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   "source": [
    "<h1 align=\"center\">Simple beam modeling</h1> \n",
    "<div  align=\"center\">\n",
    "<img align=\"center\" src=\"https://upload.wikimedia.org/wikipedia/commons/6/6f/Simple_beam_with_center_load.svg\"  />\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b132a882-6f77-46ae-a371-1acaa75d8dda",
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    import piplite\n",
    "    await piplite.install(['ipywidgets==7.7.0', 'ipyflex', 'plotly', 'cosapp'])\n",
    "except:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "01ddcc7d-6223-4296-9884-3a9bcb19bd7a",
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   "outputs": [],
   "source": [
    "from cosapp.ports import Port\n",
    "from cosapp.systems import System\n",
    "import numpy as np\n",
    "\n",
    "class GeometryPort(Port):\n",
    "    def setup(self):\n",
    "        self.add_variable(\"visible\", True, desc=\"Should this geometry be shown?\")\n",
    "        self.add_variable(\"shape\", None, desc=\"Geometrical object\")\n",
    "class BeamGeo(System):\n",
    "    \n",
    "    def setup(self):\n",
    "        self.add_inward(\"file\",\"path\")\n",
    "        self.add_inward(\"mesh_size\",100)\n",
    "        self.add_inward('width', 0.5, unit = 'm')\n",
    "        self.add_inward('height',0.5, unit = 'm')\n",
    "        self.add_inward('length', 5., unit = 'm')\n",
    "        self.add_outward('I', desc='Second area moment')\n",
    "        self.add_outward('grid', np.zeros(1))\n",
    "        self.add_outward(\"section\", [])\n",
    "        self.add_output(GeometryPort, 'geom')\n",
    "    def compute(self):\n",
    "        self.I = self.width*self.height**3/12.\n",
    "        self.grid = np.array([i*self.length/self.mesh_size for i in range(0,int(self.mesh_size)+1)])\n",
    "        section = [[],[]]\n",
    "        for i in range(0,100):\n",
    "            section[0].append((- 0.5 + i/100.)*self.width)\n",
    "            section[1].append(-0.5*self.height)\n",
    "        for i in range(0,100):\n",
    "            section[0].append(0.5*self.width)\n",
    "            section[1].append((- 0.5 + i/100.)*self.height) \n",
    "        for i in range(0,100):\n",
    "            section[0].append((0.5 - i/100.)*self.width)\n",
    "            section[1].append(0.5*self.height)  \n",
    "        for i in range(0,100):\n",
    "            section[0].append( -0.5*self.width)\n",
    "            section[1].append((0.5 - i/100.)*self.height)  \n",
    "        self.section = section\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5cc948e4-115b-459b-80fc-b24d8546b426",
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   "outputs": [],
   "source": [
    "class BeamMeca(System):\n",
    "    def setup(self):\n",
    "        \n",
    "        self.add_inward('E', 270, desc = \"Young modulus\",  valid_range = [100,150],limits = [50,200])\n",
    "        self.add_inward(\"grid\", np.zeros(101), valid_range = [2,4],limits = [-np.inf,10] )\n",
    "        self.add_inward(\"I\", 1., desc='Second area moment' )\n",
    "        self.add_inward(\"force\", -1., desc='Force value', unit = 'N' )\n",
    "        self.add_inward(\"position\", 0.5, desc=\"force relative position\",limits= [0.2,0.3], valid_range = [0.1,0.8] )\n",
    "        self.add_outward(\"M\", np.zeros(1), desc = \"Bending moments\" )\n",
    "        self.add_outward(\"Q\", np.zeros(1), desc = \"Shear forces\" )\n",
    "        self.add_outward(\"W\", np.zeros(1), desc = \"Deflections\" )\n",
    "        self.add_outward(\"maxW\", 0, desc = \"Max deflections\" )\n",
    "        self.add_outward(\"f_position\", 0.5, desc=\"force  position\")\n",
    "        self.add_outward(\"maxW_loc\", 0, desc = \"Max deflections location\" )\n",
    "    def compute(self):\n",
    "        if self.position > 1.:\n",
    "            position = 0.99\n",
    "        elif self.position < 0:\n",
    "            position = 0.\n",
    "        else:\n",
    "            position = self.position\n",
    "        mesh_size = len(self.grid)\n",
    "        L = self.grid[-1]\n",
    "        b = (1.- position)*L\n",
    "        a = position*L\n",
    "        M =[]\n",
    "        Q = []\n",
    "        W = []\n",
    "        for i in range(0, int(mesh_size*position)):\n",
    "            x = self.grid[i]\n",
    "            M.append(self.force*b*x/L)\n",
    "            Q.append(self.force*b/L)\n",
    "            W.append(self.force*b*x*(L**2 - b**2 - x**2)/(6*L*self.E*self.I))  \n",
    "        for j in range(int(mesh_size*position), mesh_size):\n",
    "            x = self.grid[j]\n",
    "            M.append(self.force*a*(L - x)/L)\n",
    "            Q.append(self.force*(b/L-1))\n",
    "            W.append(self.force*b*x*(L**2 - b**2 - x**2)/(6*L*self.E*self.I)+ self.force*(x-a)**3/(6*self.E*self.I))\n",
    "        self.M = np.array(M)\n",
    "        self.Q = np.array(Q) \n",
    "        self.W = np.array(W)\n",
    "        self.maxW_loc = int(np.argmax(np.absolute(self.W)))-1\n",
    "        self.maxW = self.W[self.maxW_loc]\n",
    "        self.f_position = mesh_size*position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3f5f7ee7-819e-4690-b6ec-34f57ce9a3fb",
   "metadata": {
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   "outputs": [],
   "source": [
    "class Main(System):\n",
    "    def setup(self):\n",
    "        self.add_inward(\"maintest\",0)\n",
    "        self.add_child(BeamGeo(\"geo\"))\n",
    "        self.add_child(BeamMeca(\"meca\"))\n",
    "        self.connect(self.geo.outwards, self.meca.inwards, [\"I\", \"grid\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "20ec9af0-99e4-40dc-8ccd-cdade154b36b",
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    }
   },
   "outputs": [],
   "source": [
    "main = Main(\"main\")\n",
    "main.run_drivers()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9cad584d-3a0e-4278-95fd-90b216d458a7",
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        "row": null,
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     }
    }
   },
   "outputs": [],
   "source": [
    "import ipywidgets\n",
    "import ipyflex\n",
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d2247985-b5fb-474c-a31c-8cdd8c7178bd",
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   },
   "outputs": [],
   "source": [
    "widget_M = go.FigureWidget(go.Bar(\n",
    "    y=main.meca.M,\n",
    "    # marker_color='rgba(91, 91, 91, 0.73)',\n",
    "    name='M',\n",
    "))\n",
    "widget_Q = go.FigureWidget(go.Scatter(\n",
    "    y=main.meca.Q ,\n",
    "    # marker_color='rgba(91, 91, 91, 0.73)',\n",
    "    name='M',\n",
    "))\n",
    "widget_W = go.FigureWidget(go.Bar(\n",
    "    y=main.meca.W,\n",
    "    # marker_color='rgba(91, 91, 91, 0.73)',\n",
    "    name='M',\n",
    "), layout_yaxis_range=[-10,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ce89045a-45c3-4409-b1d5-75896ace81db",
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    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "87ad8d18-1628-4a58-89b8-cdde8bae95a1",
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   },
   "outputs": [],
   "source": [
    "E_slider = ipywidgets.FloatSlider(    value=150,\n",
    "    min=50,\n",
    "    max=250,description='Young modulus:',\n",
    "                                 continuous_update=False,)\n",
    "def on_E_change(change):\n",
    "    main.meca.E = change['new']\n",
    "    main.run_drivers()\n",
    "    widget_M.data[0].y = main.meca.M\n",
    "    widget_Q.data[0].y = main.meca.Q\n",
    "    widget_W.data[0].y = main.meca.W\n",
    "E_slider.observe(on_E_change, names='value')\n",
    "\n",
    "position_slider = ipywidgets.FloatSlider(    value=0.5,\n",
    "    min=0.1,\n",
    "    max=0.8,\n",
    "                                         continuous_update=False,\n",
    "                                        description='Force position',)\n",
    "def on_position_change(change):\n",
    "    main.meca.position = change['new']\n",
    "    main.run_drivers()\n",
    "    widget_M.data[0].y = main.meca.M\n",
    "    widget_Q.data[0].y = main.meca.Q\n",
    "    widget_W.data[0].y = main.meca.W\n",
    "position_slider.observe(on_position_change, names='value')\n",
    "control = ipywidgets.VBox([E_slider, position_slider])\n"
   ]
  },
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   "execution_count": 8,
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   },
   "outputs": [],
   "source": [
    "widget_dict = {'Moment': widget_M, 'Deflection': widget_W, 'Shear forces':widget_Q, 'Control':  control}\n",
    "w = ipyflex.FlexLayout(widget_dict, \n",
    "                       template='beam.json',\n",
    "                       editable=False,\n",
    "                       header={'title':'Simply supported beam', 'buttons':[]},\n",
    "                      )"
   ]
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       "FlexLayout(children={'Moment': FigureWidget({\n",
       "    'data': [{'name': 'M',\n",
       "              'type': 'bar',\n",
       "        …"
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