{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Análisis no-lineal aproximado"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introducción"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entre las aproximaciones fundamentales de la teoría linealizada de la elasticidad se asume que no hay diferencias importantes entre la configuración original y la configuración deformada de una estructura.\n",
    "\n",
    "Nótese que si se desprecia esta hipótesis se hace necesario conocer la configuración deformada antes de poder plantear las ecuaciones de equilibrio pero, a la vez, para poder conocer la configuración deformada es necesario cargar el sistema y resolver las ecuaciones de equilibrio. En consecuencia el problema es no lineal.\n",
    "\n",
    "Este puede verse en la matriz de rigidez local de un elemento cercha:\n",
    "\n",
    "$$\n",
    "\\begin{Bmatrix}f_1\\\\f_2\\end{Bmatrix} = \\frac{AE}{l}\n",
    "\\begin{bmatrix}\n",
    "1&-1\\\\\n",
    "-1&1\\end{bmatrix}\n",
    "\\begin{Bmatrix}u_1\\\\u_2\\end{Bmatrix}\\, ,\n",
    "$$\n",
    "\n",
    "de la cual se aprecia que la rigidez depende de la longitud del elemento, la cual depende a la vez de la deformación del mismo.\n",
    "\n",
    "En este notebook utilizaremos la implementación de los elementos tipo cercha (desarrollada en NB anteriores) para resolver una estructura considerando de manera aproximada la no linealidad.\n",
    "\n",
    "En particular, abordaremos el problema de una cercha de von Mises (ver figura), sometida a una carga vertical $F$. \n",
    "\n",
    "<center>\n",
    "    <img src=\"img/cercha_mises.svg\"\n",
    "         alt=\"Cercha de von Mises\"\n",
    "         style=\"width:400px\">\n",
    "</center>\n",
    "\n",
    "\n",
    "Esta cercha tiene la particularidad de que dependiendo del valor de la carga la estructura puede desarrollar un colapso por pandeo subito e invertir su configuración. Para determinar el valor de la carga de colapso es necesario:\n",
    "\n",
    "1. Resolver el problema incrementalmente dividiendo la aplicación de la carga en varios pasos o incrementos $\\triangle F$.\n",
    "\n",
    "2. Considerar el efecto de la deformación en la solución del problema de equilibrio."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Método de solución"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para resolver el problema se asumirá, en cada incremento, que la rigidez de los elementos, y por ende la rigidez de la estructura, corresponde a la configuración original antes de imponer el incremento de carga. Denotemos esta configuración y su rigidez asociada como ${}^0X$ y ${}^0K$ respectivamente y escribamos la ecuación de equilibrio en esta configuración como:\n",
    "\n",
    "$$\n",
    "[^0K] \\{\\triangle U\\} = \\{\\triangle F \\}\n",
    "$$\n",
    "\n",
    "donde $\\triangle U$ sería el desplazamiento producido por $\\triangle F$ si es que la rigidez fuera ${}^0K$.\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    \n",
    "¿De qué depende que las rigideces correspondientes a la configuración original ${}^0K$ y deformada ${}^1K$ sean diferentes?\n",
    "\n",
    "</div>\n",
    "\n",
    "Para verificar que tanto se esta violando la condición de equilibrio actualicemos el sistema a la configuración deformada de acuerdo con:\n",
    "\n",
    "\n",
    "$$\n",
    "X_i \\leftarrow{}^0X+\\triangle U\n",
    "$$\n",
    "\n",
    "y en la cual $X_i$ denota la aproximación $i$ a la configuración deformada.\n",
    "\n",
    "Recalculemos ahora la rigidez $K=K(X_i)$ en función de la nueva configuración $X_i$ y determinemos también los residuales o fuerzas sin equilibrar dadas por:\n",
    "\n",
    "$$\n",
    "R = \\triangle F-K(X_i)\\triangle U\n",
    "$$\n",
    "\n",
    "\n",
    "Una configuración de equilibrio se habrá encontrado cuando $R<tol$ o equivalentemente cuando el sistema\n",
    "\n",
    "$$\n",
    "\\left[K\\right]\\left\\{\\triangle U\\right\\}=\\left\\{R\\right\\}\n",
    "$$\n",
    "\n",
    "\n",
    "arroje como resultado un incremento de desplazamiento muy pequeño o tal que $\\triangle U<tol$.\n",
    "\n",
    "Para verificar esta condición hacemos:\n",
    "\n",
    "$$\n",
    "\\triangle F \\leftarrow R\n",
    "$$\n",
    "\n",
    "y resolvemos\n",
    "\n",
    "$$\n",
    "\\left[K\\right]\\left\\{\\triangle U\\right\\}=\\left\\{\\triangle F\\right\\}\n",
    "$$\n",
    "\n",
    "para determinar el nuevo incremento $\\triangle U$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Algoritmo "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If $\\triangle U < Tol$ Then (estado de equilibrio encontrado):\n",
    "\n",
    "Almacene la solución:\n",
    "\n",
    "\n",
    "$$\n",
    "^1X \\leftarrow X_i\n",
    "$$\n",
    "\n",
    "$$\n",
    "{}^1U \\leftarrow {}^1X - {}^0X\n",
    "$$\n",
    "\n",
    "$$\n",
    "{}^1F \\leftarrow  \\triangle F\n",
    "$$\n",
    "\n",
    "\n",
    "Else\n",
    "\n",
    "Actualice la configuración:\n",
    "\n",
    "$$\n",
    "X_{i+1}\\leftarrow{} X_i+\\triangle U\n",
    "$$\n",
    "\n",
    "\n",
    "$$\n",
    "U \\leftarrow X_{i+1} - {}^0X\n",
    "$$\n",
    "\n",
    "Recalcule $K=K(X_{i+1})$\n",
    "\n",
    "\n",
    "Calcule el residual:\n",
    "\n",
    "$$\n",
    "R = \\triangle F-K(X_{i+1}) U\n",
    "$$\n",
    "\n",
    "\n",
    "y resuelva el sistema:\n",
    "\n",
    "$$\n",
    "\\left[K\\right]\\left\\{\\triangle U\\right\\}=\\left\\{R\\right\\}\n",
    "$$\n",
    "\n",
    "para determinar un nuevo incremento $\\triangle U$ hasta alcanzar convergencia."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solución por elementos finitos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subrutinas generales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from solidspy.postprocesor import plot_truss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def readin():\n",
    "    nodes = np.loadtxt('files/Cnodes.txt', ndmin=2)\n",
    "    mats = np.loadtxt('files/Cmater.txt', ndmin=2)\n",
    "    elements = np.loadtxt('files/Celes.txt', ndmin=2, dtype=np.int)\n",
    "    loads = np.loadtxt('files/Cloads.txt', ndmin=2)\n",
    "    return nodes, mats, elements, loads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eqcounter(nodes):\n",
    "    nnodes = nodes.shape[0]\n",
    "    IBC = np.zeros((nnodes, 2), dtype=np.integer)\n",
    "    for node in range(nnodes):\n",
    "        for dof in range(2):\n",
    "            IBC[node, dof] = int(nodes[node, dof + 3])\n",
    "    neq = 0\n",
    "    for node in range(nnodes):\n",
    "        for dof in range(2):\n",
    "            if IBC[node, dof] == 0:\n",
    "                IBC[node, dof] = neq\n",
    "                neq = neq + 1\n",
    "    return neq, IBC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def assembly(elements, mats, nodes, neq, DME):\n",
    "    IELCON = np.zeros((2), dtype=np.integer)\n",
    "    KG = np.zeros((neq, neq))\n",
    "    nels = elements.shape[0]\n",
    "    nnodes = 2\n",
    "    ndof = 4\n",
    "    for el in range(nels):\n",
    "        elcoor = np.zeros((nnodes, 2))\n",
    "        im = np.int(elements[el, 2])\n",
    "        par0 = mats[im, 0]\n",
    "        par1 = mats[im, 1]\n",
    "        for j in range(nnodes):\n",
    "            IELCON[j] = elements[el, j+3]\n",
    "            elcoor[j, 0] = nodes[IELCON[j], 1]\n",
    "            elcoor[j, 1] = nodes[IELCON[j], 2]\n",
    "        kloc = ueltruss2D(elcoor, par0, par1)\n",
    "        dme = DME[el, :ndof]\n",
    "        for row in range(ndof):\n",
    "            glob_row = dme[row]\n",
    "            if glob_row != -1:\n",
    "                for col in range(ndof):\n",
    "                    glob_col = dme[col]\n",
    "                    if glob_col != -1:\n",
    "                        KG[glob_row, glob_col] = KG[glob_row, glob_col] +\\\n",
    "                                                 kloc[row, col]\n",
    "    return KG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ueltruss2D(coord, A, Emod):\n",
    "    vec = coord[1, :] - coord[0, :]\n",
    "    length = np.linalg.norm(vec)\n",
    "    nx = vec[0]/length\n",
    "    ny = vec[1]/length\n",
    "    Q = np.array([\n",
    "        [nx, ny, 0, 0],\n",
    "        [0,  0, nx, ny]])\n",
    "    kl = (A*Emod/length) * np.array([\n",
    "        [1, -1],\n",
    "        [-1, 1]])\n",
    "    kG = Q.T @ kl @ Q\n",
    "    return kG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loadasem(loads, IBC, neq, nl):\n",
    "    RHSG = np.zeros([neq])\n",
    "    for cont in range(nl):\n",
    "        il = int(loads[cont, 0])\n",
    "        ilx = IBC[il, 0]\n",
    "        ily = IBC[il, 1]\n",
    "        if ilx != -1:\n",
    "            RHSG[ilx] = loads[cont, 1]\n",
    "        if ily != -1:\n",
    "            RHSG[ily] = loads[cont, 2]\n",
    "    return RHSG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def DME(nodes, elements):\n",
    "    nels = elements.shape[0]\n",
    "    IELCON = np.zeros((nels, 2), dtype=np.integer)\n",
    "    DME_mat = np.zeros((nels, 4), dtype=np.integer)\n",
    "    neq, IBC = eqcounter(nodes)\n",
    "    ndof = 4\n",
    "    nnodes = 2\n",
    "    for ele in range(nels):\n",
    "        for node in range(nnodes):\n",
    "            IELCON[ele, node] = elements[ele, node + 3]\n",
    "            glob_num = IELCON[ele, node]\n",
    "            for loc_num in range(2):\n",
    "                DME_mat[ele, 2*node + loc_num] = IBC[glob_num, loc_num]\n",
    "    return DME_mat, IBC, neq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calcule el operador ensamblador y déjelo listo para iterar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "ndof = 4\n",
    "nnodes = 2\n",
    "nels = 2\n",
    "nodes, mats, elements, loads = readin()\n",
    "neq, IBC = eqcounter(nodes)\n",
    "R = np.zeros((neq))\n",
    "F = np.zeros((neq))\n",
    "UG = np.zeros((neq))\n",
    "DME_mat, IBC, neq = DME(nodes, elements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
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       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
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       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
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       "mpl.figure.prototype._init_canvas = function() {\n",
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       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
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       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
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       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
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       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
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       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
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       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
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       "\n",
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       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img 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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_truss(nodes, elements, mats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Iteraciones\n",
    "A conitnuación se describen de manera completa algunas iteraciones. Para el primer incremento se explica cada paso de la iteración.\n",
    "\n",
    "### Incremento 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Asuma estado de equilibrio conocido y dado por: ${}^0X$ , ${}^0F$ and ${}^0U$ .\n",
    "\n",
    "Calcule $K=K({}^0X)$ para la configuración conicida ${}^0X$, aplique el incremento $\\triangle F$ y resuelva:\n",
    "\n",
    "$$\n",
    "\\left[K({}^0X)\\right]\\left\\{\\triangle U\\right\\}=\\left\\{\\triangle F\\right\\}\n",
    "$$\n",
    "\n",
    "para determinar el incremento $\\triangle U$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -0.15018948]\n"
     ]
    }
   ],
   "source": [
    "ini_x = nodes[2, 2]\n",
    "KG = assembly(elements, mats, nodes, neq, DME_mat)\n",
    "RHSG = loadasem(loads, IBC, neq, 1)\n",
    "delu = np.linalg.solve(KG, RHSG)\n",
    "print(delu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Actualice:\n",
    "\n",
    "$$\n",
    "X_i \\leftarrow{}^0X+\\triangle U\n",
    "$$\n",
    "\n",
    "Recalcule $K=K(X_i)$\n",
    "\n",
    "y calcue el residual:\n",
    "\n",
    "$$\n",
    "R = \\triangle F-K(X_i)\\triangle U\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -0.41952316]\n"
     ]
    }
   ],
   "source": [
    "nodes[2, 2] = ini_x + delu[1]\n",
    "UG[1] = nodes[2, 2] - ini_x\n",
    "KG = assembly(elements, mats, nodes, neq, DME_mat)\n",
    "R = RHSG - KG.dot(UG)\n",
    "print(R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Haga:\n",
    "\n",
    "$$\n",
    "\\triangle F \\leftarrow R\n",
    "$$\n",
    "\n",
    "y resuelva:\n",
    "\n",
    "$$\n",
    "\\left[K\\right]\\left\\{\\triangle U\\right\\}=\\left\\{\\triangle F\\right\\}\n",
    "$$\n",
    "\n",
    "para el nuevo incremento $\\triangle U$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -0.00945998]\n"
     ]
    }
   ],
   "source": [
    "loads[0, 2] = R[1]\n",
    "RHSG = loadasem(loads, IBC, neq, 1)\n",
    "delu = np.linalg.solve(KG, RHSG)\n",
    "print(delu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If $\\triangle U < Tol$ Then (equilibrio):\n",
    "\n",
    "Almacene la solución:\n",
    "\n",
    "\n",
    "$$\n",
    "{}^1X \\leftarrow X_i\n",
    "$$\n",
    "\n",
    "$$\n",
    "{}^1U \\leftarrow {}^1X - {}^0X\n",
    "$$\n",
    "\n",
    "$$\n",
    "{}^1F \\leftarrow  \\triangle F\n",
    "$$\n",
    "\n",
    "\n",
    "Else\n",
    "\n",
    "Actualice:\n",
    "\n",
    "$$\n",
    "X_{i+1}\\leftarrow{} X_i+\\triangle U\n",
    "$$\n",
    "\n",
    "\n",
    "$$\n",
    "U \\leftarrow X_{i+1} - {}^0X\n",
    "$$\n",
    "\n",
    "Recalcule $K=K(X_{i+1})$\n",
    "\n",
    "\n",
    "Calcule residual:\n",
    "\n",
    "$$\n",
    "R = \\triangle F-K(X_{i+1}) U\n",
    "$$\n",
    "\n",
    "\n",
    "y resuelva:\n",
    "\n",
    "$$\n",
    "\\left[K\\right]\\left\\{\\triangle U\\right\\}=\\left\\{R\\right\\}\n",
    "$$\n",
    "\n",
    "para determinar un nuevo incremento $\\triangle U$ hasta alcanzar convergencia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3403505416069965\n",
      "[ 0.        -0.0019513]\n",
      "[ 0.0000000e+00 -4.4206067e-05]\n"
     ]
    }
   ],
   "source": [
    "nodes[2, 2] = nodes[2, 2] + delu[1]\n",
    "print(nodes[2, 2])\n",
    "UG[1] = nodes[2, 2] - ini_x\n",
    "KG = assembly(elements, mats, nodes, neq, DME_mat)\n",
    "R = RHSG - KG.dot(delu)\n",
    "print(R)\n",
    "#\n",
    "loads[0, 2] = R[1]\n",
    "RHSG = loadasem(loads, IBC, neq, 1)\n",
    "delu = np.linalg.solve(KG, RHSG)\n",
    "print(delu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -0.15964946]\n",
      "1.3403505416069965\n"
     ]
    }
   ],
   "source": [
    "nodes[2, 2] = nodes[2, 2]\n",
    "UG[1] = nodes[2, 2] - ini_x\n",
    "print(UG)\n",
    "print(nodes[2, 2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Incremento 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -0.16039549]\n"
     ]
    }
   ],
   "source": [
    "ini_x = nodes[2, 2]\n",
    "KG = assembly(elements, mats, nodes, neq, DME_mat)\n",
    "loads = np.loadtxt('files/Cloads.txt', ndmin=2)\n",
    "RHSG = loadasem(loads, IBC, neq, 1)\n",
    "delu = np.linalg.solve(KG, RHSG)\n",
    "print(delu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -0.65474157]\n"
     ]
    }
   ],
   "source": [
    "nodes[2, 2] = ini_x + delu[1]\n",
    "UG[1] = nodes[2, 2] - ini_x\n",
    "KG = assembly(elements, mats, nodes, neq, DME_mat)\n",
    "R = RHSG - KG.dot(UG)\n",
    "print(R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -0.01634449]\n"
     ]
    }
   ],
   "source": [
    "loads[0, 2] = R[1]\n",
    "RHSG = loadasem(loads, IBC, neq, 1)\n",
    "delu = np.linalg.solve(KG, RHSG)\n",
    "print(delu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1636105543819666\n",
      "[ 0.        -0.0078351]\n",
      "[ 0.         -0.00019796]\n"
     ]
    }
   ],
   "source": [
    "nodes[2, 2] = nodes[2, 2] + delu[1]\n",
    "print(nodes[2, 2])\n",
    "UG[1] = nodes[2, 2] - ini_x\n",
    "KG = assembly(elements, mats, nodes, neq, DME_mat)\n",
    "R = RHSG-KG.dot(delu)\n",
    "print(R)\n",
    "#\n",
    "loads[0, 2] = R[1]\n",
    "RHSG = loadasem(loads, IBC, neq, 1)\n",
    "delu = np.linalg.solve(KG, RHSG)\n",
    "print(delu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -0.17673999]\n",
      "1.1636105543819666\n"
     ]
    }
   ],
   "source": [
    "nodes[2, 2] = nodes[2, 2]\n",
    "UG[1] = nodes[2, 2] - ini_x\n",
    "print(UG)\n",
    "print(nodes[2, 2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Incremento 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.        -0.1788806]\n"
     ]
    }
   ],
   "source": [
    "ini_x = nodes[2, 2]\n",
    "KG = assembly(elements, mats, nodes, neq, DME_mat)\n",
    "loads = np.loadtxt('files/Cloads.txt', ndmin=2)\n",
    "RHSG = loadasem(loads, IBC, neq, 1)\n",
    "delu = np.linalg.solve(KG, RHSG)\n",
    "print(delu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -1.07509943]\n"
     ]
    }
   ],
   "source": [
    "nodes[2, 2] = ini_x + delu[1]\n",
    "UG[1] = nodes[2, 2] - ini_x\n",
    "KG = assembly(elements, mats, nodes, neq, DME_mat)\n",
    "R = RHSG-KG.dot(UG)\n",
    "print(R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -0.03202625]\n"
     ]
    }
   ],
   "source": [
    "loads[0, 2] = R[1]\n",
    "RHSG = loadasem(loads, IBC, neq, 1)\n",
    "delu = np.linalg.solve(KG, RHSG)\n",
    "print(delu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9527037093117487\n",
      "[ 0.         -0.03898688]\n",
      "[ 0.         -0.00120508]\n"
     ]
    }
   ],
   "source": [
    "nodes[2, 2] = nodes[2, 2] + delu[1]\n",
    "print(nodes[2, 2])\n",
    "UG[1] = nodes[2, 2] - ini_x\n",
    "KG = assembly(elements, mats, nodes, neq, DME_mat)\n",
    "R = RHSG-KG.dot(delu)\n",
    "print(R)\n",
    "#\n",
    "loads[0, 2] = R[1]\n",
    "RHSG = loadasem(loads, IBC, neq, 1)\n",
    "delu = np.linalg.solve(KG, RHSG)\n",
    "print(delu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.         -0.21090685]\n",
      "0.9527037093117487\n"
     ]
    }
   ],
   "source": [
    "nodes[2, 2] = nodes[2, 2]\n",
    "UG[1] = nodes[2, 2] - ini_x\n",
    "print(UG)\n",
    "print(nodes[2, 2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problema\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    \n",
    "Implemente un algoritmo que realice de manera automática los pasos de cada incremento y aplique el mismo para determinar al menos 5 configuraciones equilibradas.\n",
    " \n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formato del notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La siguiente celda cambia el formato del Notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link href='http://fonts.googleapis.com/css?family=Fenix' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Source+Code+Pro:300,400' rel='stylesheet' type='text/css'>\n",
       "\n",
       "<style>\n",
       "\n",
       "/*\n",
       "Template for Notebooks for Modelación computacional.\n",
       "\n",
       "Based on Lorena Barba template available at:\n",
       "\n",
       "    https://github.com/barbagroup/AeroPython/blob/master/styles/custom.css\n",
       "*/\n",
       "\n",
       "/* Fonts */\n",
       "@font-face {\n",
       "font-family: \"Computer Modern\";\n",
       "src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "}\n",
       "\n",
       "/* Text */\n",
       "div.cell{\n",
       "width:800px;\n",
       "margin-left:16% !important;\n",
       "margin-right:auto;\n",
       "}\n",
       "h1 {\n",
       "font-family: 'Alegreya Sans', sans-serif;\n",
       "}\n",
       "h2 {\n",
       "font-family: 'Fenix', serif;\n",
       "}\n",
       "h3{\n",
       "font-family: 'Fenix', serif;\n",
       "margin-top:12px;\n",
       "margin-bottom: 3px;\n",
       "}\n",
       "h4{\n",
       "font-family: 'Fenix', serif;\n",
       "}\n",
       "h5 {\n",
       "font-family: 'Alegreya Sans', sans-serif;\n",
       "}\t\n",
       "div.text_cell_render{\n",
       "font-family: 'Alegreya Sans',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "line-height: 135%;\n",
       "font-size: 120%;\n",
       "width:600px;\n",
       "margin-left:auto;\n",
       "margin-right:auto;\n",
       "}\n",
       ".CodeMirror{\n",
       "font-family: \"Source Code Pro\";\n",
       "font-size: 90%;\n",
       "}\n",
       "/* .prompt{\n",
       "display: None;\n",
       "}*/\n",
       ".text_cell_render h1 {\n",
       "font-weight: 200;\n",
       "font-size: 50pt;\n",
       "line-height: 100%;\n",
       "color:#CD2305;\n",
       "margin-bottom: 0.5em;\n",
       "margin-top: 0.5em;\n",
       "display: block;\n",
       "}\t\n",
       ".text_cell_render h5 {\n",
       "font-weight: 300;\n",
       "font-size: 16pt;\n",
       "color: #CD2305;\n",
       "font-style: italic;\n",
       "margin-bottom: .5em;\n",
       "margin-top: 0.5em;\n",
       "display: block;\n",
       "}\n",
       ".warning{\n",
       "color: rgb( 240, 20, 20 )\n",
       "}\n",
       "</style>\n",
       "\n",
       "<script>\n",
       "/* Equations */\n",
       "\n",
       "MathJax.Hub.Config({\n",
       "TeX: {\n",
       "extensions: [\"AMSmath.js\"]\n",
       "},\n",
       "tex2jax: {\n",
       "inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "},\n",
       "displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "\"HTML-CSS\": {\n",
       "styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "}\n",
       "});\n",
       "</script>\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    styles = open('./nb_style.css', 'r').read()\n",
    "    return HTML(styles)\n",
    "\n",
    "\n",
    "css_styling()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}