pile_analysis.ipynb

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    "%matplotlib widget\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import FloatSlider,BoundedFloatText, BoundedIntText, IntSlider, Layout, VBox, HBox, Output, Label\n",
    "from IPython.display import clear_output"
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    "- **In this app, we can plot the horizontal deformation, shear force and bending moment for specific pile properties.**\n",
    "- **Use the Slider and Text widgets to change the parameters.**\n",
    "- **Find the code here [link](https://github.com/Sinamhd9/pileAnalysis).**"
   ]
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   "source": [
    "def stiff_rel_fun(E, I, L):\n",
    "    k = np.array([[12*E*I/L**3, 6*E*I/L**2, -12*E*I/L**3, 6*E*I/L**2],\n",
    "    [6*E*I/L**2, 4*E*I/L, -6*E*I/L**2, 2*E*I/L],\n",
    "    [-12*E*I/L**3, -6*E*I/L**2, 12*E*I/L**3, -6*E*I/L**2],\n",
    "    [6*E*I/L**2, 2*E*I/L, -6*E*I/L**2, 4*E*I/L]], dtype=np.float64)\n",
    "    return k"
   ]
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       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
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    "fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(10,5), sharey=True)"
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       "HBox(children=(VBox(children=(FloatSlider(value=0.6, description='Pile diameter ($m$):', layout=Layout(width='…"
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    "style = {'description_width': 'initial', 'handle_color': 'lightgreen'}\n",
    "d_slider = FloatSlider(\n",
    "    value=0.6,\n",
    "    min=0.1,\n",
    "    max=2.0,\n",
    "    step=0.1,\n",
    "    description='Pile diameter ($m$):',style=style,layout=Layout(width='500px')\n",
    ")\n",
    "facw_slider = FloatSlider(\n",
    "    value=0.8,\n",
    "    min=0.0,\n",
    "    max=1.0,\n",
    "    step=0.1,\n",
    "    description='Fraction of section width in spring stiffness:',style=style,\n",
    "    layout=Layout(width='500px')\n",
    ")\n",
    "\n",
    "L_slider = FloatSlider(\n",
    "    value=31.5,\n",
    "    min=0.5,\n",
    "    max=50.0,\n",
    "    step=0.1,\n",
    "    description='Pile length ($m$):',style=style,\n",
    "    layout=Layout(width='500px')\n",
    ")\n",
    "N_slider = IntSlider(\n",
    "    value=100,\n",
    "    min=10,\n",
    "    max=300,\n",
    "    step=10,\n",
    "    description='Number of elements',\n",
    "    style=style,\n",
    "    layout=Layout(width='500px')\n",
    ")\n",
    "\n",
    "k_slider = IntSlider(\n",
    "    value=5800,\n",
    "    min=1000,\n",
    "    max=10000,\n",
    "    step=100,\n",
    "    description='Soil stiffness ($kN/m^2$)',\n",
    "    style=style,\n",
    "    layout=Layout(width='500px')\n",
    ")\n",
    "\n",
    "\n",
    "E_btb = BoundedIntText(\n",
    " value=2e8,\n",
    " min=1e7,\n",
    " max=1e10,\n",
    "    step=1e6,\n",
    " description='Modulus of elasticity ($kN/m^2$):',\n",
    "    style=style,\n",
    "    layout=Layout(width='300px')\n",
    " )\n",
    "\n",
    "I_btb = BoundedFloatText(\n",
    " value=0.00187,\n",
    " min=0.00001,\n",
    " max=0.1,\n",
    "step=0.001,\n",
    " description='Second moment of inertia ($m^4$):',\n",
    "    style=style,\n",
    "    layout=Layout(width='300px')\n",
    " )\n",
    "\n",
    "\n",
    "H_btb = BoundedIntText(\n",
    " value=200,\n",
    " min=1,\n",
    " max=1000,\n",
    " description='Lateral load at pile top ($kN$)',\n",
    "    style=style,\n",
    "    layout=Layout(width='300px')\n",
    " )\n",
    "\n",
    "\n",
    "Ktheta_btb = BoundedIntText(\n",
    " value=1e8,\n",
    " min=0,\n",
    " max=1e12,\n",
    "step=1e6,\n",
    " description='Rotational spring ($kNm/rad$)',\n",
    "    style=style,\n",
    "    layout=Layout(width='300px')\n",
    " )\n",
    "\n",
    "\n",
    "ui = VBox([d_slider, facw_slider, L_slider, N_slider,  k_slider])\n",
    "ui2 = VBox([E_btb, I_btb, H_btb, Ktheta_btb])\n",
    "uis = HBox([ui, ui2])\n",
    "display(uis)"
   ]
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    "\n",
    "def run_calcs():\n",
    "    d =  d_slider.value  \n",
    "    facw = facw_slider.value\n",
    "    L = L_slider.value\n",
    "    E = E_btb.value                       \n",
    "    I = I_btb.value\n",
    "    N = N_slider.value\n",
    "    H = H_btb.value\n",
    "    k = k_slider.value\n",
    "    Ktheta = Ktheta_btb.value \n",
    "    delta_x = L/N                               # Length of one element (in)\n",
    "    K = stiff_rel_fun(E, I, delta_x)\n",
    "    x = np.arange(0,L+0.01,delta_x, dtype=np.float64)                   # x-vector (in)\n",
    "    u_y = np.zeros((len(x)), dtype=np.float64)\n",
    "    F_u = np.zeros((2*(N+1), 1), dtype=np.float64)\n",
    "    F_u[0] = H\n",
    "    k_S = np.zeros((2*(N+1)), dtype=np.float64)\n",
    "    k_S[0] = k*delta_x*facw*d/2\n",
    "    k_S[2:-3:2] = k*delta_x*facw*d\n",
    "    k_S[-2] = k*delta_x*facw*d/2\n",
    "    k_S[1] = Ktheta\n",
    "\n",
    "    # Create stiffness matrix\n",
    "    K_uu = np.zeros((2*(N+1), 2*(N+1)), dtype=np.float64)\n",
    "    K_uu[:2, :2] = K[:2, :2]\n",
    "    K_uu[:2, 2:4] = K[:2, 2:]\n",
    "    K_uu[0, 0] += k_S[0]\n",
    "    K_uu[1, 1] += k_S[1]\n",
    "    \n",
    "    for j in range(2,2*N,2):\n",
    "        K_uu[j:j+2, j-2:j] = K[2:, :2]\n",
    "        K_uu[j:j+2, j:j+2] = K[2:, 2:]+K[:2, :2]\n",
    "        K_uu[j, j] += k_S[j]\n",
    "        K_uu[j+1, j+1] += k_S[j+1]\n",
    "        K_uu[j:j+2, j+2:j+4] = K[:2, 2:]\n",
    "    \n",
    "    K_uu[-2:, -4:-2] = K[2:, :2]\n",
    "    K_uu[-2:, -2:] = K[2:, 2:]\n",
    "    K_uu[-2, -2] += k_S[-2]\n",
    "    K_uu[-1, -1] += k_S[-1]\n",
    "    delta_u = np.linalg.solve(K_uu, F_u)\n",
    "    Q = np.zeros((4, N), dtype=np.float64)\n",
    "    M = np.zeros_like(x, dtype=np.float64)\n",
    "    V = np.zeros_like(x, dtype=np.float64)\n",
    "    j = 0\n",
    "    for i in range(N):\n",
    "        Q[:, i] = (K@(np.array([delta_u[j],-delta_u[j+1],-delta_u[j+2],delta_u[j+3]], dtype=np.float64))).reshape(4,)\n",
    "        j = j+2\n",
    "    V[:-1] = Q[0,:]\n",
    "    M[:-1] = Q[1,:]\n",
    "    V[-1] = Q[2,-1]\n",
    "    M[-1] = Q[3,-1]\n",
    "    u_y = delta_u[::2] * 1000\n",
    "    return u_y, V, M, x, L\n",
    "\n",
    "def visualize(u_y, V, M, x, L):\n",
    "    axes[0].cla()\n",
    "    axes[1].cla()\n",
    "    axes[2].cla()\n",
    "    axes[0].plot(u_y-0.15*max(abs(u_y)), x, 'k', linestyle='-.')\n",
    "    axes[0].plot(u_y, x,'k', linestyle='-.')\n",
    "    axes[0].plot(u_y+0.15*max(abs(u_y)), x, 'k', linestyle='-.')\n",
    "    axes[0].plot([u_y[0]-0.15*max(abs(u_y)), u_y[0]+0.15*max(abs(u_y))], [x[0], x[0]], 'k', linestyle='-.')\n",
    "    axes[0].plot([u_y[-1]-0.15*max(abs(u_y)), u_y[-1]+0.15*max(abs(u_y))], [x[-1], x[-1]], 'k', linestyle='-.')\n",
    "    axes[0].axis([1.01*min(u_y-0.25*max(abs(u_y)))-2,1.01*max(u_y+0.25*max(abs(u_y)))+2,0, L+1])\n",
    "    axes[0].invert_yaxis()\n",
    "    axes[1].plot(np.zeros((len(x))), x, 'k',linestyle='-.')\n",
    "    axes[1].fill_between(V, x, color='b')  \n",
    "    axes[1].axis([1.01*min(V)-5, 1.01*max(V)+5, 0, L+1])\n",
    "    axes[1].invert_yaxis()\n",
    "    axes[2].plot(np.zeros((len(x))), x, 'k', linestyle='-.')\n",
    "    axes[2].fill_between(M, x, color='r')\n",
    "    axes[2].axis([1.01*min(M)-5, 1.01*max(M)+5, 0, L+1])\n",
    "    axes[2].invert_yaxis()\n",
    "    axes[0].set_xlabel('Horizontal deformation, u_x (mm)')\n",
    "    axes[0].set_ylabel('Depth, h (m)')\n",
    "    axes[1].set_xlabel('Shear force, V (kN)')\n",
    "    axes[1].set_ylabel('Depth, h (m)')\n",
    "    axes[2].set_ylabel('Depth, h (m)')\n",
    "    axes[2].set_xlabel('Bending moment, M (kNm)')"
   ]
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       "Output()"
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    "out=Output()\n",
    "def on_value_change(change):\n",
    "    u_y, V, M, x, L = run_calcs()\n",
    "    with out:\n",
    "        clear_output()\n",
    "        visualize(u_y, V, M, x, L)\n",
    "\n",
    "        \n",
    "for i in uis.children:\n",
    "    for j in i.children:\n",
    "        j.observe(on_value_change, 'value')\n",
    "out"
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