{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "091efb0b",
   "metadata": {},
   "source": [
    "# Cantilever cylinder under a follower pressure\n",
    "\n",
    "Schweizerhof and Ramm [1], Section 6.4 (Fig. 12 on p. 1110, Table 4 on\n",
    "p. 1111, Fig. 13 on p. 1112), computed the buckling of cylindrical\n",
    "cantilever shells under a uniform external pressure, with the upper edge\n",
    "free and the lower edge hinged, $E = 2.1 \\times 10^6$, $\\mu = 0.3$, for a\n",
    "pressure of constant direction (dead load, index $c$) and for a pressure\n",
    "that stays normal to the deformed surface (follower load, index $f$). The\n",
    "free edge makes the follower pressure nonconservative: its load stiffness\n",
    "matrix is unsymmetric. The pressure is normalized by their eq. (60),\n",
    "\n",
    "$$\n",
    "p_{cr} = k \\frac{E}{12 (1 - \\mu^2)} \\left(\\frac{t}{R}\\right)^3\n",
    "$$\n",
    "\n",
    "The three shells are 1: $L/R = 6$, $R/t = 100$, $n = 3$ circumferential\n",
    "waves; 2: $L/R = 3$, $R/t = 100$, $n = 4$; 3: $L/R = 3$, $R/t = 500$, $n =\n",
    "6$; the lower edge is either B1, \"warping completely restrained\", $v = w = u\n",
    "= m_x = 0$, or B2, \"warping partially restrained\", $v = w = m_x = 0$ with\n",
    "the axial displacement $u_0$ restrained at one point only. The paper models\n",
    "a sector of $180°/n$ with 24 bicubic elements, 8 along the axis and 3\n",
    "around, and symmetrizes the load stiffness matrix for the linear buckling\n",
    "analyses of Table 4 in three ways, its eqs. (63) to (65). Fig. 13 traces\n",
    "the path of shell 1, B1, under the follower pressure, with an imperfection\n",
    "of 1 % of $t$ in the shape of the linear buckling mode, as the load $K = p\n",
    "\\, 12 (1 - \\mu^2)/E \\, (R/t)^3$ against the maximum displacement $w_i/t$,\n",
    "with the current stiffness parameter of Bergan.\n",
    "\n",
    "Here the same sectors are meshed with the Sanders-type element\n",
    "`BFSCCylinderSanders`, with the follower pressure of `update_fext_follower`\n",
    "and its full, unsymmetric, load stiffness matrix of `update_KCfollower`\n",
    "(first-order area vector, `quadratic=0`), and the path is traced with the\n",
    "Riks method of [structsolve](https://saullocastro.github.io/structsolve/)\n",
    "(0.10.0 or newer), counting the negative eigenvalues of the unsymmetric\n",
    "tangent stiffness matrix. The model is in the module\n",
    "`schweizerhof1984_cylinder.py` of this folder, also used by\n",
    "`tests/test_schweizerhof1984_cylinder.py`.\n",
    "\n",
    "## The model\n",
    "\n",
    "The sector has $x$ from 0, the lower edge, to $L$, the free edge, and $y$\n",
    "from 0 to $b = \\pi R/n$, with $R = 100$ (the factors $k$ do not depend on\n",
    "it). With the degrees of freedom $u$, $u_{,x}$, $u_{,y}$, $v$, $v_{,x}$,\n",
    "$v_{,y}$, $w$, $w_{,x}$, $w_{,y}$, $w_{,xy}$ of the nodes:\n",
    "\n",
    "- $x = 0$, B1: $u = u_{,y} = v = v_{,y} = w = w_{,y} = 0$, the rotation\n",
    "  $w_{,x}$ free ($m_x = 0$);\n",
    "- $x = 0$, B2: $v = v_{,y} = w = w_{,y} = 0$, and $u = 0$ at the node $x =\n",
    "  y = 0$ only, which removes the axial translation of the sector;\n",
    "- $y = 0$ and $y = b$, symmetry planes: $u_{,y} = v = v_{,x} = w_{,y} =\n",
    "  w_{,xy} = 0$, such that the sector keeps the modes of $n$, $2n$, ...\n",
    "  waves;\n",
    "- $x = L$: free.\n",
    "\n",
    "The pressure of $k = 1$ is the reference load, negative (external) in the\n",
    "sign convention of the element, so that the load multipliers are the\n",
    "factors $k$ of Table 4 and the load $K$ of Fig. 13. The linear buckling\n",
    "problems are\n",
    "\n",
    "$$\n",
    "\\left(\\boldsymbol{K}_{C0} + k \\boldsymbol{K}_G(\\boldsymbol{u}_{lin})\\right)\n",
    "\\boldsymbol{\\phi} = \\boldsymbol{0}, \\qquad\n",
    "\\left(\\boldsymbol{K}_{C0} + k \\left(\\boldsymbol{K}_G(\\boldsymbol{u}_{lin})\n",
    "+ \\boldsymbol{K}_F\\right)\\right) \\boldsymbol{\\phi} = \\boldsymbol{0}\n",
    "$$\n",
    "\n",
    "for $k_c$ and $k_f$, with $\\boldsymbol{u}_{lin}$ the linear solution of\n",
    "the dead load of $k = 1$ and $\\boldsymbol{K}_F$ its load stiffness matrix,\n",
    "solved with `structsolve.lb`, `symmetric=False` for $k_f$.\n",
    "\n",
    "The kinematics: with $n = 3$ waves over a length of $6R$ the displacements\n",
    "vary over lengths comparable with $R$, and the Donnell-type kinematics,\n",
    "whose curvatures are those of a flat plate, are not accurate; the\n",
    "Sanders-type element is used, and the Donnell-type one is shown for\n",
    "comparison in Table 4."
   ]
  },
  {
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   "execution_count": 1,
   "id": "ae5f56d8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T12:06:53.499707Z",
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     "shell.execute_reply": "2026-11-03T12:06:54.221455Z"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shell 1: L = 600, t = 1, n = 3, sector 60 deg, p(k = 1) = 0.19231\n",
      "shell 2: L = 300, t = 1, n = 4, sector 45 deg, p(k = 1) = 0.19231\n",
      "shell 3: L = 300, t = 0.2, n = 6, sector 30 deg, p(k = 1) = 0.00154\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import schweizerhof1984_cylinder as sr\n",
    "\n",
    "for shell, (LR, Rt, n) in sr.SHELLS.items():\n",
    "    L, t, n = sr.shell_geometry(shell)\n",
    "    print('shell %d: L = %g, t = %g, n = %d, sector %g deg, p(k = 1) = %.5f'\n",
    "          % (shell, L, t, n, 180/n, sr.p_ref(t)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7402953",
   "metadata": {},
   "source": [
    "## Convergence of the linear buckling factors\n",
    "\n",
    "Shell 1, B1 and B2, with $n_x$ elements along the axis and $n_y$ around\n",
    "the $60°$ sector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3db4e132",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T12:06:54.224901Z",
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     "shell.execute_reply": "2026-11-03T12:07:53.014130Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1   8 x  3,   252 unknowns: k_c 12.2919 (n = 3), k_f 10.9432 (n = 3),  0.1 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1  16 x  4,   656 unknowns: k_c 11.3324 (n = 3), k_f 10.0889 (n = 3),  0.2 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1  32 x  4,  1296 unknowns: k_c 11.1109 (n = 3), k_f 9.8920 (n = 3),  0.2 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1  32 x  8,  2592 unknowns: k_c 10.9546 (n = 3), k_f 9.7527 (n = 3),  0.7 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1  32 x 12,  3888 unknowns: k_c 10.9432 (n = 3), k_f 9.7426 (n = 3),  2.1 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1  64 x  8,  5152 unknowns: k_c 10.9006 (n = 3), k_f 9.7048 (n = 3),  2.3 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1 128 x  8, 10272 unknowns: k_c 10.8870 (n = 3), k_f 9.6926 (n = 3),  4.6 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1 128 x 12, 15408 unknowns: k_c 10.8770 (n = 3), k_f 9.6838 (n = 3),  8.8 s\n",
      "B2   8 x  3,   257 unknowns: k_c 10.1728 (n = 3), k_f 9.0534 (n = 3),  0.1 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B2  16 x  4,   663 unknowns: k_c 9.4341 (n = 3), k_f 8.3956 (n = 3),  0.3 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B2  32 x  8,  2607 unknowns: k_c 9.1474 (n = 3), k_f 8.1404 (n = 3),  2.9 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B2  64 x  8,  5167 unknowns: k_c 9.1110 (n = 3), k_f 8.1080 (n = 3), 11.8 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B2 128 x  8, 10287 unknowns: k_c 9.1018 (n = 3), k_f 8.0999 (n = 3), 24.7 s\n"
     ]
    }
   ],
   "source": [
    "for bc, meshes in (('B1', ((8, 3), (16, 4), (32, 4), (32, 8), (32, 12),\n",
    "                           (64, 8), (128, 8), (128, 12))),\n",
    "                   ('B2', ((8, 3), (16, 4), (32, 8), (64, 8), (128, 8)))):\n",
    "    for nx, ny in meshes:\n",
    "        t0 = time.perf_counter()\n",
    "        model = sr.CantileverModel(1, bc, nx, ny)\n",
    "        kc, mc, _ = sr.linear_buckling(model, 'dead')\n",
    "        kf, mf, _ = sr.linear_buckling(model, 'follower')\n",
    "        print('%s %3d x %2d, %5d unknowns: k_c %.4f (n = %d), k_f %.4f '\n",
    "              '(n = %d), %4.1f s'\n",
    "              % (bc, nx, ny, model.bu.sum(), kc[0], sr.num_waves(model, mc[:, 0]),\n",
    "                 kf[0], sr.num_waves(model, mf[:, 0]),\n",
    "                 time.perf_counter() - t0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0df6d018",
   "metadata": {},
   "source": [
    "The circumferential direction converges with 8 elements over the $60°$\n",
    "sector (12 change the factors by 0.1 %), and the axial one slowly, from\n",
    "the bending boundary layer at the hinged edge: with 8 elements around, the\n",
    "factors change by 0.4 % from 32 to 64 and by 0.1 % from 64 to 128\n",
    "elements along the axis. The 64 x 8 mesh is within 0.2 % of the 128 x 12\n",
    "one, $k_c = 10.877$ and $k_f = 9.684$ for B1, and is used below. The\n",
    "linear buckling mode has $n = 3$ waves in every case, as in the paper."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6410ea80",
   "metadata": {},
   "source": [
    "## Table 4\n",
    "\n",
    "The three shells, 64 x 8 elements, both kinematics; for the Sanders-type\n",
    "kinematics also $k_f$ with the load stiffness matrix symmetrized by eqs.\n",
    "(63), (64) and (65) of the paper: with its skew part $\\boldsymbol{S} =\n",
    "(\\boldsymbol{K}_F - \\boldsymbol{K}_F^\\top)/2 = [\\boldsymbol{0}\\\n",
    "\\hat{\\boldsymbol{K}};\\ -\\hat{\\boldsymbol{K}}^\\top\\ \\boldsymbol{0}]$, which\n",
    "couples the in-plane degrees of freedom with those of $w$, (63) is the\n",
    "symmetric part, and (64) and (65) add and subtract $[\\boldsymbol{0}\\\n",
    "\\hat{\\boldsymbol{K}};\\ \\hat{\\boldsymbol{K}}^\\top\\ \\boldsymbol{0}]$\n",
    "(`symmetrized_KF` of the module)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f864fe62",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T12:07:53.019374Z",
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     "iopub.status.idle": "2026-11-03T12:10:02.100343Z",
     "shell.execute_reply": "2026-11-03T12:10:02.098152Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shell bc  kin.          k_c      k_f      %   k_f (63), (64), (65)     |   paper k_c, k_f            \n",
      "1     B2  sanders     9.111    8.108   12.4   8.108, 8.117, 8.099      |    9.11 8.10, 8.09, 8.12\n",
      "1     B2  donnell     9.106    8.203   11.0                            |    9.11 8.10, 8.09, 8.12\n",
      "1     B1  sanders    10.901    9.705   12.3   9.705, 9.724, 9.685      |   10.88 9.70\n",
      "1     B1  donnell    10.529    9.488   11.0                            |   10.88 9.70\n",
      "2     B2  sanders    16.389   15.386    6.5   15.386, 15.408, 15.364   |   16.43 15.42, 15.38, 15.46\n",
      "2     B2  donnell    16.387   15.442    6.1                            |   16.43 15.42, 15.38, 15.46\n",
      "2     B1  sanders    20.797   19.532    6.5   19.532, 19.577, 19.487   |   20.85 19.58\n",
      "2     B1  donnell    20.280   19.117    6.1                            |   20.85 19.58\n",
      "3     B2  sanders    36.483   35.479    2.8   35.479, 35.489, 35.470   |   36.48 35.48, 35.46, 35.50\n",
      "3     B2  donnell    36.476   35.500    2.8                            |   36.48 35.48, 35.46, 35.50\n",
      "3     B1  sanders    45.797   44.541    2.8   44.541, 44.561, 44.520   |   45.83 \n",
      "3     B1  donnell    45.290   44.081    2.7                            |   45.83 \n"
     ]
    }
   ],
   "source": [
    "table = {}\n",
    "for shell in (1, 2, 3):\n",
    "    for bc in ('B2', 'B1'):\n",
    "        for kin in ('sanders', 'donnell'):\n",
    "            model = sr.CantileverModel(shell, bc, 64, 8, kin)\n",
    "            kc, mc, _ = sr.linear_buckling(model, 'dead')\n",
    "            kf, mf, _ = sr.linear_buckling(model, 'follower')\n",
    "            sym = []\n",
    "            if kin == 'sanders':\n",
    "                for variant in (63, 64, 65):\n",
    "                    k, _, _ = sr.linear_buckling(\n",
    "                        model, KF=sr.symmetrized_KF(model, variant))\n",
    "                    sym.append(k[0])\n",
    "            table[shell, bc, kin] = (kc[0], kf[0], sym,\n",
    "                                     sr.num_waves(model, mf[:, 0]))\n",
    "\n",
    "print('%-5s %-3s %-8s %8s %8s %6s   %-24s | %7s %-20s'\n",
    "      % ('shell', 'bc', 'kin.', 'k_c', 'k_f', '%', 'k_f (63), (64), (65)',\n",
    "         'paper', 'k_c, k_f'))\n",
    "for (shell, bc, kin), (kc, kf, sym, n) in table.items():\n",
    "    pc, pf = sr.TABLE4[shell, bc]\n",
    "    print('%-5d %-3s %-8s %8.3f %8.3f %6.1f   %-24s | %7.2f %s'\n",
    "          % (shell, bc, kin, kc, kf, 100*(kc - kf)/kf,\n",
    "             ', '.join('%.3f' % k for k in sym), pc,\n",
    "             ', '.join('%.2f' % k for k in pf)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e83fe21e",
   "metadata": {},
   "source": [
    "With the Sanders-type kinematics, all the factors of Table 4 are reproduced\n",
    "within 0.3 %: shell 1, B1, $k_c = 10.90$ and $k_f = 9.70$ (10.88 and 9.70),\n",
    "B2, 9.11 and 8.11 (9.11 and 8.10); shell 2, B1, 20.80 and 19.53 (20.85 and\n",
    "19.58), B2, 16.39 and 15.39 (16.43 and 15.42); shell 3, B2, 36.48 and 35.48\n",
    "(36.48 and 35.48), B1, $k_c = 45.80$ (45.83). The paper gives no $k_f$ of\n",
    "shell 3, B1; the model gives 44.54. The relative differences\n",
    "$(k_c - k_f)/k_f$ of the paper, 12.5 %, 12.3 %, 6.5 %, 6.5 % and 2.8 %,\n",
    "are those of the model, 12.4 %, 12.3 %, 6.5 %, 6.5 % and 2.8 %. The\n",
    "nonconservative part of the load stiffness matrix has little influence, as\n",
    "the paper concludes: the symmetric part alone, eq. (63), gives the factor\n",
    "of the full unsymmetric matrix to four digits, and eqs. (64) and (65)\n",
    "bracket it by $\\pm 0.2$ %. The paper's (64) and (65) are in the reverse\n",
    "order, 8.09 and 8.12 for shell 1, B2, against 8.117 and 8.099 here; adding\n",
    "or subtracting the substitute matrix depends on the sign convention of the\n",
    "load stiffness matrix and on which block is called $\\hat{\\boldsymbol{K}}$,\n",
    "which the paper does not state, and the spread, 0.03, is the same.\n",
    "\n",
    "The Donnell-type kinematics underestimate the B1 factors of the long shell\n",
    "1 by 3.4 % ($k_c$) and 2.2 % ($k_f$), and those of shell 2 by 2.5 % and\n",
    "2.1 %, whereas for B2 they agree within 0.05 % in $k_c$ and 1.2 % in $k_f$; with $n = 3$ waves the terms in $1/R$ of the\n",
    "Sanders-type curvatures and rotations matter, and the Sanders-type element\n",
    "is the one compared with the paper. The closed cylinder confirms that $n\n",
    "= 3$ is the lowest mode of shell 1, B1, at the factors of the sector, with\n",
    "$n = 4$ next, 16.40 and 15.38."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2f0d09c",
   "metadata": {},
   "source": [
    "The sector of $60°$ keeps only the modes of 3, 6, ... waves. The closed\n",
    "cylinder, shell 1, B1, 64 x 48 elements around the whole circumference,\n",
    "gives the lowest modes of any number of waves, each twice ($\\cos n\\theta$\n",
    "and $\\sin n\\theta$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d1cea2d5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T12:10:02.103797Z",
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     "shell.execute_reply": "2026-11-03T12:11:16.562297Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dead     k = [10.901 10.901 16.402 16.402 25.156 25.156], n = [3, 3, 4, 4, 5, 5]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "follower k = [ 9.705  9.705 15.384 15.384 23.328 23.328], n = [3, 3, 4, 4, 2, 2]\n"
     ]
    }
   ],
   "source": [
    "model = sr.CantileverModel(1, 'B1', 64, 48, full=True)\n",
    "for load in ('dead', 'follower'):\n",
    "    k, modes, _ = sr.linear_buckling(model, load, num_eigvalues=6)\n",
    "    print('%-8s k = %s, n = %s' % (load, np.array2string(k, precision=3),\n",
    "          [sr.num_waves(model, modes[:, i]) for i in range(6)]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd41a232",
   "metadata": {},
   "source": [
    "The lowest modes of the sector, 64 x 8 elements, $w$ normalized:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fbc4d7c3",
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     "shell.execute_reply": "2026-11-03T12:11:23.904805Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(10, 3.6), sharey=True)\n",
    "for ax, bc in zip(axes, ('B1', 'B2')):\n",
    "    model = sr.CantileverModel(1, bc, 64, 8)\n",
    "    kf, modes, _ = sr.linear_buckling(model, 'follower')\n",
    "    w = modes[6::10, 0].reshape(65, 9)\n",
    "    w = w/w.flat[np.argmax(np.abs(w))]\n",
    "    cs = ax.contourf(model.y.reshape(65, 9)/sr.R*180/np.pi,\n",
    "                     model.x.reshape(65, 9)/sr.R, w, 21, cmap='RdBu_r')\n",
    "    ax.set_xlabel(r'$\\theta$ (deg)')\n",
    "    ax.set_title('%s, follower, $k_f$ = %.3f' % (bc, kf[0]))\n",
    "axes[0].set_ylabel('$x/R$, free edge at 6')\n",
    "fig.colorbar(cs, ax=axes, label='$w/w_{max}$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "829d14d9",
   "metadata": {},
   "source": [
    "## Riks analyses of the imperfect shell, Fig. 13\n",
    "\n",
    "The imperfection is the $w$ part of the lowest mode of the follower\n",
    "pressure, scaled to a largest $|w_0|$ of 1 % of $t$, outwards at the free\n",
    "edge. The element takes no initial geometric imperfection; it is added\n",
    "exactly as in the tutorial of the cylinder of Simo, Fox and Rifai: the\n",
    "membrane strains of the imperfect shell are $\\boldsymbol{\\varepsilon}\n",
    "(\\boldsymbol{u} + \\boldsymbol{u}_0) - \\boldsymbol{\\varepsilon}\n",
    "(\\boldsymbol{u}_0)$ and its curvatures $\\boldsymbol{\\kappa}\n",
    "(\\boldsymbol{u})$, which gives\n",
    "\n",
    "$$\n",
    "\\boldsymbol{F}_{int,imp}(\\boldsymbol{u}) =\n",
    "\\boldsymbol{F}_{int}(\\boldsymbol{u} + \\boldsymbol{u}_0) -\n",
    "\\boldsymbol{F}_{int}(\\boldsymbol{u}_0) -\n",
    "\\boldsymbol{K}_G(\\boldsymbol{N}_0) \\boldsymbol{u}\n",
    "$$\n",
    "\n",
    "The derivation needs only non-linear membrane strains that are quadratic\n",
    "forms of the rotations $\\boldsymbol{G} \\boldsymbol{u}$, and holds for the\n",
    "Sanders-type kinematics with the rows $\\boldsymbol{S}^w_{,x}$ and\n",
    "$\\boldsymbol{S}^w_{,y} - \\boldsymbol{S}^v/R$ of $\\boldsymbol{G}$; it is\n",
    "verified in `tests/test_schweizerhof1984_cylinder.py` against the gradient\n",
    "of a strain energy computed independently of the kernels. The pressure acts\n",
    "on the imperfect surface, and the residual is\n",
    "\n",
    "$$\n",
    "\\boldsymbol{R} = \\boldsymbol{F}_{int,imp}(\\boldsymbol{u}) - k\n",
    "\\boldsymbol{F}_p(\\boldsymbol{u} + \\boldsymbol{u}_0), \\qquad\n",
    "\\boldsymbol{K}_T = \\boldsymbol{K}_{C0} + \\boldsymbol{K}_{CNL}(\\boldsymbol{u}\n",
    "+ \\boldsymbol{u}_0) + \\boldsymbol{K}_G(\\boldsymbol{u}) -\n",
    "\\boldsymbol{K}_{GNL}(\\boldsymbol{u}_0) + k \\boldsymbol{K}_F\n",
    "$$\n",
    "\n",
    "with `calc_fext` the force vector $k \\boldsymbol{F}_p(\\boldsymbol{u}_0)$\n",
    "and `calc_fint` the rest, the callables receiving the load factor `inc`\n",
    "from structsolve (class `FollowerCylinder`). The tangent stiffness matrix\n",
    "of the kernels, $\\boldsymbol{K}_{C0} + \\boldsymbol{K}_{CNL} +\n",
    "\\boldsymbol{K}_G$, is assembled by `CantileverModel.calc_KT`, vectorized\n",
    "over the elements with NumPy, equal to that of `update_KCNL` to the\n",
    "round-off and about 7 times faster than this kernel of the Sanders-type\n",
    "element, which takes most of the run time otherwise.\n",
    "\n",
    "The Riks method starts with an increment of 0.5 of $k$ and stops at the\n",
    "first increment with a largest $|w|$ of $3t$, the end of the axis of Fig.\n",
    "13. With `inertia=True` and `inertia_num_eigvals=6` structsolve factorizes\n",
    "the tangent stiffness matrix of every converged increment with SuperLU and\n",
    "records the sign of its determinant and, since the matrix is unsymmetric\n",
    "and PARDISO's inertia does not apply, the number of negative real\n",
    "eigenvalues among the 6 of smallest magnitude, by shift-invert with ARPACK\n",
    "on the LU factorization. The current stiffness parameter of Bergan [2] is\n",
    "computed as the stiffness $\\Delta k/\\|\\Delta \\boldsymbol{u}\\|$ of each\n",
    "increment, with the Euclidean norm of the increment of the unknown degrees\n",
    "of freedom, over that of the first increment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b38a19f3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T12:11:23.909129Z",
     "iopub.status.busy": "2026-11-03T12:11:23.908855Z",
     "iopub.status.idle": "2026-11-03T12:16:12.691033Z",
     "shell.execute_reply": "2026-11-03T12:16:12.689579Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1  8 x 3: k_f (linear) 10.9432,  33 increments,   2.2 s, max. residual 1e-09; maximum k 10.8551 at w/t 1.816\n",
      "    negative eigenvalues: {np.int64(0): np.int64(20), np.int64(1): np.int64(13)}; determinant signs: {np.int64(-1): np.int64(13), np.int64(1): np.int64(20)}\n",
      "    first negative eigenvalue at increment 21, k 10.8540, w/t 2.140, after the maximum by 1.1e-03 in k\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1 16 x 4: k_f (linear) 10.0889,  31 increments,   5.9 s, max. residual 2e-09; maximum k 10.0301 at w/t 2.669\n",
      "    negative eigenvalues: {np.int64(0): np.int64(22), np.int64(1): np.int64(9)}; determinant signs: {np.int64(-1): np.int64(9), np.int64(1): np.int64(22)}\n",
      "    first negative eigenvalue at increment 23, k 10.0296, w/t 3.028, after the maximum by 4.9e-04 in k\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1 32 x 8: k_f (linear) 9.7527,  30 increments,  23.3 s, max. residual 4e-09; maximum k 9.7154 at w/t 3.994\n",
      "    negative eigenvalues: {np.int64(0): np.int64(25), np.int64(1): np.int64(5)}; determinant signs: {np.int64(-1): np.int64(5), np.int64(1): np.int64(25)}\n",
      "    first negative eigenvalue at increment 26, k 9.7152, w/t 4.391, after the maximum by 1.9e-04 in k\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B1 64 x 8: k_f (linear) 9.7048,  30 increments,  46.6 s, max. residual 3e-09; maximum k 9.6688 at w/t 4.033\n",
      "    negative eigenvalues: {np.int64(0): np.int64(25), np.int64(1): np.int64(5)}; determinant signs: {np.int64(-1): np.int64(5), np.int64(1): np.int64(25)}\n",
      "    first negative eigenvalue at increment 26, k 9.6687, w/t 4.433, after the maximum by 6.4e-05 in k\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B2 64 x 8: k_f (linear) 8.1080,  32 increments, 196.2 s, max. residual 1e-09; maximum k 8.1154 at w/t 6.214 (last increment)\n",
      "    negative eigenvalues: {np.int64(0): np.int64(32)}; determinant signs: {np.int64(1): np.int64(32)}\n"
     ]
    }
   ],
   "source": [
    "runs = {}\n",
    "for bc, nx, ny in (('B1', 8, 3), ('B1', 16, 4), ('B1', 32, 8), ('B1', 64, 8),\n",
    "                   ('B2', 64, 8)):\n",
    "    r = sr.run_riks(1, bc, nx, ny, wmax=6.)\n",
    "    runs[bc, nx, ny] = r\n",
    "    an = r['an']\n",
    "    fext = an.calc_fext()\n",
    "    res = max(np.linalg.norm(an.calc_fint(c, inc=k) - k*fext)\n",
    "              /np.linalg.norm(k*fext) for k, c in zip(an.increments, an.cs))\n",
    "    ks, wt, neg, det = r['ks'], r['wt'], np.array(r['neg']), np.array(r['det'])\n",
    "    imax = np.argmax(ks)\n",
    "    print('%s %2d x %d: k_f (linear) %.4f, %3d increments, %5.1f s, max. '\n",
    "          'residual %.0e; maximum k %.4f at w/t %.3f%s'\n",
    "          % (bc, nx, ny, r['k_lin'], len(ks) - 1, r['elapsed'], res,\n",
    "             ks[imax], wt[imax], ' (last increment)' if imax == len(ks) - 1\n",
    "             else ''))\n",
    "    print('    negative eigenvalues: %s; determinant signs: %s'\n",
    "          % (dict(zip(*np.unique(neg, return_counts=True))),\n",
    "             dict(zip(*np.unique(det, return_counts=True)))))\n",
    "    first = np.flatnonzero(neg > 0)\n",
    "    if first.size:\n",
    "        i = first[0]\n",
    "        print('    first negative eigenvalue at increment %d, k %.4f, w/t '\n",
    "              '%.3f, after the maximum by %.1e in k' % (i + 1, ks[i + 1],\n",
    "              wt[i + 1], ks[imax] - ks[i + 1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22785f37",
   "metadata": {},
   "source": [
    "The residual of every converged increment, that of the whole follower\n",
    "pressure on the imperfect shell, is below $10^{-8}$ of the load. The\n",
    "iterations converge quadratically, with 3 to 5 corrections per increment,\n",
    "because `calc_fext` declares the configuration `c` and returns the load\n",
    "vector of the current configuration $\\boldsymbol{F}_p(\\boldsymbol{u} +\n",
    "\\boldsymbol{u}_0) = -\\partial \\boldsymbol{R}/\\partial k$: with the constant\n",
    "reference vector instead, the bordered system of the Riks method misses the\n",
    "term $\\partial \\boldsymbol{F}_p/\\partial \\boldsymbol{u} \\, \\boldsymbol{u}$\n",
    "of the derivative, the iterations converge linearly, by a factor of about\n",
    "0.1 per correction, and the analyses take ten times longer.\n",
    "\n",
    "Shell 1, B1: the load rises monotonically to a very flat maximum, $k =\n",
    "9.669$ at $w/t = 4.03$ (64 x 8), 0.4 % below the linear $k_f$ of the same\n",
    "mesh, and then decreases slowly; the maximum converges with the mesh like\n",
    "$k_f$, 9.715 with 32 x 8 elements, 9.657 with 128 x 8 (run separately, 74\n",
    "s). It is a limit point, not a bifurcation: the count of negative\n",
    "eigenvalues of the tangent stiffness matrix is 0 up to the maximum and 1\n",
    "from the first increment after it, together with the sign of the\n",
    "determinant, and stays 1 up to $w/t = 6$ (8 in a separate run). Since the\n",
    "count never exceeds 1, the sign of the determinant alone sees the same\n",
    "critical point here. The coarse meshes have their maximum at smaller\n",
    "deflections, 1.8 (8 x 3) and 2.7 (16 x 4), with the same pattern. With\n",
    "B2 the load still rises at $w/t = 6$ (8.12 at 6.2, and 8.163 at $w/t = 8$\n",
    "with 32 x 8 elements in a separate run), and the count stays 0: there is\n",
    "no critical point on the computed path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3ffdfc85",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T12:16:12.695493Z",
     "iopub.status.busy": "2026-11-03T12:16:12.695073Z",
     "iopub.status.idle": "2026-11-03T12:16:13.073701Z",
     "shell.execute_reply": "2026-11-03T12:16:13.072384Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x460 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(11, 4.6), sharey=True,\n",
    "                               gridspec_kw=dict(width_ratios=(1, 2.2)))\n",
    "colors = {('B1', 8, 3): 'C1', ('B1', 16, 4): 'C2', ('B1', 32, 8): 'C4',\n",
    "          ('B1', 64, 8): 'C0', ('B2', 64, 8): 'C3'}\n",
    "for key, r in runs.items():\n",
    "    bc, nx, ny = key\n",
    "    ax1.plot(r['wt'], r['ks'], '-', color=colors[key],\n",
    "             marker='.', ms=3, lw=1.5 if nx == 64 else 0.8,\n",
    "             label='%s, %d x %d, $k_f$ = %.2f' % (bc, nx, ny, r['k_lin']))\n",
    "    ax1.axhline(r['k_lin'], color=colors[key], lw=0.5, ls=':')\n",
    "    if nx == 64:\n",
    "        ax0.plot(r['cs_param'], r['ks'][1:], '.-', ms=3, color=colors[key],\n",
    "                 label='%s, %d x %d' % key)\n",
    "d = np.array(sr.FIG13_IMPERFECT)\n",
    "ax1.plot(d[:, 0], d[:, 1], 'o', mfc='none', color='k', ms=4,\n",
    "         label='Fig. 13, imperfect shell')\n",
    "ax1.axhline(sr.FIG13_PERFECT, color='k', lw=0.8, ls='--',\n",
    "            label='Fig. 13, perfect shell')\n",
    "d = np.array(sr.FIG13_CS)\n",
    "ax0.plot(d[:, 0], d[:, 1], 'o', mfc='none', color='k', ms=4,\n",
    "         label='Fig. 13, CS parameter')\n",
    "ax0.set_xlim(1.05, -0.05)\n",
    "ax0.set_xlabel('current stiffness parameter')\n",
    "ax0.set_ylabel(r'$K = p \\, 12 (1 - \\mu^2)/E \\, (R/t)^3$')\n",
    "ax0.legend(fontsize=7, loc='lower left')\n",
    "ax1.set_xlim(0, 6)\n",
    "ax1.set_ylim(0, 11.5)\n",
    "ax1.set_xlabel('maximum displacement $w_i/t$')\n",
    "ax1.legend(fontsize=7, loc='lower right')\n",
    "for ax in (ax0, ax1):\n",
    "    ax.grid(lw=0.3)\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b667cb6",
   "metadata": {},
   "source": [
    "Fig. 13 is read on the page rendered at 300 dpi, from the centre line of\n",
    "the thick curve, with the axes calibrated on their ticks, to about $\\pm\n",
    "0.05$ in $K$ and $\\pm 0.01$ in $w_i/t$; the horizontal line of the perfect\n",
    "shell is at $K = 8.06$, and the curve of the imperfect shell reaches 8.01\n",
    "at $w_i/t = 3$ without a maximum. The table compares the curve with the\n",
    "paths of B1 and B2 (64 x 8) at the abscissae of the readings, and the\n",
    "current stiffness parameter at the ordinates of the dashed curve (read to\n",
    "$\\pm 0.02$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9d52953d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T12:16:13.076766Z",
     "iopub.status.busy": "2026-11-03T12:16:13.076381Z",
     "iopub.status.idle": "2026-11-03T12:16:13.086328Z",
     "shell.execute_reply": "2026-11-03T12:16:13.085074Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   w/t  Fig. 13  B1 64x8  B2 64x8\n",
      " 0.058     6.72    8.089    6.773\n",
      " 0.095     7.19    8.695    7.265\n",
      " 0.133     7.41    8.983    7.497\n",
      " 0.170     7.54    9.128    7.633\n",
      " 0.245     7.71    9.306    7.774\n",
      " 0.319     7.77    9.394    7.854\n",
      " 0.506     7.85    9.512    7.943\n",
      " 0.693     7.91    9.563    7.988\n",
      " 1.002     7.93    9.606    8.025\n",
      " 1.439     7.95    9.635    8.051\n",
      " 2.007     7.99    9.653    8.068\n",
      " 2.559     8.00    9.661    8.079\n",
      " 2.970     8.01    9.665    8.085\n",
      "\n",
      "     K CS Fig. 13 CS B1 64x8 CS B2 64x8\n",
      "  0.98      0.970      0.990      0.980\n",
      "  1.44      0.948      0.979      0.955\n",
      "  1.90      0.930      0.965      0.927\n",
      "  2.36      0.880      0.948      0.889\n",
      "  2.82      0.810      0.926      0.842\n",
      "  3.28      0.747      0.903      0.794\n",
      "  3.74      0.667      0.869      0.716\n",
      "  4.20      0.570      0.824      0.632\n",
      "  4.66      0.475      0.779      0.539\n",
      "  5.11      0.370      0.736      0.432\n",
      "  5.57      0.260      0.652      0.324\n",
      "  6.03      0.180      0.563      0.218\n",
      "  6.49      0.100      0.474      0.131\n",
      "  6.95      0.047      0.368      0.070\n",
      "  7.41      0.020      0.260      0.026\n"
     ]
    }
   ],
   "source": [
    "d = np.array(sr.FIG13_IMPERFECT)\n",
    "print('%6s %8s %8s %8s' % ('w/t', 'Fig. 13', 'B1 64x8', 'B2 64x8'))\n",
    "for wt, K in d:\n",
    "    print('%6.3f %8.2f %8.3f %8.3f'\n",
    "          % (wt, K, np.interp(wt, runs['B1', 64, 8]['wt'], runs['B1', 64, 8]['ks']),\n",
    "             np.interp(wt, runs['B2', 64, 8]['wt'], runs['B2', 64, 8]['ks'])))\n",
    "d = np.array(sr.FIG13_CS)\n",
    "print()\n",
    "print('%6s %10s %10s %10s' % ('K', 'CS Fig. 13', 'CS B1 64x8', 'CS B2 64x8'))\n",
    "for cs, K in d:\n",
    "    out = []\n",
    "    for key in (('B1', 64, 8), ('B2', 64, 8)):\n",
    "        r = runs[key]\n",
    "        out.append(np.interp(K, r['ks'][1:], r['cs_param']))\n",
    "    print('%6.2f %10.3f %10.3f %10.3f' % ((K, cs) + tuple(out)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7afb0754",
   "metadata": {},
   "source": [
    "The path of B1 does not match Fig. 13: its plateau, 9.67, is 21 % above\n",
    "the 8.0 of the figure, as is its $k_f$, 9.70 in Table 4 and here. The path\n",
    "of B2 matches it: within 0.10 (1.3 %) at every reading, the\n",
    "plateau 8.09 at $w_i/t = 3$ against 8.01, with the knee at the same place,\n",
    "$K = 6.77$ and 7.27 at $w_i/t = 0.058$ and 0.095 against 6.72 and 7.19,\n",
    "and the current stiffness parameter within 0.07, 0.5 at $K = 4.55$ in the\n",
    "figure and 4.85 here, a difference of the size of the error of the secant estimate of an\n",
    "incremental quantity over the increments of the Riks method, which are\n",
    "not those of the paper. The horizontal line of the perfect shell in the\n",
    "figure, 8.06, is the $k_f$ of B2 of Table 4, 8.09 to 8.12, and of this\n",
    "model, 8.11, within 0.6 %, and far from that of B1, 9.70. The text of the\n",
    "paper, p. 1111, says that the nonlinear analysis is of shell 1 \"with\n",
    "boundary conditions B1\"; the figure, its perfect-shell line and its\n",
    "current stiffness parameter are those of B2, and the label of the text is\n",
    "most likely wrong. The conclusion that the paper draws from the figure,\n",
    "that the linear buckling load with the symmetrized load stiffness matrix\n",
    "is an upper bound approached by the imperfect shell, holds for both\n",
    "boundary conditions: with B1 the path tends to the limit point 0.4 %\n",
    "below $k_f$, with B2 it rises slowly to $k_f$ and beyond it, the\n",
    "post-buckling path of the perfect shell being stable at least up to $w/t\n",
    "= 8$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c3f4703",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Schweizerhof, K., and Ramm, E., Displacement dependent pressure loads in\n",
    "nonlinear finite element analyses, Computers & Structures, 18(6),\n",
    "1099-1114, 1984, doi:10.1016/0045-7949(84)90154-8.\n",
    "\n",
    "[2] Bergan, P. G., Automated incremental-iterative solution schemes, in\n",
    "Numerical Methods for Nonlinear Problems, edited by C. Taylor, E. Hinton\n",
    "and D. R. J. Owen, Pineridge Press, Swansea, 1980 (ref. [7] of [1])."
   ]
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