{
 "cells": [
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   "source": [
    "# Axial buckling of stringer-stiffened cylinders\n",
    "\n",
    "Card and Jones [1] tested in axial compression aluminium cylinders with\n",
    "external or internal longitudinal stiffeners, and compared the buckling\n",
    "loads with a theory of eccentrically stiffened cylinders with the\n",
    "stiffeners averaged (\"smeared\") over the skin, a membrane pre-buckling\n",
    "state, and clamped or simply supported ends. Here two of their cylinders\n",
    "with integral rectangular stringers are modelled with discrete stringers,\n",
    "as in [Natural frequencies of stringer-stiffened\n",
    "cylinders](stiffened_cylinder_frequencies.ipynb):\n",
    "\n",
    "- the skin with the BFSC cylinder element of Sanders-type kinematics,\n",
    "  `BFSCCylinderSanders`;\n",
    "- each stringer with the BFSC plate element `BFSCPlate2D` of\n",
    "  [bfscplate2d](https://github.com/saullocastro/bfscplate2d), in the\n",
    "  plane $(x, r)$ of the stringer, connected to the skin as described in\n",
    "  that tutorial.\n",
    "\n",
    "The linear buckling problems $(\\boldsymbol{K}_{C0} + \\lambda \\boldsymbol{K}_G)\\boldsymbol{\\phi} = \\boldsymbol{0}$,\n",
    "see [Analyses](../analyses.rst), are solved with `structsolve.lb`. The\n",
    "model is given by the module `stiffened_cylinder.py`, next to this\n",
    "notebook, see [Tutorials](../tutorials.rst)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a7ac3c5",
   "metadata": {},
   "source": [
    "## Cylinders, geometry and material\n",
    "\n",
    "Table I of [1] gives four cylinders with integral stiffeners, machined from\n",
    "aluminium plates, two 38.00 in long (cylinders 1 and 2) and two 23.75 in\n",
    "long (cylinders 3 and 4), each pair with external and internal stiffeners.\n",
    "Cylinders 3 and 4, the shorter ones, are modelled here: their models need\n",
    "fewer elements along the axis and are solved within about a minute each.\n",
    "The values below, in inches and pounds-force, are those of Table I for\n",
    "$t$, $L$ and $R$, the radius of the middle surface, and of its footnote for\n",
    "$E$ and $\\mu$, and those of Figure 2(b) of [1] for the stiffeners:\n",
    "0.097 in wide, at a spacing of 1.00 in, 0.33 in from the surface of the\n",
    "skin opposite to the stiffeners to their tip, as drawn in Figure 2(b), with\n",
    "fillets of radius 0.03 in, which are not modelled. The spacing gives 60\n",
    "stiffeners, $2 \\pi \\, 9.55/1.00 = 60.0$. The plate of a stringer goes from\n",
    "the middle surface of the skin to the tip, of height $H_s = 0.33 - t/2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "83bad007",
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cylinder 3: H_s = 0.3163 in, modelled area 3.49 in^2, A_t of Table I 3.70 in^2, P_e/(2 pi R) = 2120 lb/in\n",
      "cylinder 4: H_s = 0.3160 in, modelled area 3.52 in^2, A_t of Table I 3.63 in^2, P_e/(2 pi R) = 967 lb/in\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.sparse.linalg import spsolve\n",
    "from structsolve import lb\n",
    "\n",
    "from stiffened_cylinder import StiffenedCylinder, wave_numbers, W\n",
    "\n",
    "# Table I of Card and Jones (1966), with the values of N in lb/in\n",
    "cylinders = {\n",
    "    3: dict(side='external', t=0.0275, L=23.75, R=9.55, At=3.70,\n",
    "            Pe=127.2e3, ne=7, Ne=2120., Nc=2595., Ns=1326.),\n",
    "    4: dict(side='internal', t=0.0280, L=23.75, R=9.55, At=3.63,\n",
    "            Pe=58.0e3, ne=6, Ne=965., Nc=1226., Ns=722.),\n",
    "}\n",
    "E = 10.5e6  # psi\n",
    "mu = 0.32\n",
    "nstringers = 60\n",
    "bs = 0.097  # in, Figure 2(b)\n",
    "depth = 0.33  # in, from the skin surface opposite to the stiffeners\n",
    "\n",
    "for k, c in cylinders.items():\n",
    "    Hs = depth - c['t']/2\n",
    "    area = 2*np.pi*c['R']*c['t'] + nstringers*bs*Hs\n",
    "    print('cylinder %d: H_s = %.4f in, modelled area %.2f in^2, '\n",
    "          'A_t of Table I %.2f in^2, P_e/(2 pi R) = %.0f lb/in'\n",
    "          % (k, Hs, area, c['At'], c['Pe']/(2*np.pi*c['R'])))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87c1b176",
   "metadata": {},
   "source": [
    "Two remarks on Table I of [1]:\n",
    "\n",
    "- the columns $\\bar{N}_e$, $\\bar{N}_c$ and $\\bar{N}_s$ of Table I(a) are\n",
    "  headed kips/in., but their values are in lb/in: the experimental load\n",
    "  $\\bar{P}_e$ = 127.2 kips of cylinder 3 gives $\\bar{P}_e/(2 \\pi R)$ =\n",
    "  2120 lb/in, the value of $\\bar{N}_e$, as printed above; in Table I(b),\n",
    "  headed MN/m, the values are in kN/m;\n",
    "- the total areas $A_t$ of Table I are 6 % and 4 % larger than the areas\n",
    "  of the model, from the dimensions of Figure 2(b) with the overlap of the\n",
    "  stringers with the half thickness of the skin. The model follows Figure\n",
    "  2(b) and is not adjusted to $A_t$.\n",
    "\n",
    "The three linear buckling analyses below differ in their pre-buckling state\n",
    "and end conditions:\n",
    "\n",
    "- **membrane, clamped**: the membrane pre-buckling state of the theory of\n",
    "  [1], a uniform axial strain $\\epsilon$ without hoop stress, $N_{xx} = E t\n",
    "  \\epsilon$ in the skin and $E b_s \\epsilon$ in the stringers, `KG_membrane()`\n",
    "  in `stiffened_cylinder.py`, with the clamped ends of the theory, $u = v =\n",
    "  w = w_{,x} = 0$, and the end edges of the stringers clamped; compared with\n",
    "  $\\bar{N}_c$;\n",
    "- **membrane, simply supported**: the same pre-buckling state with the\n",
    "  simply supported ends of the theory, $N_x = v = w = M_x = 0$, i.e. $v = w\n",
    "  = 0$ and $u$, $w_{,x}$ free, and $V = W = W_{,Y} = 0$ along the end\n",
    "  edges of the stringers; compared with $\\bar{N}_s$;\n",
    "- **linear pre-buckling, clamped**: the test idealized, ends potted, ground\n",
    "  flat and loaded by the platens of the testing machine [1]: both ends\n",
    "  clamped, one with a uniform axial shortening of the skin and of the\n",
    "  stringers, the pre-buckling state being the linear static solution, with\n",
    "  the radial displacement restrained at the ends, `KG()` in\n",
    "  `stiffened_cylinder.py`; compared with the experimental $\\bar{N}_e$.\n",
    "\n",
    "The half $0 \\le \\theta \\le \\pi$ of each cylinder is modelled, with planes\n",
    "of symmetry midway between two stringers, which gives one mode of each pair\n",
    "of modes $\\cos n\\theta$ and $\\sin n\\theta$ of the same load. The critical\n",
    "load is given as the axial force per unit length of circumference,\n",
    "$\\bar{N} = P/(2 \\pi R)$, with $P$ the force on the whole cylinder.\n",
    "\n",
    "## The geometric stiffness of the stringers in their plane\n",
    "\n",
    "The geometric stiffness matrix of the BFSC plate element has the terms of\n",
    "its out-of-plane displacement $W$ only, those of the von Karman\n",
    "kinematics, see `bfscplate2d`. A stringer carries about half of the axial\n",
    "force and buckles with the skin in its own plane, with the radial\n",
    "displacement $V = w$. Its geometric stiffness in its plane, the counterpart\n",
    "of the terms of $w$ of the skin,\n",
    "\n",
    "$$\n",
    "\\int \\left( N_{xx} V_{,X}^2 + 2 N_{xy} V_{,X} V_{,Y} + N_{yy} V_{,Y}^2\n",
    "\\right) dX \\, dY\n",
    "$$\n",
    "\n",
    "is added by `KG_inplane()` in `stiffened_cylinder.py`, with the\n",
    "interpolation rows of the element, `update_Sv_x()` and `update_Sv_y()`.\n",
    "Without it, the axial force of the stringers does not destabilize the\n",
    "cylinder, as the cell below shows for cylinder 3, membrane pre-buckling and\n",
    "simply supported ends, on the mesh used below:"
   ]
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   "id": "5cae8871",
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    "execution": {
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     "shell.execute_reply": "2026-10-22T22:21:05.500571Z"
    }
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in-plane terms True : N_cr = 1354 lb/in, (m, n) = (1, 7), 10 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in-plane terms False: N_cr = 2856 lb/in, (m, n) = (1, 7), 49 s\n"
     ]
    }
   ],
   "source": [
    "def build(k, nx, nbay, nh, ends):\n",
    "    c = cylinders[k]\n",
    "    return StiffenedCylinder(R=c['R'], L=c['L'], h=c['t'], E=E, nu=mu,\n",
    "                             rho=0., nstringers=nstringers, bs=bs,\n",
    "                             Hs=depth - c['t']/2, side=c['side'], nx=nx,\n",
    "                             nbay=nbay, nh=nh, kinematics='sanders',\n",
    "                             half=True, free_axial=(ends == 'SS'))\n",
    "\n",
    "\n",
    "def modes_full(model, bu, eigvecs):\n",
    "    out = np.zeros((model.N, eigvecs.shape[1]))\n",
    "    for i in range(eigvecs.shape[1]):\n",
    "        ur = np.zeros(model.Nr)\n",
    "        ur[bu] = eigvecs[:, i]\n",
    "        out[:, i] = model.Z @ ur\n",
    "    return out\n",
    "\n",
    "\n",
    "def membrane(k, nx, nbay, nh, ends, inplane=True, num_eigvalues=10):\n",
    "    model = build(k, nx, nbay, nh, ends)\n",
    "    c = cylinders[k]\n",
    "    K = model.reduce(model.KC0())\n",
    "    eps = -1e-3\n",
    "    KG = model.KG_membrane(eps)\n",
    "    if not inplane:\n",
    "        N = np.zeros((len(model.str_elements), len(model.points)**2, 3))\n",
    "        N[:, :, 0] = E*bs*eps\n",
    "        KG = KG - model.KG_inplane(N)\n",
    "    KG = model.reduce(KG)\n",
    "    bu = ~model.constrained(ends)\n",
    "    lam, eigvecs = lb(K[bu, :][:, bu], KG[bu, :][:, bu],\n",
    "                      num_eigvalues=num_eigvalues, silent=True)\n",
    "    P = model.axial_force_membrane(eps)\n",
    "    Ncr = lam*abs(P)/(2*np.pi*c['R'])\n",
    "    modes = modes_full(model, bu, eigvecs)\n",
    "    mn = [wave_numbers(model, modes[:, i]) for i in range(len(lam))]\n",
    "    return model, Ncr, mn, modes\n",
    "\n",
    "\n",
    "mesh = (25, 2, 2)\n",
    "for inplane in [True, False]:\n",
    "    t0 = time.time()\n",
    "    model, Ncr, mn, modes = membrane(3, *mesh, 'SS', inplane=inplane,\n",
    "                                     num_eigvalues=4)\n",
    "    print('in-plane terms %-5s: N_cr = %.0f lb/in, (m, n) = %s, %.0f s'\n",
    "          % (inplane, Ncr[0], mn[0], time.time() - t0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b875ec0a",
   "metadata": {},
   "source": [
    "Without the in-plane terms the critical load is 2.1 times larger, with the\n",
    "same mode. The stringers carry 53 % of the axial force of the model of\n",
    "cylinder 3, the ratio of their area to the total area, and without these\n",
    "terms this part of the force does not act on the radial displacement of\n",
    "the stringers, which is the normal displacement $w$ of the skin. The\n",
    "analyses below include the terms.\n",
    "\n",
    "## Mesh convergence\n",
    "\n",
    "Cylinder 3, membrane pre-buckling and clamped ends, with three meshes of\n",
    "`nx` nodes along $x$, `nbay` skin elements between two stringers and `nh`\n",
    "stringer elements along the height, the three lowest critical loads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b092e8ce",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:21:05.504318Z",
     "iopub.status.busy": "2026-10-22T22:21:05.504097Z",
     "iopub.status.idle": "2026-10-22T22:21:55.451993Z",
     "shell.execute_reply": "2026-10-22T22:21:55.451184Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nx=13, nbay=2, nh=1,  12610 dofs: N_cr = [2643. 2662. 2842.] lb/in, (m, n) = [(1, 8), (1, 9), (1, 7)], 3 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nx=25, nbay=2, nh=2,  31750 dofs: N_cr = [2601. 2618. 2797.] lb/in, (m, n) = [(1, 8), (1, 9), (1, 10)], 10 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nx=37, nbay=4, nh=3,  80290 dofs: N_cr = [2590. 2607. 2785.] lb/in, (m, n) = [(1, 8), (1, 9), (1, 10)], 38 s\n"
     ]
    }
   ],
   "source": [
    "meshes = [(13, 2, 1), (25, 2, 2), (37, 4, 3)]\n",
    "for m in meshes:\n",
    "    t0 = time.time()\n",
    "    model, Ncr, mn, modes = membrane(3, *m, 'CC', num_eigvalues=4)\n",
    "    print('nx=%2d, nbay=%d, nh=%d, %6d dofs: N_cr = %s lb/in, '\n",
    "          '(m, n) = %s, %.0f s'\n",
    "          % (*m, model.Nr, np.array2string(Ncr[:3], precision=0),\n",
    "             mn[:3], time.time() - t0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f79d759",
   "metadata": {},
   "source": [
    "The three lowest critical loads, of modes with one axial half-wave, change\n",
    "by 0.4 % from the middle mesh, used below, to the finest one. The modes of\n",
    "the skin between the stringers, with one half-wave in each bay, need finer\n",
    "meshes than these modes of the whole stiffened shell; they are above them\n",
    "for these cylinders, see the last figure below.\n",
    "\n",
    "## Membrane pre-buckling: discrete stringers and the smeared theory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f4e11753",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:21:55.454713Z",
     "iopub.status.busy": "2026-10-22T22:21:55.454487Z",
     "iopub.status.idle": "2026-10-22T22:22:41.273846Z",
     "shell.execute_reply": "2026-10-22T22:22:41.273207Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cylinder 3, CC: 12 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cylinder 3, SS: 12 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cylinder 4, CC: 10 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cylinder 4, SS: 12 s\n"
     ]
    }
   ],
   "source": [
    "results = {}\n",
    "for k in cylinders:\n",
    "    for ends in ['CC', 'SS']:\n",
    "        t0 = time.time()\n",
    "        results[(k, ends)] = membrane(k, *mesh, ends)\n",
    "        print('cylinder %d, %s: %.0f s' % (k, ends, time.time() - t0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de04cfa1",
   "metadata": {},
   "source": [
    "## Linear pre-buckling with clamped ends\n",
    "\n",
    "The end $x = 0$ is clamped and the end $x = L$ is clamped with the\n",
    "prescribed axial displacement $u = U = -\\delta$ of the skin and of the\n",
    "stringers, see [Assembling a model](../assembling.rst). The force $P$ is\n",
    "the sum of the reactions at the degrees of freedom of $u$ and $U$ of the\n",
    "end $x = L$, twice that of the half model, and the critical load is\n",
    "$\\lambda P$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e2cb1ece",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:22:41.275858Z",
     "iopub.status.busy": "2026-10-22T22:22:41.275681Z",
     "iopub.status.idle": "2026-10-22T22:23:37.843176Z",
     "shell.execute_reply": "2026-10-22T22:23:37.842497Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cylinder 3: P/delta = 1.554e+06 lb/in, E A/L of the model = 1.543e+06 lb/in\n",
      "cylinder 3, linear pre-buckling: 46 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cylinder 4: P/delta = 1.568e+06 lb/in, E A/L of the model = 1.556e+06 lb/in\n",
      "cylinder 4, linear pre-buckling: 11 s\n"
     ]
    }
   ],
   "source": [
    "def linear_prebuckling(k, nx, nbay, nh, num_eigvalues=10):\n",
    "    c = cylinders[k]\n",
    "    model = build(k, nx, nbay, nh, 'CC')\n",
    "    K = model.reduce(model.KC0())\n",
    "    bk = model.constrained('CC')\n",
    "    bu_end, bu_end_y = model.axial_dofs(nx - 1)\n",
    "    bk |= bu_end | bu_end_y\n",
    "    bu = ~bk\n",
    "    delta = 1e-3\n",
    "    ur = np.zeros(model.Nr)\n",
    "    ur[bu_end] = -delta\n",
    "    Kuu = K[bu, :][:, bu].tocsc()\n",
    "    Kuk = K[bu, :][:, bk]\n",
    "    ur[bu] = spsolve(Kuu, -Kuk @ ur[bk])\n",
    "    P = 2*(K @ ur)[bu_end].sum()\n",
    "    KG = model.reduce(model.KG(model.Z @ ur))\n",
    "    lam, eigvecs = lb(K[bu, :][:, bu], KG[bu, :][:, bu],\n",
    "                      num_eigvalues=num_eigvalues, silent=True)\n",
    "    Ncr = lam*abs(P)/(2*np.pi*c['R'])\n",
    "    modes = modes_full(model, bu, eigvecs)\n",
    "    mn = [wave_numbers(model, modes[:, i]) for i in range(len(lam))]\n",
    "    print('cylinder %d: P/delta = %.4g lb/in, E A/L of the model = %.4g lb/in'\n",
    "          % (k, abs(P)/delta, model.axial_force_membrane(1.)/c['L']))\n",
    "    return model, Ncr, mn, modes\n",
    "\n",
    "\n",
    "for k in cylinders:\n",
    "    t0 = time.time()\n",
    "    results[(k, 'test')] = linear_prebuckling(k, *mesh)\n",
    "    print('cylinder %d, linear pre-buckling: %.0f s' % (k, time.time() - t0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca325b4b",
   "metadata": {},
   "source": [
    "## Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "18889f6f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:23:37.845165Z",
     "iopub.status.busy": "2026-10-22T22:23:37.845007Z",
     "iopub.status.idle": "2026-10-22T22:23:37.925763Z",
     "shell.execute_reply": "2026-10-22T22:23:37.924974Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cyl.  side      analysis                     FE N_cr  (m, n)   [1]: N            FE/[1]\n",
      "  3   external  membrane, clamped              2601  (1, 8)    2595 N_c (theory)         1.002\n",
      "  3   external  membrane, simply supp.         1354  (1, 7)    1326 N_s (theory)         1.021\n",
      "  3   external  linear pre-buckling, clamped   2655  (1, 8)    2120 N_e (test), n_e = 7  1.252\n",
      "  4   internal  membrane, clamped              1226  (1, 7)    1226 N_c (theory)         1.000\n",
      "  4   internal  membrane, simply supp.          726  (1, 6)     722 N_s (theory)         1.006\n",
      "  4   internal  linear pre-buckling, clamped   1240  (1, 7)     965 N_e (test), n_e = 6  1.284\n"
     ]
    }
   ],
   "source": [
    "print('cyl.  side      analysis                     FE N_cr  (m, n)'\n",
    "      '   [1]: N            FE/[1]')\n",
    "for k, c in cylinders.items():\n",
    "    for key, name, ref, label in [\n",
    "            ('CC', 'membrane, clamped', c['Nc'], 'N_c (theory)'),\n",
    "            ('SS', 'membrane, simply supp.', c['Ns'], 'N_s (theory)'),\n",
    "            ('test', 'linear pre-buckling, clamped', c['Ne'],\n",
    "             'N_e (test), n_e = %d' % c['ne'])]:\n",
    "        model, Ncr, mn, modes = results[(k, key)]\n",
    "        print('%3d   %-8s  %-28s %6.0f  %-8s %5.0f %-20s %5.3f'\n",
    "              % (k, c['side'], name, Ncr[0], mn[0], ref, label,\n",
    "                 Ncr[0]/ref))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a44e702",
   "metadata": {},
   "source": [
    "The ten lowest critical loads of the membrane pre-buckling state with\n",
    "clamped ends:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "710d1153",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:23:37.927724Z",
     "iopub.status.busy": "2026-10-22T22:23:37.927556Z",
     "iopub.status.idle": "2026-10-22T22:23:37.931421Z",
     "shell.execute_reply": "2026-10-22T22:23:37.930787Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cylinder 3: 2601 (1, 8), 2618 (1, 9), 2797 (1, 10), 2800 (1, 7), 3087 (1, 11), 3094 (2, 10), 3135 (2, 11), 3146 (2, 9), 3256 (2, 12), 3310 (1, 6)\n",
      "cylinder 4: 1226 (1, 7), 1248 (1, 8), 1436 (1, 9), 1481 (1, 6), 1486 (2, 9), 1488 (2, 8), 1593 (2, 10), 1652 (2, 7), 1708 (1, 10), 1781 (2, 11)\n"
     ]
    }
   ],
   "source": [
    "for k in cylinders:\n",
    "    model, Ncr, mn, modes = results[(k, 'CC')]\n",
    "    print('cylinder %d: ' % k + ', '.join('%.0f (%d, %d)' % (N, m, n)\n",
    "                                         for N, (m, n) in zip(Ncr, mn)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a11c21bb",
   "metadata": {},
   "source": [
    "The buckling modes of the linear pre-buckling analyses, the normal\n",
    "displacement $w$ of the skin over the developed half cylinder, with the\n",
    "stringers as thin lines. The lowest mode of the skin between the stringers\n",
    "of cylinder 3, with one half-wave in each bay, is also shown:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "12c4d3ef",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-22T22:23:37.933449Z",
     "iopub.status.busy": "2026-10-22T22:23:37.933260Z",
     "iopub.status.idle": "2026-10-22T22:23:38.408040Z",
     "shell.execute_reply": "2026-10-22T22:23:38.407234Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x350 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_w(ax, model, mode, title):\n",
    "    w = model.skin_field(mode, W)\n",
    "    xx, tt = np.meshgrid(model.xlin, np.degrees(model.theta), indexing='ij')\n",
    "    lim = np.abs(w).max()\n",
    "    ax.contourf(tt, xx, w, levels=np.linspace(-lim, lim, 41), cmap='RdBu_r')\n",
    "    for th in np.degrees(model.theta_stringer):\n",
    "        ax.axvline(th, color='k', lw=0.2)\n",
    "    ax.set_title(title, fontsize=10)\n",
    "    ax.set_xlabel(r'$\\theta$ (degrees)')\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(12, 3.5), sharey=True)\n",
    "for ax, k in zip(axes[:2], [3, 4]):\n",
    "    model, Ncr, mn, modes = results[(k, 'test')]\n",
    "    plot_w(ax, model, modes[:, 0], 'cylinder %d, m = %d, n = %d, %.0f lb/in'\n",
    "           % (k, *mn[0], Ncr[0]))\n",
    "model, Ncr, mn, modes = results[(3, 'test')]\n",
    "local = [i for i, (m, n) in enumerate(mn) if n >= 25]\n",
    "if local:\n",
    "    i = local[0]\n",
    "    plot_w(axes[2], model, modes[:, i],\n",
    "           'cylinder 3, skin between stringers, %.0f lb/in' % Ncr[i])\n",
    "axes[0].set_ylabel('$x$ (in)')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "119a2ed6",
   "metadata": {},
   "source": [
    "## Discussion\n",
    "\n",
    "**Discrete and smeared stringers.** With the membrane pre-buckling state of\n",
    "the theory, the discrete model is within 0.2 % of $\\bar{N}_c$ and 2.1 % of\n",
    "$\\bar{N}_s$ for cylinder 3, and within 0.6 % of both for cylinder 4. The\n",
    "ratio of the clamped critical loads of the external and internal\n",
    "stringers, 2.12, is that of the theory. The stringers are closely spaced,\n",
    "about 7 to 9 stringers per circumferential wave of the modes, and the\n",
    "discrete model, with the bending, extension and torsion of the stringers\n",
    "given by the plate elements, behaves as the smeared theory for these\n",
    "cylinders. The lowest modes have $n = 8$ and $n = 7$ circumferential\n",
    "waves, one more than the numbers of waves into which the cylinders buckled\n",
    "in the tests, $n_e$ of Table I; the modes with $n_e$ waves are 8 % and\n",
    "21 % above the lowest ones, see the list above.\n",
    "\n",
    "**Pre-buckling state.** The linear pre-buckling state of the clamped\n",
    "cylinders, with the radial displacement restrained at the ends, gives\n",
    "critical loads 2.1 % and 1.1 % above those of the membrane state, in line\n",
    "with the conclusion of [1] that a membrane pre-buckled shape is sufficient\n",
    "for the assessment of the eccentricity effects. The lowest mode of the skin\n",
    "between the stringers, near the ends, where the pre-buckling state departs\n",
    "from the membrane state, is above the lowest mode of the whole cylinder\n",
    "(the value of the figure, with the mesh used, is not converged). This\n",
    "agrees with the strain gages of [1], which indicated no local buckling\n",
    "before general buckling.\n",
    "\n",
    "**Tests.** The experimental loads are 80 % and 78 % of the linear\n",
    "pre-buckling loads of the model, close to their ratios to the clamped\n",
    "theory, 82 % and 79 %; for all their cylinders, [1] gives the experimental\n",
    "loads as 70 to 95 % of the clamped theory. The model is that of a perfect\n",
    "cylinder: [1] names the neglect of initial imperfections, besides the\n",
    "boundary conditions and the pre-buckling solution of the theory, as a\n",
    "contribution to the difference between theory and experiment. The externally stiffened cylinders buckled with a loud report\n",
    "and diamond-shaped buckles of large amplitude [1]. The model also leaves\n",
    "out the two butt joints of each cylinder, with doubler plates and rivets,\n",
    "the actual restraint of the potted ends and the fillets of the stiffeners,\n",
    "and assumes a linear elastic material, whereas the stress-strain curves of\n",
    "[1] are linear up to at least 85 % of the maximum stress.\n",
    "The model is not adjusted to the tests.\n",
    "\n",
    "## Reference\n",
    "\n",
    "[1] Card, M. F., and Jones, R. M., *Experimental and theoretical results\n",
    "for buckling of eccentrically stiffened cylinders*, NASA TN D-3639, 1966,\n",
    "[NTRS 19660027866](https://ntrs.nasa.gov/citations/19660027866)."
   ]
  }
 ],
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