added lecture 24

README.md

@@ -1,7 +1,6 @@
 # Computational Mechanics
 ## ME 3255 Spring 2017
 ### Github page: [https://github.uconn.edu/rcc02007/ME3255S2017.git]
-### Public (ipynb rendering)[https://github.com/cooperrc/ME3255S2017]
 
 ### Course Description
 This course introduces students to scientific programming utilizing Matlab/Octave.

final_project/README.md

@@ -56,7 +56,7 @@ b. Use a Monte Carlo model to determine the mean and standard deviation  for the
 maximum deflection $\delta x$ if b and h are normally distributed random variables
 with 0.1 % standard deviations at q=50 N/m. 
 
-3. Now use the central difference approximation to set up a system of equations for the
+2. Now use the central difference approximation to set up a system of equations for the
 beam for q(x)=cst, P=0, and $\omega=0$. Use the boundary conditions with a numerical
 differentiation to determine the valuea of the end points
 
@@ -71,7 +71,7 @@ differentiation to determine the valuea of the end points
     e. Comment on the results from the analytical and numerical approaches (if you used
     functions then provide help files, if you used scripts, then describe the steps used)
 
-4. Now set up the system of equations using a central difference method if P>0 and
+3. Now set up the system of equations using a central difference method if P>0 and
 $\omega=0$
 
     a. set up the system of equations for 6 segments as a function of q and P
@@ -83,7 +83,7 @@ $\omega=0$
     d. solve a-c for q=1,10,20,30,50 and plot the numerical results of q vs $\delta x$ for
     P=0, 100, 200, 300 (4 lines, labeled as P=0,P=100,...)
 
-5. Now set up an eigenvalue problem to solve for the natural frequencies of the simply
+4. Now set up an eigenvalue problem to solve for the natural frequencies of the simply
 supported beam if P=0 and q=0. 
 
     a. set up the system of equations for 6 segments
@@ -96,7 +96,7 @@ supported beam if P=0 and q=0.
 
     e. Plot the shape of the beam for the first 3 natural frequencies
 
-6. (Bonus 5pt) Create a function to return the system of equations for the eigenvalue
+5. (Bonus 5pt) Create a function to return the system of equations for the eigenvalue
 problem as a function of P, if P>0. Then, plot the lowest natural frequency vs the applied
 load P. 
 

lecture_23/boussinesq_lookup.m

@@ -0,0 +1,32 @@
+function sigma_z=boussinesq_lookup(q,a,b,z)
+  % function that determines stress under corner of an a by b rectangular platform
+  % z-meters below the platform. The calculated solutions are in the fmn data
+  % m=fmn(:,1)
+  % in column 2, fmn(:,2), n=1.2
+  % in column 3, fmn(:,2), n=1.4
+  % in column 4, fmn(:,2), n=1.6
+
+  fmn= [0.1,0.02926,0.03007,0.03058
+        0.2,0.05733,0.05894,0.05994
+        0.3,0.08323,0.08561,0.08709
+        0.4,0.10631,0.10941,0.11135
+        0.5,0.12626,0.13003,0.13241
+        0.6,0.14309,0.14749,0.15027
+        0.7,0.15703,0.16199,0.16515
+        0.8,0.16843,0.17389,0.17739];
+
+  m=a/z;
+  n=b/z;
+  if n < 1.3
+      f=fmn(:,2);
+    elseif n > 1.5
+        f=fmn(:,4);
+    else
+        f=fmn(:,3);
+  end
+  [~,i_fit]=sort(abs(m-fmn(:,1)));
+  x=fmn(i_fit(1:4),1);
+  y=f(i_fit(1:4));
+  f_out = Newtint(x,y,m);
+  sigma_z=q*f_out;
+end

lecture_24/.ipynb_checkpoints/lecture_24-checkpoint.ipynb

@@ -0,0 +1,6 @@
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+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

lecture_24/lecture_24.ipynb

@@ -0,0 +1,88 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "![q1](q1.png)\n",
+    "\n",
+    "![q2](q2.png)\n",
+    "\n",
+    "### How do Runge-Kutta methods increase the order of convergence?\n",
+    "![q3](q3.png)\n",
+    "\n",
+    "## Questions from you\n",
+    "\n",
+    "- How do Runge-Kutta methods increase the order of convergence?\n",
+    "\n",
+    "- Can you provide more assistance for the final project?\n",
+    "\n",
+    "- Will there be another homework? Or is it just the final project for the rest of the semester.\n",
+    "\n",
+    "- will the competition be limited to numerical methods or general engineering problems (like the hack-a-thon)?\n",
+    "\n",
+    "- On the final project, to get the GitHub bonus, do you have to solve the issue? Or do the points go to the one who opens the issue?\n",
+    "\n",
+    "- can we go over the final project\n",
+    "\n",
+    "Tues - more background and help"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Paper Airplane Design challenge\n",
+    "\n",
+    "We looked at a Phugoid model comparing Euler and Runge-Kutta second order solutions. Now, use this model to maximize the distance your paper airplane will fly. \n",
+    "\n",
+    "Using the phugoid model, write a new code to analyze the flight of a paper airplane, with the following conditions:\n",
+    "\n",
+    "*  Assume $L/D$ of 5.2 (a value close to measurements in [Feng et al. 2009](./feng et al 2009-paper_airplane.pdf))\n",
+    "*  For the trim velocity, $v_{t}$=5.5 m/s.\n",
+    "\n",
+    "Submit your github repository to the following Google form:\n",
+    "\n",
+    "[https://goo.gl/forms/mI2CKcyRvfOWz5FF3](https://goo.gl/forms/mI2CKcyRvfOWz5FF3)\n",
+    "\n",
+    "Initial judging by Prof. Cooper will be based upon clarity of solution (e.g. documents, files, results in README)\n",
+    "\n",
+    "The top groups will be distributed to the class to be voted on\n",
+    "\n",
+    "We have focused on Matlab/Octave in our work this semester, but if you prefer Python or some other language, feel free to code your solution in your language of choice. \n",
+    "\n",
+    "**Good Luck!**"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Octave",
+   "language": "octave",
+   "name": "octave"
+  },
+  "language_info": {
+   "file_extension": ".m",
+   "help_links": [
+    {
+     "text": "MetaKernel Magics",
+     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+    }
+   ],
+   "mimetype": "text/x-octave",
+   "name": "octave",
+   "version": "0.19.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

lecture_26/.ipynb_checkpoints/lecture_26-checkpoint.ipynb

@@ -0,0 +1,6 @@
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+ "metadata": {},
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