{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a764d93c",
   "metadata": {},
   "source": [
    "Benchmark: shell obstacle course\n",
    "===\n",
    "\n",
    "Date: 22 of October 2026\n",
    "\n",
    "Author: Saullo G. P. Castro\n",
    "\n",
    "Belytschko et al. [1] assembled three linear problems, the \"obstacle course\" of their Section 5, that together test whether a shell element represents inextensional bending, rigid-body rotations about the normal and complex membrane states: the Scordelis-Lo roof, the pinched cylinder with rigid diaphragms and the pinched hemispherical shell. This notebook runs the three problems with the four shell elements of `pyfe3d`, `Quad4`, `Quad4R`, `Tria3R` and `Tria3DSG`, each with its default attributes, on $N \\times N$ meshes of the symmetric part of each shell, and compares the converged and the coarse-mesh results with the reference values of Table 3 of [1] (p. 239). The roof and the hemisphere are also problems of MacNeal and Harder [2], whose Tables 13 and 14 give the results of the QUAD4 of MSC/NASTRAN, compared at the end.\n",
    "\n",
    "| | Scordelis-Lo roof | Pinched cylinder | Hemispherical shell |\n",
    "|---|---|---|---|\n",
    "| Length $L$ | 50.0 | 600.0 | - |\n",
    "| Radius $R$ | 25.0 | 300.0 | 10.0 |\n",
    "| Thickness $t$ | 0.25 | 3.0 | 0.04 |\n",
    "| $E$ | $4.32 \\times 10^8$ | $3.0 \\times 10^6$ | $6.825 \\times 10^7$ |\n",
    "| $\\nu$ | 0.0 | 0.3 | 0.3 |\n",
    "| Load | gravity, 90.0 per unit area | two opposite radial forces $F = 1.0$ | radial forces $F = \\pm 2.0$ alternating at 90 degrees |\n",
    "| Reference | vertical displacement at the midside of the free edge, 0.3024 | radial displacement under the load, $0.18248 \\times 10^{-4}$ | radial displacement under the load, 0.0924 |\n",
    "\n",
    "The table is Table 3 of [1]. The modelling choices that [1] does not state are given with each problem. The triangular meshes are obtained by cutting every quadrilateral along its diagonal 1-3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "193f99c3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:04:47.920751Z",
     "iopub.status.busy": "2026-10-22T22:04:47.920602Z",
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     "shell.execute_reply": "2026-10-22T22:04:48.638538Z"
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.sparse import coo_matrix\n",
    "from scipy.sparse.linalg import spsolve\n",
    "\n",
    "from pyfe3d.shellprop_utils import isotropic_plate\n",
    "from pyfe3d import (Quad4, Quad4Data, Quad4Probe, Quad4R, Quad4RData,\n",
    "                    Quad4RProbe, Tria3R, Tria3RData, Tria3RProbe, Tria3DSG,\n",
    "                    Tria3DSGData, Tria3DSGProbe, INT, DOUBLE, DOF)\n",
    "\n",
    "ELEMENTS = {\n",
    "    'Quad4': (Quad4, Quad4Data, Quad4Probe),\n",
    "    'Quad4R': (Quad4R, Quad4RData, Quad4RProbe),\n",
    "    'Tria3R': (Tria3R, Tria3RData, Tria3RProbe),\n",
    "    'Tria3DSG': (Tria3DSG, Tria3DSGData, Tria3DSGProbe),\n",
    "}\n",
    "\n",
    "\n",
    "def split(quads):\n",
    "    # two triangles per quadrilateral, cut along the diagonal 1-3\n",
    "    return [t for (n1, n2, n3, n4) in quads for t in ((n1, n2, n3), (n1, n3, n4))]\n",
    "\n",
    "\n",
    "def stiffness(ncoords, quads, name, prop):\n",
    "    Elem, Data, Probe = ELEMENTS[name]\n",
    "    conn = split(quads) if name.startswith('Tria') else quads\n",
    "    data, probe = Data(), Probe()\n",
    "    ncf = np.ascontiguousarray(ncoords, dtype=DOUBLE).flatten()\n",
    "    N = DOF*ncoords.shape[0]\n",
    "    size = data.KC0_SPARSE_SIZE*len(conn)\n",
    "    KC0r = np.zeros(size, dtype=INT)\n",
    "    KC0c = np.zeros(size, dtype=INT)\n",
    "    KC0v = np.zeros(size, dtype=DOUBLE)\n",
    "    areas = np.zeros(len(conn))\n",
    "    for k, nodes in enumerate(conn):\n",
    "        e = Elem(probe)\n",
    "        for i, n in enumerate(nodes):\n",
    "            setattr(e, 'n%d' % (i + 1), n)\n",
    "            setattr(e, 'c%d' % (i + 1), DOF*n)\n",
    "        e.init_k_KC0 = k*data.KC0_SPARSE_SIZE\n",
    "        e.update_rotation_matrix(ncf)\n",
    "        e.update_probe_xe(ncf)\n",
    "        e.update_area()\n",
    "        e.update_KC0(KC0r, KC0c, KC0v, prop)\n",
    "        areas[k] = e.area\n",
    "    K = coo_matrix((KC0v, (KC0r, KC0c)), shape=(N, N)).tocsc()\n",
    "    return K, conn, areas\n",
    "\n",
    "\n",
    "def solve(K, bk, f):\n",
    "    u = np.zeros(K.shape[0])\n",
    "    bu = ~bk\n",
    "    u[bu] = spsolve(K[bu][:, bu], f[bu])\n",
    "    return u\n",
    "\n",
    "\n",
    "def area_load(ncoords, conn, areas, q):\n",
    "    # nodal forces of a load per unit area q, lumped equally to the nodes\n",
    "    f = np.zeros(DOF*ncoords.shape[0])\n",
    "    for nodes, A in zip(conn, areas):\n",
    "        for n in nodes:\n",
    "            f[DOF*n:DOF*n + 3] += np.asarray(q)*A/len(nodes)\n",
    "    return f\n",
    "\n",
    "\n",
    "def mapped_grid(n, X, Y, Z):\n",
    "    # an n by n grid of quadrilaterals on the surface given by the\n",
    "    # (n + 1, n + 1) arrays of coordinates X, Y and Z\n",
    "    ids = np.arange((n + 1)**2).reshape(n + 1, n + 1)\n",
    "    quads = [(ids[i, j], ids[i + 1, j], ids[i + 1, j + 1], ids[i, j + 1])\n",
    "             for i in range(n) for j in range(n)]\n",
    "    return np.column_stack((X.ravel(), Y.ravel(), Z.ravel())), ids, quads\n",
    "\n",
    "\n",
    "def fix(bk, mask, dofs):\n",
    "    for d in dofs:\n",
    "        bk[d::DOF] |= mask\n",
    "\n",
    "\n",
    "def grade(normalised):\n",
    "    # letter grade of MacNeal and Harder [2], p. 14\n",
    "    err = 100*abs(normalised - 1.)\n",
    "    for letter, limit in (('A', 2.), ('B', 10.), ('C', 20.), ('D', 50.)):\n",
    "        if err <= limit:\n",
    "            return letter\n",
    "    return 'F'\n",
    "\n",
    "\n",
    "NS = (2, 4, 6, 8, 10, 12, 16, 24, 32, 48)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44226902",
   "metadata": {},
   "source": [
    "Scordelis-Lo roof\n",
    "---\n",
    "\n",
    "A cylindrical roof of radius 25.0 and length 50.0, with its axis along $y$, $z$ vertical and a half-angle of 40 degrees, supported at both ends by rigid diaphragms and loaded by its own weight, 90.0 per unit area in the $-z$ direction (Fig. 5 and Table 3 of [1]). One quarter is modelled, $0 \\le \\theta \\le 40^\\circ$ from the crown and $0 \\le y \\le 25$ from the diaphragm, with symmetry at the crown, $u_x = r_y = r_z = 0$, and at mid-length, $u_y = r_x = r_z = 0$. [1] does not define the diaphragm for this problem; it is taken from Fig. 8 of [2], $u_x = u_z = 0$ on the curved edge. The gravity load is lumped to the nodes. The result is the vertical displacement at the midside of the free edge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "265135ef",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:04:48.642501Z",
     "iopub.status.busy": "2026-10-22T22:04:48.642169Z",
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     "shell.execute_reply": "2026-10-22T22:04:48.646885Z"
    }
   },
   "outputs": [],
   "source": [
    "def scordelis_lo(name, n):\n",
    "    R, L = 25., 50.\n",
    "    T, Y = np.meshgrid(np.linspace(0., np.deg2rad(40.), n + 1),\n",
    "                       np.linspace(0., L/2, n + 1), indexing='ij')\n",
    "    ncoords, ids, quads = mapped_grid(n, R*np.sin(T), Y, R*np.cos(T))\n",
    "    prop = isotropic_plate(thickness=0.25, E=4.32e8, nu=0.)\n",
    "    K, conn, areas = stiffness(ncoords, quads, name, prop)\n",
    "    x, y, z = ncoords.T\n",
    "    bk = np.zeros(K.shape[0], dtype=bool)\n",
    "    fix(bk, np.isclose(y, 0.), (0, 2))        # diaphragm\n",
    "    fix(bk, np.isclose(y, L/2), (1, 3, 5))    # symmetry at mid-length\n",
    "    fix(bk, np.isclose(x, 0.), (0, 4, 5))     # symmetry at the crown\n",
    "    u = solve(K, bk, area_load(ncoords, conn, areas, (0., 0., -90.)))\n",
    "    return -u[DOF*ids[n, n] + 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8328fb04",
   "metadata": {},
   "source": [
    "Pinched cylinder with rigid diaphragms\n",
    "---\n",
    "\n",
    "A cylinder of radius 300.0 and length 600.0, axis along $y$, pinched at mid-length by two diametrically opposite radial forces $F = 1.0$, and constrained at each end by a rigid diaphragm, defined in Table 3 of [1] as $u_x = u_y = \\phi_z = 0$ with $z$ the axis of the cylinder in their Fig. 5, here $u_x = u_z = r_y = 0$. One eighth is modelled, $0 \\le \\theta \\le 90^\\circ$ from the loaded generator and $0 \\le y \\le 300$ from mid-length, with symmetry on the three cut planes: $u_x = r_y = r_z = 0$ at $x = 0$, $u_z = r_x = r_y = 0$ at $z = 0$ and $u_y = r_x = r_z = 0$ at mid-length. The load node carries $F/4$. The result is the radial displacement under the load."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "abb86203",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:04:48.649986Z",
     "iopub.status.busy": "2026-10-22T22:04:48.649772Z",
     "iopub.status.idle": "2026-10-22T22:04:48.654979Z",
     "shell.execute_reply": "2026-10-22T22:04:48.654184Z"
    }
   },
   "outputs": [],
   "source": [
    "def pinched_cylinder(name, n):\n",
    "    R, L, F = 300., 600., 1.\n",
    "    T, Y = np.meshgrid(np.linspace(0., np.pi/2, n + 1),\n",
    "                       np.linspace(0., L/2, n + 1), indexing='ij')\n",
    "    ncoords, ids, quads = mapped_grid(n, R*np.sin(T), Y, R*np.cos(T))\n",
    "    prop = isotropic_plate(thickness=3., E=3.e6, nu=0.3)\n",
    "    K, conn, areas = stiffness(ncoords, quads, name, prop)\n",
    "    x, y, z = ncoords.T\n",
    "    bk = np.zeros(K.shape[0], dtype=bool)\n",
    "    fix(bk, np.isclose(y, L/2), (0, 2, 4))          # diaphragm\n",
    "    fix(bk, np.isclose(y, 0.), (1, 3, 5))           # symmetry at mid-length\n",
    "    fix(bk, np.isclose(x, 0.), (0, 4, 5))           # symmetry, plane x = 0\n",
    "    fix(bk, np.isclose(z, 0., atol=1e-9), (2, 3, 4))  # symmetry, plane z = 0\n",
    "    f = np.zeros(K.shape[0])\n",
    "    load = ids[0, 0]\n",
    "    f[DOF*load + 2] = -F/4\n",
    "    u = solve(K, bk, f)\n",
    "    return -u[DOF*load + 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31c8a40f",
   "metadata": {},
   "source": [
    "Pinched hemispherical shell\n",
    "---\n",
    "\n",
    "A hemisphere of radius 10.0 with a free equator, loaded at the equator by four radial point loads alternating in sign at 90 degrees. Fig. 1(b) of [1], whose caption refers to their Table 3 for the data of the problem, and Fig. 9 of [2] give a hole at the pole, of 18 degrees, which is modelled here; the reference 0.0924 of [1] is, according to [2] (Table 5(b)), a lower bound computed for the hemisphere without the hole, and [2] normalises the results with the hole by 0.094 instead. One quadrant is modelled with symmetry on the planes $x = 0$, $u_x = r_y = r_z = 0$, and $y = 0$, $u_y = r_x = r_z = 0$. The quadrant carries $F = 1.0$ at each load point, outward along $x$ and inward along $y$, as drawn in Figs. 1(b) and 5 of [1], half of the $F = \\pm 2.0$ of their Table 3 because each load point lies on a plane of symmetry. Fig. 9 of [2] labels the forces \"F = 2.0 (on quadrant)\"; with 2.0 applied to the quadrant every result below doubles. Nothing in the quadrant prevents a translation along $z$, so $u_z = 0$ is imposed at one node of the hole, which does not change the solution because the loads have no component along $z$. The result is the radial displacement under the load along $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "45897beb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:04:48.657317Z",
     "iopub.status.busy": "2026-10-22T22:04:48.657157Z",
     "iopub.status.idle": "2026-10-22T22:04:48.662778Z",
     "shell.execute_reply": "2026-10-22T22:04:48.661896Z"
    }
   },
   "outputs": [],
   "source": [
    "def hemisphere(name, n):\n",
    "    R, F = 10., 1.\n",
    "    PSI, PHI = np.meshgrid(np.linspace(np.pi/2, np.deg2rad(18.), n + 1),\n",
    "                           np.linspace(0., np.pi/2, n + 1), indexing='ij')\n",
    "    ncoords, ids, quads = mapped_grid(n, R*np.sin(PSI)*np.cos(PHI),\n",
    "                                      R*np.sin(PSI)*np.sin(PHI), R*np.cos(PSI))\n",
    "    prop = isotropic_plate(thickness=0.04, E=6.825e7, nu=0.3)\n",
    "    K, conn, areas = stiffness(ncoords, quads, name, prop)\n",
    "    x, y, z = ncoords.T\n",
    "    bk = np.zeros(K.shape[0], dtype=bool)\n",
    "    fix(bk, np.isclose(x, 0., atol=1e-9), (0, 4, 5))\n",
    "    fix(bk, np.isclose(y, 0., atol=1e-9), (1, 3, 5))\n",
    "    bk[DOF*ids[n, 0] + 2] = True\n",
    "    f = np.zeros(K.shape[0])\n",
    "    f[DOF*ids[0, 0] + 0] = +F\n",
    "    f[DOF*ids[0, n] + 1] = -F\n",
    "    u = solve(K, bk, f)\n",
    "    return u[DOF*ids[0, 0] + 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e89b1fdf",
   "metadata": {},
   "source": [
    "Convergence\n",
    "---\n",
    "\n",
    "Every problem is solved with $N$ from 2 to 48 elements per side, on the quadrilateral mesh or on the triangles obtained from it, and the result is normalised by the reference of Table 3 of [1]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0f7e3553",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:04:48.665080Z",
     "iopub.status.busy": "2026-10-22T22:04:48.664859Z",
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     "shell.execute_reply": "2026-10-22T22:05:05.706475Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scordelis-Lo roof, normalised displacement\n",
      "N        Quad4    Quad4R    Tria3R  Tria3DSG\n",
      "2        1.416     0.858     1.544     0.665\n",
      "4        1.059     0.779     0.929     0.675\n",
      "6        1.022     0.809     0.892     0.783\n",
      "8        1.010     0.830     0.882     0.853\n",
      "10       1.006     0.845     0.877     0.895\n",
      "12       1.003     0.859     0.874     0.922\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16       1.001     0.882     0.872     0.951\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24       1.000     0.917     0.871     0.975\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32       0.999     0.941     0.873     0.984\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "48       0.999     0.967     0.882     0.991\n",
      "\n",
      "Pinched cylinder, normalised displacement\n",
      "N        Quad4    Quad4R    Tria3R  Tria3DSG\n",
      "2        0.035     0.034     0.082     0.022\n",
      "4        0.370     0.339     0.854     0.142\n",
      "6        0.604     0.545     1.194     0.357\n",
      "8        0.743     0.666     1.271     0.545\n",
      "10       0.827     0.740     1.300     0.667\n",
      "12       0.879     0.789     1.303     0.747\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16       0.935     0.848     1.267     0.843\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24       0.980     0.899     1.169     0.925\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32       0.998     0.921     1.105     0.958\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "48       1.012     0.940     1.045     0.985\n",
      "\n",
      "Hemispherical shell, normalised displacement\n",
      "N        Quad4    Quad4R    Tria3R  Tria3DSG\n",
      "2        0.021     0.021     0.228     0.004\n",
      "4        0.106     0.118     0.069     0.049\n",
      "6        0.356     0.345     0.188     0.206\n",
      "8        0.633     0.549     0.364     0.451\n",
      "10       0.811     0.675     0.533     0.666\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12       0.903     0.749     0.653     0.803\n",
      "16       0.975     0.832     0.770     0.926\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24       1.005     0.911     0.821     0.985\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32       1.011     0.948     0.826     0.998\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "48       1.013     0.982     0.825     1.006\n",
      "\n"
     ]
    }
   ],
   "source": [
    "PROBLEMS = {'Scordelis-Lo roof': (scordelis_lo, 0.3024),\n",
    "            'Pinched cylinder': (pinched_cylinder, 0.18248e-4),\n",
    "            'Hemispherical shell': (hemisphere, 0.0924)}\n",
    "\n",
    "res = {}\n",
    "for problem, (func, ref) in PROBLEMS.items():\n",
    "    print(problem + ', normalised displacement')\n",
    "    print('%-4s' % 'N' + ''.join('%10s' % name for name in ELEMENTS))\n",
    "    for n in NS:\n",
    "        for name in ELEMENTS:\n",
    "            res[problem, name, n] = func(name, n)/ref\n",
    "        print('%-4d' % n + ''.join('%10.3f' % res[problem, name, n] for name in ELEMENTS))\n",
    "    print()"
   ]
  },
  {
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   "id": "30c17733",
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     "shell.execute_reply": "2026-10-22T22:05:06.312107Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x380 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = ['#2a78d6', '#eb6834', '#1baf7a', '#eda100']\n",
    "markers = ['o', 's', '^', 'D']\n",
    "fig, axes = plt.subplots(1, 3, figsize=(12, 3.8), sharey=True)\n",
    "for ax, problem in zip(axes, PROBLEMS):\n",
    "    for name, c, m in zip(ELEMENTS, colors, markers):\n",
    "        ax.plot(np.array(NS) + 1, [res[problem, name, n] for n in NS],\n",
    "                color=c, marker=m, markersize=5, lw=1.5, label=name)\n",
    "    ax.axhline(1., color='0.4', lw=1, ls='--')\n",
    "    ax.set_title(problem, fontsize=11)\n",
    "    ax.set_xlabel('nodes per side')\n",
    "    ax.set_ylim(0., 1.6)\n",
    "    ax.grid(color='0.9')\n",
    "axes[0].set_ylabel('normalised displacement')\n",
    "axes[0].legend(frameon=False)\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c937b2aa",
   "metadata": {},
   "source": [
    "Checks\n",
    "---\n",
    "\n",
    "The convergence is checked on the finest mesh, $N = 48$, with the tolerance of grade A of [2], 2%. On the coarse meshes the grade of [2] is printed for the meshes it uses in its Table 16, $N = 4$ for the roof and $N = 8$ for the hemisphere, and for $N = 16$ (17 nodes per side) for the cylinder, the mesh on which [1] (p. 242) finds their 4-node element with selective reduced integration \"still 5% in error\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8a62d447",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:05:06.317992Z",
     "iopub.status.busy": "2026-10-22T22:05:06.317533Z",
     "iopub.status.idle": "2026-10-22T22:05:06.326012Z",
     "shell.execute_reply": "2026-10-22T22:05:06.324707Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "problem                element        N = 48    converged   coarse N    grade [2]\n",
      "Scordelis-Lo roof      Quad4          0.9991         PASS          4            B\n",
      "Scordelis-Lo roof      Quad4R         0.9672         FAIL          4            D\n",
      "Scordelis-Lo roof      Tria3R         0.8825         FAIL          4            B\n",
      "Scordelis-Lo roof      Tria3DSG       0.9910         PASS          4            D\n",
      "Pinched cylinder       Quad4          1.0120         PASS         16            B\n",
      "Pinched cylinder       Quad4R         0.9402         FAIL         16            C\n",
      "Pinched cylinder       Tria3R         1.0447         FAIL         16            D\n",
      "Pinched cylinder       Tria3DSG       0.9848         PASS         16            C\n",
      "Hemispherical shell    Quad4          1.0134         PASS          8            D\n",
      "Hemispherical shell    Quad4R         0.9817         PASS          8            D\n",
      "Hemispherical shell    Tria3R         0.8250         FAIL          8            F\n",
      "Hemispherical shell    Tria3DSG       1.0061         PASS          8            F\n"
     ]
    }
   ],
   "source": [
    "COARSE = {'Scordelis-Lo roof': 4, 'Pinched cylinder': 16, 'Hemispherical shell': 8}\n",
    "print('%-22s %-8s %12s %12s %10s %12s' % ('problem', 'element', 'N = 48', 'converged', 'coarse N',\n",
    "                                          'grade [2]'))\n",
    "for problem in PROBLEMS:\n",
    "    for name in ELEMENTS:\n",
    "        v = res[problem, name, 48]\n",
    "        nc = COARSE[problem]\n",
    "        print('%-22s %-8s %12.4f %12s %10d %12s'\n",
    "              % (problem, name, v, 'PASS' if abs(v - 1.) <= 0.02 else 'FAIL', nc,\n",
    "                 grade(res[problem, name, nc])))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7ceff1c",
   "metadata": {},
   "source": [
    "Comparison with MacNeal and Harder\n",
    "---\n",
    "\n",
    "Tables 13 and 14 of [2] give the QUAD4 of MSC/NASTRAN on the roof and on the hemisphere, normalised by 0.3024 and 0.094 respectively. The results of `pyfe3d` are normalised in the same way below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6c27a738",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:05:06.329529Z",
     "iopub.status.busy": "2026-10-22T22:05:06.329203Z",
     "iopub.status.idle": "2026-10-22T22:05:06.337757Z",
     "shell.execute_reply": "2026-10-22T22:05:06.336518Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scordelis-Lo roof, displacement normalised by 0.3024\n",
      "N        Quad4    Quad4R    Tria3R  Tria3DSG  MH QUAD4\n",
      "2        1.416     0.858     1.544     0.665     1.376\n",
      "4        1.059     0.779     0.929     0.675     1.050\n",
      "6        1.022     0.809     0.892     0.783     1.018\n",
      "8        1.010     0.830     0.882     0.853     1.008\n",
      "10       1.006     0.845     0.877     0.895     1.004\n",
      "\n",
      "Hemispherical shell, displacement normalised by 0.094\n",
      "N        Quad4    Quad4R    Tria3R  Tria3DSG  MH QUAD4\n",
      "2        0.021     0.021     0.225     0.004     0.972\n",
      "4        0.104     0.116     0.068     0.049     1.024\n",
      "6        0.350     0.339     0.184     0.202     1.013\n",
      "8        0.622     0.540     0.358     0.443     1.005\n",
      "10       0.797     0.663     0.524     0.654     1.001\n",
      "12       0.888     0.736     0.642     0.789     0.998\n",
      "\n"
     ]
    }
   ],
   "source": [
    "MH_QUAD4 = {'Scordelis-Lo roof': (0.3024, {2: 1.376, 4: 1.050, 6: 1.018, 8: 1.008, 10: 1.004}),   # Table 13 of [2]\n",
    "            'Hemispherical shell': (0.094, {2: 0.972, 4: 1.024, 6: 1.013, 8: 1.005, 10: 1.001,\n",
    "                                            12: 0.998})}                                          # Table 14 of [2]\n",
    "for problem, (ref_mh, table) in MH_QUAD4.items():\n",
    "    ref = PROBLEMS[problem][1]\n",
    "    print(problem + ', displacement normalised by %g' % ref_mh)\n",
    "    print('%-4s' % 'N' + ''.join('%10s' % name for name in ELEMENTS) + '  MH QUAD4')\n",
    "    for n, v in table.items():\n",
    "        print('%-4d' % n + ''.join('%10.3f' % (res[problem, name, n]*ref/ref_mh) for name in ELEMENTS)\n",
    "              + '%10.3f' % v)\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee4985ad",
   "metadata": {},
   "source": [
    "Discussion\n",
    "---\n",
    "\n",
    "The output above is the result of the default elements, with no parameter adjusted to these problems.\n",
    "\n",
    "- **`Quad4`** is within 2% of the three references at $N = 48$. On the roof it behaves like the QUAD4 of [2] on every mesh, over-flexible on the coarsest. On the pinched cylinder it converges from below, with an error of 6.5% at 17 nodes per side, close to the 5% that [1] (p. 242) reports for their 4-node element with selective reduced integration on that mesh, and ends 1.2% above the reference. The hemisphere is where it differs most from the QUAD4 of [2]: far too stiff on the coarse meshes, 10% of the displacement at $N = 4$ against 102% for the QUAD4, and within 3% of the reference of [1] only from $N = 16$.\n",
    "- **`Quad4R`** converges from below on the three problems, more slowly than `Quad4`, and is still 3% and 6% too stiff on the roof and on the cylinder at $N = 48$.\n",
    "- **`Tria3R`** does not converge to the references within $N = 48$: it settles 12% below the reference on the roof and 18% below on the hemisphere, and on the cylinder it overshoots by up to 30% before coming down to 4.5% above. Its transverse shear stiffness is divided by $1 + \\alpha \\ell^2/t^2$ with the default `alpha_shear_locking = 0.7`, and the Notes of `pyfe3d.tria3r` explain why no single value of $\\alpha$ serves every problem class; this notebook records the default.\n",
    "- **`Tria3DSG`** is within 2% of the three references at $N = 48$, converging from below and more slowly than `Quad4` on the coarse meshes, with no parameter to set.\n",
    "\n",
    "References\n",
    "---\n",
    "\n",
    "[1] Belytschko, T., Stolarski, H., Liu, W. K., Carpenter, N., and Ong, J. S.-J., Stress projection for membrane and shear locking in shell finite elements, Computer Methods in Applied Mechanics and Engineering, 51(1-3), 221-258, 1985. https://doi.org/10.1016/0045-7825(85)90035-0\n",
    "\n",
    "[2] MacNeal, R. H., and Harder, R. L., A proposed standard set of problems to test finite element accuracy, Finite Elements in Analysis and Design, 1(1), 3-20, 1985. https://doi.org/10.1016/0168-874X(85)90003-4"
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