diff --git a/README.md b/README.md index 134beea..cc10ff0 100644 --- a/README.md +++ b/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. diff --git a/final_project/README.md b/final_project/README.md index cee3ee3..7a7b0ac 100644 --- a/final_project/README.md +++ b/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. diff --git a/final_project/final_project.pdf b/final_project/final_project.pdf index 3df5f1f..7c6fa9e 100644 Binary files a/final_project/final_project.pdf and b/final_project/final_project.pdf differ diff --git a/lecture_23/boussinesq_lookup.m b/lecture_23/boussinesq_lookup.m new file mode 100644 index 0000000..65b35a1 --- /dev/null +++ b/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 diff --git a/lecture_23/lecture_23.ipynb b/lecture_23/lecture_23.ipynb index 751c348..7bcd6e9 100644 --- a/lecture_23/lecture_23.ipynb +++ b/lecture_23/lecture_23.ipynb @@ -22,6 +22,21 @@ "%plot --format svg" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is Z?\n", + "\n", + "if $f(x) = a_{0}sin(x)+a_{1}sin(2x)+a_{2}e^{-x}$\n", + "\n", + "then Z\n", + "\n", + "$Z=[sin(x)~sin(2x)~e^{-x}]$\n", + "\n", + "$a=[a_{0}~a_{1}~a_{2}]^{T}$" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -36,7 +51,11 @@ " % function to perform linear least squares regression \n", " % based upon Z (independent-variable operators)\n", " % and y (dependent variable predictions)\n", - "\n", + " a=Z\\y;\n", + " fx=Z*a;\n", + " St=std(y);\n", + " Sr=std(y-fx);\n", + " r2=1-Sr/St;\n", "end" ] }, @@ -55,16 +74,35 @@ " % cost function \n", " % J = cost\n", " % grad = [dJ/da0,dJ/da1]\n", + " m=length(x);\n", + " a0=a(1);\n", + " a1=a(2);\n", + " t=a0+a1*x;\n", + " sigma=1./(1+exp(-t));\n", + " J= 1/m*sum(-y.*log(sigma)-(1-y).*log(1-sigma));\n", + " grad=zeros(2,1);\n", + " grad(1)=1/m*sum((sigma-y).*x.^0);\n", + " grad(2)=1/m*sum((sigma-y).*x.^1);\n", + " \n", "end" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "metadata": { - "collapsed": true + "collapsed": false }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[0;31mError: Function definitions are not permitted in this context.\n", + "\u001b[0m" + ] + } + ], "source": [ "% Homework 6 P3\n", "\n", @@ -87,12 +125,44 @@ "\n", " m=a/z;\n", " n=b/z;\n", + " if n < 1.3\n", + " f=fmn(:,2);\n", + " elseif n > 1.5\n", + " f=fmn(:,4);\n", + " else\n", + " f=fmn(:,3);\n", + " end\n", + " [~,i_fit]=sort(abs(m-fmn(:,1)));\n", + " x=fmn(i_fit(1:4),1);\n", + " y=f(i_fit(1:4));\n", + " f_out = Newtint(x,y,m);\n", + " sigma_z=q*f_out;\n", "end" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[0;31mUndefined function 'Newtint' for input arguments of type 'double'.\n", + "\u001b[0m" + ] + } + ], + "source": [ + "boussinesq_lookup(10,1,1,10)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, "metadata": { "collapsed": false }, @@ -103,26 +173,26 @@ "text": [ "i =\n", "\n", - " 2\n", - " 3\n", - " 1\n", - " 4\n", - " 5\n", - " 6\n", - " 7\n", - " 8\n", + " 2\n", + " 3\n", + " 1\n", + " 4\n", + " 5\n", + " 6\n", + " 7\n", + " 8\n", + "\n", "\n", "ans =\n", "\n", - " 0.20000\n", - " 0.30000\n", - " 0.10000\n", - " 0.40000\n", - " 0.50000\n", - " 0.60000\n", - " 0.70000\n", - " 0.80000\n", - "\n" + " 0.2000\n", + " 0.3000\n", + " 0.1000\n", + " 0.4000\n", + " 0.5000\n", + " 0.6000\n", + " 0.7000\n", + " 0.8000\n" ] } ], @@ -169,7 +239,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": { "collapsed": true }, @@ -181,7 +251,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -203,14 +273,14 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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Nn3zySWpq6oMHD7y9vdu1a8dVwWHw4MHC614OHjx48ODBpaWl6enp9+7ds9vt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\njRua9BAwATt37uzbt++333778OFDcm9ubm50dDR+07p3715TU0O2gRc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AwBDeFRJCqH379i5TdgAAAID54HoNCQAAAPAfQCEBAAAAXAAKCQAAAOACUEgAAAAAF4BC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\nnKSkpDFjxnhs13w+RlMppClTpsTExOzevVs48vPPP48cOTImJqawsFC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"text/plain": [ "" ] @@ -221,6 +291,7 @@ ], "source": [ "a=1.2;b=0.6;c=0.8;d=0.3;\n", + "h=0.001;\n", "[t y] = eulode(@predprey,tspan,y0,h,a,b,c,d);\n", "\n", "plot(t,y(:,1),t,y(:,2),'--')\n", @@ -230,14 +301,14 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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N+8idYB7xgMJ4h2CoHeIdAMCigCCdBenzAfOIKyDeAQBsDAjSGagzEGAecQjE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\n", 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UNiKEREVFvfjii83NzXv37rXYm7LHMmCBSABz6KxXif0gZrA9fE12Y8aMCQkJ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\nVdvtNqWUUsobCSGtVuvmmsxOt7FYrN/vK4qiaRr/3BNCVFX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"text/plain": [ "" ] @@ -248,19 +319,21 @@ ], "source": [ "plot(y(:,1),y(:,2))\n", - "title('(b) Euler phase plane plot')" + "title('(b) Euler phase plane plot')\n", + "xlabel('prey population')\n", + "ylabel('pred population')" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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S+uxBo4ulxaS1Xrf8kKkGxYPJ3vrhHAMUEkKmboTXbVIck+xhb72a0bSf1w1S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\nQCEBAAAAUgAKCQAAAJACUEgAAACAFPx/zW4IgobeuzoAAAAASUVORK5CYII=\n", + "image/png": 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I2OAQNz5RXV1dWVmp1+v5E+u6d+/O1lbZtm1b6FoMoD5sqXUG0QhCQJqANGrUqMjIyObm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\nWq17xC+HcTGoKly1StaDV1+yjD1VhvJ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, "text/plain": [ "" ] @@ -270,6 +343,8 @@ } ], "source": [ + "a=10;b=0.6;c=0.8;d=0.3;\n", + "tspan=[0 10];\n", "[t y] = rk4sys(@predprey,tspan,y0,h,a,b,c,d);\n", "plot(t,y(:,1),t,y(:,2),'--')\n", "title('(c) RK4 time plot')" @@ -277,14 +352,14 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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F08fJGbhgl5kzZ27dunXHjh1VVVVHjhzhzTJOCKmvrx87dmxdXZ1du33zzTd5bxqkampq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\n4sSJjIyMFStW0M3efPPN/v37q1pSAAB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LPYJYArA/BBLAb1gszVYrsvbUxuUeKalpFrtGAC4EgQQglKJW1C6Pna1WpBZU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\n9klnZ+eYMWPIZFVQNKMFra2tDz74YG1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"text/plain": [ "" ] diff --git a/lecture_24/.ipynb_checkpoints/lecture_24-checkpoint.ipynb b/lecture_24/.ipynb_checkpoints/lecture_24-checkpoint.ipynb new file mode 100644 index 0000000..2fd6442 --- /dev/null +++ b/lecture_24/.ipynb_checkpoints/lecture_24-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_24/feng et al 2009-paper_airplane.pdf b/lecture_24/feng et al 2009-paper_airplane.pdf new file mode 100644 index 0000000..d48bd26 Binary files /dev/null and b/lecture_24/feng et al 2009-paper_airplane.pdf differ diff --git a/lecture_24/lecture_24.ipynb b/lecture_24/lecture_24.ipynb new file mode 100644 index 0000000..66b8be6 --- /dev/null +++ b/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!**" + ] + }, + { + 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[], + "source": [ + "%plot --format svg" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "setdefaults" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Monte Carlo Dart Challenge\n", + "\n", + "![Dart Challenge Figure](../HW2/projectile.png)\n", + "\n", + "In homework 2, you created `projectile.m`, that calculated the height of a dart based upon initial velocity and angle. \n", + "\n", + "For extra credit, we compiled data from 40 students. \n", + "\n", + "Now, we want to calculate the control that these students had over their dart-throwing. \n", + "\n", + "This is called an *inverse problem*. Given, a mean and standard deviation of velocity and angle, we can calculate the mean and standard deviation of the final dart height with a Monte-Carlo model, but we want to determine a reasonable estimate for the mean and standard deviation of these two parameters. \n", + "\n", + "This is an open-ended design problem, so you can choose to fix or vary the parameters at your own discretion. In HW3, we used 15 m/s as an initial velocity. This is a good starting point, but is it fixed? Its up to you to decide. \n", + "\n", + "You can use the Matlab/Octave command `hist` to plot the data and the Monte Carlo model results. And you can compare statistics with `mean` and `std`\n", + "\n", + "State your assumptions and provide documentation for your functions and scripts. \n", + "\n", + "### The goal of this challenge comes down to 3 parts:\n", + "\n", + "1. Determine a range of values for initial velocity and angle (intuition or analysis)\n", + "\n", + "2. Describe initial velocity and angle with random variables (normal distribution? completely random?)\n", + "\n", + "3. Show that your random variables produce the same ditribution of dart locations as our throwers\n", + "\n", + "### Submit your repository via the Google Form:\n", + "[https://goo.gl/forms/MwdfNWgj9UlHnRV83](https://goo.gl/forms/MwdfNWgj9UlHnRV83)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans = 40\r\n" + ] + }, + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t-20\n", + "\t\n", + "\n", 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[ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hist(y_darts)" + ] + }, + { + "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 +} diff --git a/lecture_26/octave-workspace b/lecture_26/octave-workspace new file mode 100644 index 0000000..8c437bb Binary files /dev/null and b/lecture_26/octave-workspace differ diff --git a/myode.m b/myode.m new file mode 100644 index 0000000..cedefb6 --- /dev/null +++ b/myode.m @@ -0,0 +1,7 @@ +function dudt = myode(t,u) + x=u(1); + y=u(2); + dudt=zeros(2,1); + dudt(1)=0.1*x+0.3*x*y; + dudt(2)=0.1*x*y-2*y; +end \ No newline at end of file