{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {
    "pycharm": {
     "name": "#%% raw\n"
    }
   },
   "source": [
    "Code provided under BSD 3-Clause license, all other content under a Creative Commons Attribution license, CC-BY 4.0. (c) 2022 Francesco Mario Antonio Mitrotta."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Buckling Analysis of Euler's Column\n",
    "\n",
    "***\n",
    "\n",
    "This notebook shows the calculation of the buckling load of Euler's column, that is to say a pin-ended column loaded in compression. Four methods are considered: Euler's analytical formula, MSC Nastran SOL 105's linear buckling analysis, MSC Nastran SOL 106's nonlinear buckling method and monitoring the definiteness of the tangent stiffness matrix during a nonlinear static analysis (using MSC Nastran SOL 106). The notebook is freely inspired by [this article](https://simcompanion.hexagon.com/customers/s/article/buckling-analysis-of-column-kb8021539) on the buckling analysis of a column with MSC Nastran.\n",
    "* [Euler's buckling load](#euler)\n",
    "* [Setup of the numerical model](#numerical-model)\n",
    "* [SOL 105 - linear buckling analysis](#linear-buckling)\n",
    "* [SOL 106 - nonlinear buckling method](#nonlinear-buckling)\n",
    "* [SOL 106 - tangent stiffness matrix](#tangent-stiffness-matrix)\n",
    "* [Conclusion](#conclusion)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Euler's buckling load <a name=\"euler\"></a>\n",
    "\n",
    "***\n",
    "\n",
    "Let's consider a column with diameter $d=20$ mm, length $l=420$ mm and Young's modulus $E=207$ GPa. The column is pinned at one end and has a roller support at the other end, where the load is applied in compression, as shown below.\n",
    "\n",
    "![Euler's column under uniaxial load.](resources/01_EulerColumn.svg \"Euler's column under uniaxial load.\")\n",
    "\n",
    "Euler's buckling load $P_{c}$ is given by ([Megson, 2017, Chapter 8](http://www.aerostudents.com/courses/structural-analysis-and-design/Aircraft_Structures_for_Engineering_Students_6th_Edition.pdf)):\n",
    "$$P_{c}=\\frac{\\pi^2EI}{l^2},$$\n",
    "where the area moment of inertia $I$ for a circular cross-sectional shape is calculated as:\n",
    "$$I = \\frac{\\pi d^4}{64}.$$\n",
    "\n",
    "Let's calculate $P_{c}$ for our column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Euler's buckling load: 90962 N\n"
     ]
    }
   ],
   "source": [
    "import numpy as np  # package for working with arrays\n",
    "\n",
    "d = 20.    # [mm]\n",
    "l = 420.   # [mm]\n",
    "E = 207e3  # [MPa]\n",
    "I = np.pi*d**4/64  # [mm^4]\n",
    "P_c = np.pi**2*E*I/l**2  # [N]\n",
    "print(f\"Euler's buckling load: {P_c:.0f} N\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Setup of the numerical model <a name=\"numerical-model\"></a>\n",
    "\n",
    "***\n",
    "\n",
    "We want to run some linear and nonlinear FE analyses with MSC Nastran, and to do this we need to create an appropriate numerical model together with its corresponding input file. To create, manipulate, run and analyze the results of Nastran models in our jupyter notebooks, we are going to use the [`pyNastran`](https://github.com/SteveDoyle2/pyNastran) package.\n",
    "\n",
    "We are going to define a base input object for our Nastran analyses. We'll complete this input object each time depending on the analysis we want to run. We'll use the function `create_base_bdf` from the module `column_utils`, where we can find some useful functions to work with a Nastran model of Euler's column. `create_base_bdf` returns a `BDF` object representing a Nastran input file (with file extension `.bdf`) including nodes, beam elements, material properties, boundary conditions, unit compression force applied to the column and some parameters for the output format of the results. The function takes as input:\n",
    "- material properties including Young's modulus, Poisson's ratio and density;\n",
    "- geometric properties of the column, namely length and diameter;\n",
    "- number of beam elements used to discretize the column.\n",
    "\n",
    "Let's define the missing material properties and let's create a base bdf input with 420 beam elements, so that each element is 1 mm long. Note that we'll be working with the _millimeter - newton - megapascal - ton_ system of units.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "subcase=0 already exists...skipping\n"
     ]
    }
   ],
   "source": [
    "from resources import column_utils  # module with functions to work with a Nastran model of Euler's column\n",
    "\n",
    "# Define missing parameters for function create_base_bdf\n",
    "nu = 0.3  # Poisson's ratio\n",
    "rho = 7.8e-4  # material density [tons/mm^3]\n",
    "no_elements = 420  # number of beam elements used to discretize the column\n",
    "\n",
    "# Create base bdf input\n",
    "base_bdf_input = column_utils.create_base_bdf(young_modulus=E, poisson_ratio=nu, density=rho, diameter=d, length=l, no_elements=no_elements)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now let's get a summary of our `BDF` object with the `get_bdf_stats` method. The output of this method is a text with a list of the bulk data cards of our Nastran input, that we can print to the screen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---BDF Statistics---\n",
      "SOL None\n",
      "\n",
      "bdf.loads[4]: 1\n",
      "  FORCE:   1\n",
      "\n",
      "bdf.spcadds[3]: 1\n",
      "  SPCADD:  1\n",
      "\n",
      "bdf.spcs[1]: 1\n",
      "  SPC1:    1\n",
      "\n",
      "bdf.spcs[2]: 1\n",
      "  SPC1:    1\n",
      "\n",
      "bdf.params: 0\n",
      "  PARAM    : 1\n",
      "\n",
      "bdf.nodes: 0\n",
      "  GRID     : 421\n",
      "\n",
      "bdf.elements: 0\n",
      "  CBEAM    : 420\n",
      "\n",
      "bdf.properties: 0\n",
      "  PBEAML   : 1\n",
      "\n",
      "bdf.materials: 0\n",
      "  MAT1     : 1\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(base_bdf_input.get_bdf_stats())"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Note that no solution sequence is defined in the function `create_base_bdf`. We'll need to define the solution sequence for each analysis that we want to run."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## SOL 105 - linear buckling analysis <a name=\"linear-buckling\"></a>\n",
    "\n",
    "***\n",
    "\n",
    "The first numerical analysis that we are going to run is a linear buckling analysis, using solution sequence SOL 105. To complete our bdf input for such analysis, we execute the following steps:\n",
    "- create a deep copy of the base `BDF` object (in order to preserve the original `BDF` object and reuse it later);\n",
    "- define SOL 105 as solution sequence;\n",
    "- create first subcase where we apply the compression load. To accomplish this we use the function `create_static_load_subcase` from the `pynastran_utils` module, which contains many useful functions to work with `pyNastran` objects;\n",
    "- create second subcase where we solve the eigenvalue problem and consequently calculate the buckling load."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from resources import pynastran_utils  # module with useful functions to work with pyNastran objects\n",
    "\n",
    "# Create a deep copy of the original BDF object and define solution sequence\n",
    "linear_buckling_bdf = base_bdf_input.__deepcopy__({})\n",
    "linear_buckling_bdf.sol = 105\n",
    "\n",
    "# Create first subcase for the application of the compression load\n",
    "load_application_subcase_id = 1  # define subcase id\n",
    "force_set_id = list(linear_buckling_bdf.loads.keys())[0]  # retrieve id of the FORCE card representing the compression force\n",
    "pynastran_utils.create_static_load_subcase(bdf=linear_buckling_bdf, subcase_id=load_application_subcase_id,\n",
    "                                           load_set_id=force_set_id)  # create subcase\n",
    "\n",
    "# Create second subcase for the execution of the eigenvalue analysis\n",
    "eigrl_set_id = force_set_id + 1  # define id of the EIGRL card\n",
    "linear_buckling_bdf.add_eigrl(sid=eigrl_set_id, v1=0., nd=1)  # add EIGRL card to define a real eigenvalue analysis with the Lanczos method and calculate only the first positive eigenvalue\n",
    "eigenvalue_calculation_subcase_id = 2  # define subcase id\n",
    "linear_buckling_bdf.create_subcases(eigenvalue_calculation_subcase_id)  # create subcase\n",
    "linear_buckling_bdf.case_control_deck.subcases[eigenvalue_calculation_subcase_id].add_integer_type('METHOD', eigrl_set_id)  # add EIGRL card id to case control deck"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The model for the linear buckling analysis is ready to run now! Let's define the name of the directory where we will run all the analyses of this notebook and the name of our input bdf file. Then we can call the function `run_analysis` from the `pynastran_utils` module, which we imported earlier. `run_analysis` creates the analysis directory if it doesn't exist alreardy, writes the input `BDF` object to a bdf file and runs the analysis with Nastran."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import os  # module for working with the operating system\n",
    "\n",
    "# Define name of analysis directory\n",
    "analysis_directory_name = '01_Buckling_Analysis_of_Euler_Column'\n",
    "analysis_directory_path = os.path.join(os.getcwd(), 'analyses', analysis_directory_name)\n",
    "\n",
    "# Define input name\n",
    "base_input_name = 'euler_column'\n",
    "linear_buckling_input_name = base_input_name + '_linear_buckling'\n",
    "\n",
    "# Run analysis\n",
    "pynastran_utils.run_analysis(\n",
    "    directory_path=analysis_directory_path, bdf=linear_buckling_bdf, filename=linear_buckling_input_name, run_flag=False)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now we can read Nastran's op2 output file with the `read_op2` function and we can look at the eigenvalue calculated in the second subcase. Since the eigenvalue represents the ratio between the buckling and the applied load and since our applied load is exactly 1 N, the eigenvalue corresponds to the buckling load. Let's print its value and the percentage difference with respect to the analytical result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SOL 105 buckling load: 90578 N\n",
      "Difference with respect to analytical buckling load: -0.42 %\n"
     ]
    }
   ],
   "source": [
    "from pyNastran.op2.op2 import read_op2  # function to read Nastran's op2 file\n",
    "\n",
    "# Read op2 file\n",
    "op2_filename = os.path.join(analysis_directory_path, linear_buckling_input_name + '.op2')\n",
    "linear_buckling_op2 = read_op2(op2_filename=op2_filename, load_geometry=True, debug=None)  # load results and geometry and do not print any debug or info message\n",
    "\n",
    "# Find eigenvalue and print results to screen\n",
    "sol_105_buckling_load = linear_buckling_op2.eigenvectors[eigenvalue_calculation_subcase_id].eigr  # retrieve eigenvalue from the OP2 object\n",
    "print(f'SOL 105 buckling load: {sol_105_buckling_load:.0f} N')\n",
    "print(f'Difference with respect to analytical buckling load: {(sol_105_buckling_load/P_c-1)*100:.2f} %')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe only a negligible difference with respect to Euler's buckling load, which can be most probably ascribable to the discretization error.\n",
    "\n",
    "Let's visualize the buckling mode using the function `plot_buckling_mode` from the `column_utils` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt  # plotting package\n",
    "\n",
    "plt.rcParams['figure.dpi'] = 120  # set default dpi of figures\n",
    "column_utils.plot_buckling_mode(op2=linear_buckling_op2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## SOL 106 - nonlinear buckling method <a name=\"nonlinear-buckling\"></a>\n",
    "\n",
    "***\n",
    "\n",
    "Our next numerical analysis is a nonlinear analysis with solution sequence SOL 106, where we want to use the so-called nonlinear buckling method. This method was described by [Lee & Herting (1985)](https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.1620211016) and is based on the hypothesis that the components of the tangent stiffness matrix vary linearly in a small range close to the last two converged solutions. If a critical point exists sufficiently close to the last converged solution, then the tangent stiffness matrix at such point can be expressed as:\n",
    "\n",
    "$$\\boldsymbol{K_{c}}=\\boldsymbol{K_n}+\\mu\\boldsymbol{\\Delta K},$$\n",
    "\n",
    "where $\\boldsymbol{\\Delta K}=\\boldsymbol{K_n}-\\boldsymbol{K_{n-1}}$ is the differential stiffness matrix based on the last two converged solutions $n$ and $n-1$ and $\\mu$ is a proportionality factor.\n",
    "\n",
    "Since the tangent stiffness matrix is singular at the critical point, we can formulate the following eigenvalue problem:\n",
    "\n",
    "$$\\left(\\boldsymbol{K_n}+\\mu\\boldsymbol{\\Delta K}\\right)\\boldsymbol{\\phi}=\\boldsymbol{0},$$\n",
    "\n",
    "where $\\mu$ and $\\boldsymbol{\\phi}$ respectively represent the eigenvalues and the eigenvectors related to the critical displacements $\\boldsymbol{U_{c}}$:\n",
    "\n",
    "$$\\boldsymbol{U_{c}}=\\boldsymbol{U_n}+\\mu\\boldsymbol{\\Delta U},$$\n",
    "\n",
    "with $\\boldsymbol{\\Delta U}=\\boldsymbol{U_n}-\\boldsymbol{U_{n-1}}$. Nastran calculates the vector of critical buckling loads $\\boldsymbol{P_{c}}$ as:\n",
    "\n",
    "$$\\boldsymbol{P_{c}}=\\boldsymbol{P_n}+\\alpha\\boldsymbol{\\Delta P},$$\n",
    "\n",
    "where $\\boldsymbol{P_n}$ is the vector of the applied loads, $\\alpha$ is the critical buckling factor and $\\boldsymbol{\\Delta P}$ is the last load increment vector applied in the nonlinear analysis. $\\alpha$ and $\\mu$ are related by the following expression:\n",
    "\n",
    "$$\\alpha=\\frac{\\mu\\boldsymbol{\\Delta U}^\\intercal\\left(\\boldsymbol{K_n}+\\frac{1}{2}\\mu\\boldsymbol{\\Delta K}\\right)\\boldsymbol{\\Delta U}}{\\boldsymbol{\\Delta U}^\\intercal\\boldsymbol{\\Delta P}}.$$\n",
    "\n",
    "As suggested by [Lee & Herting (1985)](https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.1620211016), we need to monitor the value of $\\alpha$ because when it is greater than unity the predicted buckling point is not close to the last solution point and as a consequence the prediction should not be considered reliable.\n",
    "\n",
    "To complete our bdf input for this analysis, we execute the following steps:\n",
    "- create a deep copy of the original `BDF` object;\n",
    "- assign SOL 106 as solution sequence;\n",
    "- create first subcase where we apply a compression force equal to the buckling load predicted by SOL 105;\n",
    "- define the parameters for the eigenvalue computation, this time carried out in the same subcase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# Create deep copy of the original BDF object and define solution sequence\n",
    "nonlinear_buckling_bdf = base_bdf_input.__deepcopy__({})  # deep copy of BDF object\n",
    "nonlinear_buckling_bdf.sol = 106  # solution sequence\n",
    "\n",
    "# Creat first subcase\n",
    "nonlinear_buckling_bdf.loads[force_set_id][0].mag = sol_105_buckling_load  # set force magnitude equal to SOL 105 buckling load\n",
    "first_subcase_id = 1  # define subcase id\n",
    "pynastran_utils.create_static_load_subcase(bdf=nonlinear_buckling_bdf, subcase_id=first_subcase_id,\n",
    "                                           load_set_id=force_set_id)  # create subcase\n",
    "\n",
    "# Add EIGB card to define an eigenvalue analysis with inverse power method\n",
    "eigb_set_id = force_set_id + 1\n",
    "nonlinear_buckling_bdf.add_eigb(sid=eigb_set_id, method='INV', L1=-1e4, L2=1e4, nep=1, ndp='', ndn='', norm='', G='', C='')  # define buckling analysis with inverse power method to find one positive and one negative root\n",
    "nonlinear_buckling_bdf.case_control_deck.subcases[first_subcase_id].add_integer_type('METHOD', eigb_set_id)  # add EIGB card id to case control deck"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "In SOL 106 we need to specify some additional parameters and cards for the nonlinear analysis.\n",
    "\n",
    "First we define two `PARAM` cards to enable large displacement effects and to flag the use of the nonlinear buckling method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PARAM     BUCKLE       2"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nonlinear_buckling_bdf.add_param('LGDISP', [1])  # assume all nonlinear structural element types that have a large displacement capability to have large displacement effects\n",
    "nonlinear_buckling_bdf.add_param('BUCKLE', [2])  # request nonlinear buckling method in a SOL 106 cold start run"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Successively we define the arc-length method as our iteration method. We first add the `NLPARM` card to set the general parameters of the nonlinear iteration strategy. We use the following settings:\n",
    "* `ninc=100` to set the initial load increment $\\Delta\\mu^1 = 1/NINC$ to 1% of the total applied load;\n",
    "* `kmethod='ITER'` and `kstep=-1` to update the stiffness matrix at every iteration. The value of -1 means that the stiffness matrix is forced to be updated between the convergence of a load increment and the start of the next load increment. We don't set `KSTEP` to 1 (corresponding to no update between load increments) because in this way the solver would ignore the displacement error in the convergence criteria (see the explanation of the NLPARM card on the *MSC Nastran Quick Reference Guide* for more details);\n",
    "* `max_iter=25` to set the maximum number of iterations for each load increment;\n",
    "* `conv='PUV'` to select convergence based on the load equilibrium and the displacement errors with vector component method (convergence checking is performed on the maximum vector component of all components in the model);\n",
    "* `int_out='YES'` to process the output for every converged load increment;\n",
    "* `eps_p=1e-3` and `eps_u=1e-3` to set the error tolerance for the load and the displacement criterion, respectively;\n",
    "* `max_bisect=10` to set the maximum number of bisections allowed for each load increment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NLPARM         1     100            ITER      -1             PUV     YES\n",
       "            .001    .001\n",
       "              10"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nlparm_id = 1  # id of the NLPARM and NLPCI cards\n",
    "nonlinear_buckling_bdf.add_nlparm(nlparm_id, ninc=100, kmethod='ITER', kstep=-1, max_iter=25, conv='PUV', int_out='YES',\n",
    "                                  eps_p=1e-3, eps_u=1e-3, max_bisect=10)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Then we add a `NLPCI` card to define the parameters of the arc-length method:\n",
    "* `Type='CRIS'` to set Crisfield constraint type;\n",
    "* `minalr=.01` and `maxalr=1.0001` to set the minimum and maximum allowable arc-length adjustment ratio between increments, where $MINALR \\leq\\frac{\\Delta l_{new}}{\\Delta l_{old}}\\leq MAXALR$ and $\\frac{\\Delta l_{new}}{\\Delta l_{old}}$ is the adjument ratio of the arc-length;\n",
    "* `desiter=5` to set the desired number of iterations for convergence, which is used to calculate the arc-length for the next increment $\\Delta l_{new}=\\Delta l_{old}\\sqrt{DESITER/I_{max}}$, where $I_{max}$ represents the number of iterations required for convergence in the previous load increment;\n",
    "* `mxinc=1000` to set the maximum number of controlled increment steps allowed within a subcase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NLPCI          1    CRIS     .01  1.0001      0.               5    1000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nonlinear_buckling_bdf.add_nlpci(nlparm_id, Type='CRIS', minalr=.01, maxalr=1.0001, desiter=5, mxinc=1000)  # same identification number of NLPARM card is used becasue NLPCI card must be associated to a NLPARM card"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Finally, we need to select the NLPARM card that we have just defined in the case control deck."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "nonlinear_buckling_bdf.case_control_deck.subcases[0].add_integer_type('NLPARM', nlparm_id)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The parameters employed here are inspired by the shallow cylindrical shell snap-through example from the *MSC Nastran Demontration Problems Guide - Implicit Nonlinear*.\n",
    "\n",
    "Now the Nastran input is ready to be run, so let's define a name for our input file and call the `run_analysis` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nastran job euler_column_nonlinear_buckling_method.bdf completed\n",
      "Wall time: 6.0 s\n"
     ]
    }
   ],
   "source": [
    "nonlinear_buckling_input_name = base_input_name + '_nonlinear_buckling_method'  # input file name\n",
    "pynastran_utils.run_analysis(directory_path=analysis_directory_path, bdf=nonlinear_buckling_bdf,\n",
    "                             filename=nonlinear_buckling_input_name, run_flag=False)  # run analysis"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We read the nonlinear buckling load $\\boldsymbol{P_c}$ and the critical buckling factor $\\alpha$ using the function `read_nonlinear_buckling_load_from_f06` from the `pynastran_utils` module. The nonlinear buckling load is returned by the function as an array with dimensions _(number of subcases, number of nodes, 6)_, where 6 indicates the forces and moments along the 3 axes. In this simple case the nonlinear buckling load corresponds to the $x$ component of the force at the last node of the first subcase.\n",
    "\n",
    "We read the op2 and f06 file, find the nonlinear buckling load and critical buckling factor, print the results and plot the buckling mode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "SOL 106 buckling load: 90578 N\n",
      "Critical buckling factor ALPHA = -8.3e-06\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f06_filepath = os.path.join(analysis_directory_path, nonlinear_buckling_input_name + '.f06')  # path to .f06 file\n",
    "op2_filepath = os.path.join(analysis_directory_path, nonlinear_buckling_input_name + '.op2')  # path to .op2 file\n",
    "nonlinear_buckling_op2 = read_op2(op2_filename=op2_filepath, load_geometry=True, debug=None)  # load results and geometry and do not print any debug or info message\n",
    "buckling_load_vectors, critical_buckling_factors = pynastran_utils.read_nonlinear_buckling_load_from_f06(\n",
    "    f06_filepath=f06_filepath, op2=nonlinear_buckling_op2)  # return list of nonlinear buckling loads and list of critical buckling factors\n",
    "sol_106_buckling_load = np.abs(buckling_load_vectors[0, -1, 0])  # retrieve buckling load from first subcase, last node, x-component\n",
    "print(f\"\"\"\n",
    "SOL 106 buckling load: {sol_106_buckling_load:.0f} N\n",
    "Critical buckling factor ALPHA = {critical_buckling_factors[0]:.1e}\"\"\")  # print results\n",
    "column_utils.plot_buckling_mode(op2=nonlinear_buckling_op2)  # plot buckling mode"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that there is no noticeable difference between the linear and the nonlinear buckling load and shape. In fact, given the symmetry of the problem and the absence of material nonlinearities, there is no reason why the buckling load and shape should differ between the two analyses. Furthermore, the absolute value of $\\alpha$ is well below unity, which suggests that the points used to calculate the differential stiffness matrix are close to the critical point."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## SOL 106 - tangent stiffness matrix <a name=\"tangent-stiffness-matrix\"></a>\n",
    "\n",
    "***\n",
    "\n",
    "The stability of an equilibrium point of a structure is assessed by looking at the Hessian of the potential energy $\\Pi$, that corresponds to the tangent stiffness matrix $\\boldsymbol{K}_T$ at that point:\n",
    "\n",
    "$$\\boldsymbol{H}_\\Pi=\\frac{\\partial^2\\Pi}{\\partial\\boldsymbol{q}^2}=\\boldsymbol{K}_T,$$\n",
    "\n",
    "where $\\boldsymbol{q}$ is the vector of the generalized coordinates. For stable points the tangent stiffness matrix is positive definite, while at critical points the matrix becomes singular. This means that at least one eigenvalue must be zero. As a consequence, we can assess the buckling load of Euler's column by looking at the load where the lowest eigenvalue $\\lambda$ of the tangent stiffness matrix becomes null.\n",
    "\n",
    "For this analysis we use the same input used for the nonlinear buckling method. We only need to add a command to calculate the smallest magnitude eigenvalue of the tangent stiffness matrix at every load increment and print it in the f06 file. For this purpose, we include an appropriate DMAP sequence in the executive control statements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "nonlinear_buckling_bdf.executive_control_lines[1:1] = ['include \\'' + os.path.join(\n",
    "    os.pardir, os.pardir, 'resources', 'kllrh_eigenvalues_nobuckle.dmap') + '\\'']  # include DMAP sequence"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It should be noted that theoretically in this case we don't need the bulk data entry `PARAM,BUCKLE,2`, as we don't want to use SOL 106's nonlinear buckling method. However, without such entry Nastran does not update the tangent stiffness matrix after the last load increment. For this reason we keep the parameter `PARAM,BUCKLE,2` making sure that the DMAP sequence skips the buckling calculation.\n",
    "\n",
    "Let's apply a compression load equal to the buckling load found in the previous analyis rounded up to the next thousand, as we want to observe the lowest eigenvalue of the tangent stiffness matrix becoming negative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "nonlinear_buckling_bdf.loads[force_set_id][0].mag = np.ceil(sol_106_buckling_load/1e3)*1e3  # change magnitude of force card to buckling load found by SOL 106 nonlinear buckling method rounded up to next thousand"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let's define the input file name and run the analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nastran job euler_column_tangent_stiffness_matrix.bdf completed\n",
      "Wall time: 11.0 s\n"
     ]
    }
   ],
   "source": [
    "tangent_stiffness_matrix_input_name = base_input_name + '_tangent_stiffness_matrix'  # name of input file\n",
    "pynastran_utils.run_analysis(directory_path=analysis_directory_path, bdf=nonlinear_buckling_bdf,\n",
    "                             filename=tangent_stiffness_matrix_input_name, run_flag=False)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now we want to plot the lowest eigenvalue $\\lambda$ of the tangent stiffness matrix for every load increment versus the load history of the nonlinear analysis. We start by finding the load history of the nonlinear analysis using the function `read_load_displacement_history_from_op2` from the `pynastran_utils` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "op2_filepath = os.path.join(analysis_directory_path, tangent_stiffness_matrix_input_name + '.op2')\n",
    "tangent_stiffness_matrix_op2 = read_op2(op2_filename=op2_filepath, debug=None) # read results from op2 file and do not print any debug or info message\n",
    "_, load_history, _ = pynastran_utils.read_load_displacement_history_from_op2(op2=tangent_stiffness_matrix_op2)\n",
    "applied_load_history = -[*load_history.values()][0][:,0]  # retrieve applied load history"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Successively, we find the lowest eigenvalues in the f06 file using the function `read_kllrh_lowest_eigenvalues_from_f06` from the same module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "f06_filepath = os.path.join(analysis_directory_path, tangent_stiffness_matrix_input_name + '.f06')  # path to .f06 file\n",
    "lowest_eigenvalues = pynastran_utils.read_kllrh_lowest_eigenvalues_from_f06(f06_filepath)  # read the lowest eigenvalue of KLLRH matrices from f06 file"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Finally, we plot the results nondimensionalizing the applied load by the critical buckling load found with SOL 106's nonlinear buckling method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(applied_load_history/sol_106_buckling_load, lowest_eigenvalues[0, :], 'o')\n",
    "plt.xlabel(\"$P/P_c$\")\n",
    "plt.ylabel(\"$\\lambda$, N/mm\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We can see that the lowest eigenvalue of the tangent stiffness matrix decreases linearly with the applied load and that after the last converged iteration is slightly negative. Let's print its value to the screen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lowest eigenvalue at the last converged iteration: -0.02 N/mm\n"
     ]
    }
   ],
   "source": [
    "print(f\"Lowest eigenvalue at the last converged iteration: {lowest_eigenvalues[0, -1]:.2f} N/mm\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The eigenvalue is indeed negative and this means that the structural equilibrium at the last converged iteration is unstable. Considering the observed linear trend, we can interpolate the curve to find the load where the lowest eigenvalue is zero, which corresponds to the critical buckling load."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Load where tangent stiffness matrix becomes singular: 90578 N\n"
     ]
    }
   ],
   "source": [
    "# Fit line to eigenvalue curve\n",
    "fit = np.polyfit(lowest_eigenvalues[0, :], applied_load_history, 1)\n",
    "line = np.poly1d(fit)\n",
    "\n",
    "# Find load where eigenvalue is zero and print its value\n",
    "tangent_stiffness_matrix_buckling_load = line(0.)\n",
    "print(f\"Load where tangent stiffness matrix becomes singular: {tangent_stiffness_matrix_buckling_load:.0f} N\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We observe that there is no evident difference w.r.t. the other numerical results."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Conclusion <a name=\"conclusion\"></a>\n",
    "\n",
    "***\n",
    "\n",
    "In this notebook we analyzed the buckling load of Euler's column with different methods. First we used Euler's analytical formula, and for the considered geometry and material we obtained a buckling load of 90962 N. Successively we used MSC Nastran to compute the buckling load of the column with different types of numerical analysis.\n",
    "\n",
    "We discretized the column with beam elements and we carried out a linear buckling analysis with SOL 105. This resulted in a buckling load of 90578 N, that is 0.42% lower than the analytical result. Then we switched to Nastran's nonlinear solution sequence, SOL 106. We first used the nonlinear buckling method available with the solution sequence, resulting in the same buckling load obtained with SOL 105. Then we used SOL 106 to find the load where the lowest eigenvalue of the tangent stiffness matrix becomes null, that is to say where the matrix becomes singular. The same value of buckling load was obtained also in this case. As a consequence, the different buckling calculations carried out with Nastran appear to be consistent. This is in line with our expectations because no nonlinear behavior is supposed to be observed up to the buckling point considering the symmetry of the problem.\n",
    "\n",
    "We will continue our investigation on the Euler's column studying its supercritical pitchfork bifurcation in our [next notebook](02_Supercritical_Pitchfork_Bifurcation_of_Euler_Column.ipynb)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.17"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}