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    "# Eulerian buckling of a beam\n",
    "\n",
    "In this numerical tour, we will compute the critical buckling load of a straight beam under normal compression, the classical Euler buckling problem. Usually, buckling is an important mode of failure for slender beams so that a standard Euler-Bernoulli beam model is sufficient. However, since FEniCS does not support Hermite elements ensuring $C^1$-formulation for the transverse deflection, implementing such models is not straightforward and requires using advanced DG formulations for instance, see the `fenics-shell` [implemntation of the Love-Kirchhoff plate model](http://fenics-shells.readthedocs.io/en/latest/demo/kirchhoff-love-clamped/demo_kirchhoff-love-clamped.py.html) or the [FEniCS documented demo on the biharmonic equation](http://fenics.readthedocs.io/projects/dolfin/en/2017.2.0/demos/biharmonic/python/demo_biharmonic.py.html).\n",
    "\n",
    "As a result, we will simply formulate the buckling problem using a Timoshenko beam model.\n",
    "\n",
    "## Timoshenko beam model formulation\n",
    "\n",
    "We first formulate the stiffness bilinear form of the Timoshenko model given by:\n",
    "\\begin{equation}\n",
    "k((w,\\theta),(\\widehat{w},\\widehat{\\theta}))= \\int_0^L EI \\dfrac{d\\theta}{dx}\\dfrac{d\\widehat{\\theta}}{dx} dx +  \\int_0^L \\kappa \\mu S \\left(\\dfrac{dw}{dx}-\\theta\\right)\\left(\\dfrac{d\\widehat{w}}{dx}-\\widehat{\\theta}\\right) dx\n",
    "\\end{equation}\n",
    "where $I=bh^3/12$ is the bending inertia for a rectangular beam of width $b$ and height $h$, $S=bh$ the cross-section area, $E$ the material Young modulus and $\\mu$ the shear modulus and $\\kappa=5/6$ the shear correction factor. We will use a $P^2/P^1$ interpolation for the mixed field $(w,\\theta)$. "
   ]
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   "source": [
    "For issues related to shear-locking and reduced integration formulation, we refer to the :ref:`ReissnerMindlinQuads` tour."
   ]
  },
  {
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   "metadata": {},
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    "from dolfin import *\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib notebook\n",
    "\n",
    "L = 10.\n",
    "thick = Constant(0.03)\n",
    "width = Constant(0.01)\n",
    "E = Constant(70e3)\n",
    "nu = Constant(0.)\n",
    "\n",
    "EI = E*width*thick**3/12\n",
    "GS = E/2/(1+nu)*thick*width\n",
    "kappa = Constant(5./6.)\n",
    "\n",
    "\n",
    "N = 100\n",
    "mesh = IntervalMesh(N, 0, L) \n",
    "\n",
    "U = FiniteElement(\"CG\", mesh.ufl_cell(), 2)\n",
    "T = FiniteElement(\"CG\", mesh.ufl_cell(), 1)\n",
    "V = FunctionSpace(mesh, U*T)\n",
    "\n",
    "u_ = TestFunction(V)\n",
    "du = TrialFunction(V)\n",
    "(w_, theta_) = split(u_)\n",
    "(dw, dtheta) = split(du)\n",
    "\n",
    "\n",
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    "k_form = EI*inner(grad(theta_), grad(dtheta))*dx + \\\n",
    "         kappa*GS*dot(grad(w_)[0]-theta_, grad(dw)[0]-dtheta)*dx\n",
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    "l_form = Constant(1.)*u_[0]*dx"
   ]
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  {
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   "source": [
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    "As in the :ref:`ModalAnalysis` tour, a dummy linear form :code:`l_form` is used to call the :code:`assemble_system` function which retains the symmetric structure of the associated matrix when imposing boundary conditions. Here, we will consider clamped conditions on the left side :math:`x=0` and simple supports on the right side :math:`x=L`."
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   ]
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   "source": [
    "def both_ends(x, on_boundary):\n",
    "    return on_boundary\n",
    "def left_end(x, on_boundary):\n",
    "    return near(x[0], 0) and on_boundary\n",
    "\n",
    "bc = [DirichletBC(V.sub(0), Constant(0.), both_ends),\n",
    "      DirichletBC(V.sub(1), Constant(0.), left_end)]\n",
    "\n",
    "K = PETScMatrix()\n",
    "assemble_system(k_form, l_form, bc, A_tensor=K)"
   ]
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   "source": [
    "## Construction of the geometric stiffness matrix\n",
    "\n",
    "The buckling analysis amounts to solving an eigenvalue problem of the form:\n",
    "\n",
    "\\begin{equation}\n",
    "(\\mathbf{K}+\\lambda\\mathbf{K_G})\\mathbf{U} = 0\n",
    "\\end{equation}\n",
    "\n",
    "in which the geometric stiffness matrix $\\mathbf{K_G}$ depends (linearly) on a prestressed state, the amplitude of which is represented by $\\lambda$. The eigenvalue/eigenvector $(\\lambda,\\mathbf{U})$ solving the previous generalized eigenproblem respectively correspond to the critical buckling load and its associated buckling mode. For a beam in which the prestressed state correspond to a purely compression state of intensity $N_0>0$, the geometric stiffness bilinear form is given by:\n",
    "\n",
    "\\begin{equation}\n",
    "k_G((w,\\theta),(\\widehat{w},\\widehat{\\theta}))= -\\int_0^L N_0 \\dfrac{dw}{dx}\\dfrac{d\\widehat{w}}{dx} dx\n",
    "\\end{equation}\n",
    "\n",
    "which is assembled below into the `KG` `PETScMatrix` (up to the negative sign)."
   ]
  },
  {
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   "metadata": {},
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   "source": [
    "N0 = Constant(1e-3)\n",
    "kg_form = N0*dot(grad(w_), grad(dw))*dx\n",
    "KG = PETScMatrix()\n",
    "assemble(kg_form, tensor=KG)\n",
    "for bci in bc:\n",
    "    bci.zero(KG)"
   ]
  },
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   "source": [
    "Note that we made use of the `zero` method of `DirichletBC` making the rows of the matrix associated with the boundary condition zero. If we used instead the `apply` method, the rows would have been replaced with a row of zeros with a 1 on the diagonal (as for the stiffness matrix `K`). As a result, we would have obtained an eigenvalue equal to 1 for each row with a boundary condition which can make more troublesome the computation of eigenvalues if they happen to be close to 1. Replacing with a full row of zeros in `KG` results in infinite eigenvalues for each boundary condition which is more suitable when looking for the lowest eigenvalues of the buckling problem.\n",
    "\n",
    "##  Setting and solving the eigenvalue problem\n",
    "\n",
    "Up to the negative sign cancelling from the previous definition of `KG`, we now formulate the generalized eigenvalue problem $\\mathbf{KU}=-\\lambda\\mathbf{K_G U}$ using the `SLEPcEigenSolver`. The only difference from what has already been discussed in the dynamic modal analysis numerical tour is that buckling eigenvalue problem may be more difficult to solve than modal analysis in certain cases, it is therefore beneficial to prescribe a value of the spectral shift close to the critical buckling load."
   ]
  },
  {
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   "execution_count": 4,
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   "metadata": {},
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     "text": [
      "Computing 3 first eigenvalues...\n"
     ]
    },
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       "        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, fig.canvas.height);\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 overriden (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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Critical buckling loads:\n",
      "Exact:    0.31800  FE:    0.31805  Rel. gap 0.01%%\n",
      "Exact:    0.93995  FE:    0.94033  Rel. gap 0.04%%\n",
      "Exact:    1.87267  FE:    1.87415  Rel. gap 0.08%%\n"
     ]
    }
   ],
   "source": [
    "eigensolver = SLEPcEigenSolver(K, KG)\n",
    "eigensolver.parameters['problem_type'] = 'gen_hermitian'\n",
    "eigensolver.parameters[\"spectrum\"] = \"smallest real\"\n",
    "eigensolver.parameters['spectral_transform'] = 'shift-and-invert'\n",
    "eigensolver.parameters['spectral_shift'] = 1e-3\n",
    "eigensolver.parameters['tolerance'] = 1e-12\n",
    "\n",
    "N_eig = 3   # number of eigenvalues\n",
    "print \"Computing %i first eigenvalues...\" % N_eig\n",
    "eigensolver.solve(N_eig)\n",
    "\n",
    "# Exact solution computation\n",
    "from scipy.optimize import root\n",
    "from math import tan\n",
    "falpha = lambda x: tan(x)-x\n",
    "alpha = lambda n: root(falpha, 0.99*(2*n+1)*pi/2.)['x'][0]\n",
    "\n",
    "plt.figure()\n",
    "# Extraction\n",
    "print \"Critical buckling loads:\"\n",
    "for i in range(N_eig):\n",
    "    # Extract eigenpair\n",
    "    r, c, rx, cx = eigensolver.get_eigenpair(i)\n",
    "    \n",
    "    critical_load_an = alpha(i+1)**2*float(EI/N0)/L**2\n",
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    "    print(\"Exact: {0:>10.5f}  FE: {1:>10.5f}  Rel. gap {2:1.2f}%%\".format(\n",
    "           critical_load_an, r, 100*(r/critical_load_an-1)))\n",
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    "    \n",
    "    # Initialize function and assign eigenvector (renormalize by stiffness matrix)\n",
    "    eigenmode = Function(V,name=\"Eigenvector \"+str(i))\n",
    "    eigenmode.vector()[:] = rx/np.max(np.abs(rx.get_local()))\n",
    "\n",
    "    plot(eigenmode.sub(0), label=\"Buckling mode \"+str(i+1))\n",
    "\n",
    "plt.ylim((-1.2, 1.2))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above, we compared the computed FE critical loads with the known analytical value for the Euler-Bernoulli beam model and the considered boundary conditions given by:\n",
    "\n",
    "\\begin{equation}\n",
    "F_n = (\\alpha_n)^2 \\dfrac{EI}{L^2} \\quad \\text{with }\\alpha_n \\text{ solutions to } \\tan(\\alpha) = \\alpha\n",
    "\\end{equation}\n",
    "\n",
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    "In particular, it can be observed that the displacement-based FE solution overestimates the exact buckling load and that the error increases with the order of the buckling load."
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   ]
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  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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  }
 ],
 "metadata": {
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  "celltoolbar": "Raw Cell Format",
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  "kernelspec": {
   "display_name": "Python 2",
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