1 file changed, 20 insertions(+), 13 deletions(-) diff --git a/README.md b/README.md index 1ef15b3..902e7e6 100644 --- a/README.md +++ b/README.md @@ -11,25 +11,32 @@ function [w] = membrane_solution3(T,P) % P = Pressure (MPa) % output: % w = vector of displacement of interior nodes - - 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) + +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) +% 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)') + title('Membrane Displacement (3 x 3)') + zlabel('Z Position (micron)') + ylabel('Y Position (micron)') + xlabel('X Position (micron)') % Membrane displacement is shown on chart + +% Membrane displacement is shown on chart + +end end ``` From d6cfc11502608766ba1516c316393a7a73f2b3af Mon Sep 17 00:00:00 2001 From: Lucas T Dombroski Date: Thu, 14 Dec 2017 20:31:39 -0500 Subject: [PATCH 08/13] Update README.md --- README.md | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/README.md b/README.md index 902e7e6..ce91382 100644 --- a/README.md +++ b/README.md @@ -37,8 +37,7 @@ w = k\y; % Membrane displacement is shown on chart end - -end + ``` ### Approach - A matrix is set up using finite element analysis of the interior nodes of a 5x5 matrix From c2aaea138f10eb299886f1a2480a4f3db3415a89 Mon Sep 17 00:00:00 2001 From: Lucas T Dombroski Date: Thu, 14 Dec 2017 20:32:08 -0500 Subject: [PATCH 09/13] Update README.md --- README.md | 1 - 1 file changed, 1 deletion(-) diff --git a/README.md b/README.md index ce91382..e47dfca 100644 --- a/README.md +++ b/README.md @@ -32,7 +32,6 @@ w = k\y; zlabel('Z Position (micron)') ylabel('Y Position (micron)') xlabel('X Position (micron)') - % Membrane displacement is shown on chart % Membrane displacement is shown on chart From b6447ba3cd1e2d86baddb1b05d608597e3833813 Mon Sep 17 00:00:00 2001 From: Lucas T Dombroski Date: Thu, 14 Dec 2017 20:35:32 -0500 Subject: [PATCH 10/13] Update membrane_solution.m --- Part C/membrane_solution.m | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/Part C/membrane_solution.m b/Part C/membrane_solution.m index a3b6d3e..537747b 100644 --- a/Part C/membrane_solution.m +++ b/Part C/membrane_solution.m @@ -22,7 +22,9 @@ w = k\y; 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)') +title('Membrane Displacement (3 x 3)') +zlabel('Z Position (micron)') +ylabel('Y Position (micron)') +xlabel('X Position (micron)') % Membrane displacement is shown on chart -end \ No newline at end of file +end From 3d67587626c30fc7b49cdcf3e15b4c06807fa5dc Mon Sep 17 00:00:00 2001 From: Lucas T Dombroski Date: Thu, 14 Dec 2017 20:35:54 -0500 Subject: [PATCH 11/13] Update membrane_solution.m --- Part C/membrane_solution.m | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Part C/membrane_solution.m b/Part C/membrane_solution.m index 537747b..a0a995b 100644 --- a/Part C/membrane_solution.m +++ b/Part C/membrane_solution.m @@ -1,4 +1,4 @@ -function [w] = membrane_solution(T,P,n) +10function [w] = membrane_solution(T,P,n) % membrane_solution: dispalacement of node for membrane with nxn interior nodes % [w] = membrane_solution(T,P,n) % input: @@ -22,7 +22,7 @@ w = k\y; z = zeros(size(x)); z(2:end-1,2:end-1) = reshape(w,[n n]); surf(x,y,z) -title('Membrane Displacement (3 x 3)') +title('Membrane Displacement (10 x 10)') zlabel('Z Position (micron)') ylabel('Y Position (micron)') xlabel('X Position (micron)') From 696438b9bd9b7c5d76ba428643f3e2ff7e66bded Mon Sep 17 00:00:00 2001 From: Lucas T Dombroski Date: Thu, 14 Dec 2017 20:36:18 -0500 Subject: [PATCH 12/13] Update membrane_solution.m --- Part C/membrane_solution.m | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Part C/membrane_solution.m b/Part C/membrane_solution.m index a0a995b..656f95e 100644 --- a/Part C/membrane_solution.m +++ b/Part C/membrane_solution.m @@ -1,4 +1,4 @@ -10function [w] = membrane_solution(T,P,n) +function [w] = membrane_solution(T,P,n) % membrane_solution: dispalacement of node for membrane with nxn interior nodes % [w] = membrane_solution(T,P,n) % input: From ad38ead693bebe1189ea7a6e5630241bc7ef6928 Mon Sep 17 00:00:00 2001 From: Lucas T Dombroski Date: Thu, 14 Dec 2017 20:37:09 -0500 Subject: [PATCH 13/13] Update README.md --- README.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index e47dfca..1bd4f88 100644 --- a/README.md +++ b/README.md @@ -78,8 +78,10 @@ function [w] = membrane_solution(T,P,n) 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)') + title('Membrane Displacement (10 x 10)') + zlabel('Z Position (micron)') + ylabel('Y Position (micron)') + xlabel('X Position (micron)') % Membrane displacement is shown on chart end ```