Add advanced plot and rectangular torsion example

docs/examples/advanced/advanced_plot.ipynb

@@ -8,13 +8,130 @@
     "# Advanced Plotting"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "e5f5821a-5b0e-4195-88b3-f8aad0e6ae2c",
+   "metadata": {},
+   "source": [
+    "All plots in `sectionproperties` allow keyword arguments to be passed to [plotting_context()](../..//gen/sectionproperties.post.post.plotting_context.rst#sectionproperties.post.post.plotting_context). This example shows one application of using the `plotting_context()` to generate a custom plot in a 2 x 2 arrangement."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c4ed61cc-ab12-4e60-aa51-b5e0f52160c8",
+   "metadata": {},
+   "source": [
+    "## Create Geometry and Perform Analysis"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fbab4168-0b45-4d4e-befe-206b66e21774",
+   "metadata": {},
+   "source": [
+    "We start by creating the geometry for a 100 x 6 SHS."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "66522637-ff51-4945-ab72-a1a354ea9e67",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from sectionproperties.pre.library import rectangular_hollow_section\n",
+    "\n",
+    "geom = rectangular_hollow_section(d=100, b=100, t=6, r_out=15, n_r=8)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ebc2c4aa-a61f-4b32-abd2-c6421b413e93",
+   "metadata": {},
+   "source": [
+    "Next we create a mesh and a `Section` object."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6875e793-9338-4f0f-af26-94deee9e03bd",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from sectionproperties.analysis.section import Section\n",
+    "\n",
+    "geom.create_mesh(mesh_sizes=[5])\n",
+    "sec = Section(geometry=geom)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e9bd87c4-64f7-4fe3-8183-782559a66953",
+   "metadata": {},
+   "source": [
+    "We can now perform a stress analysis by applying a 10 kN.m torsion (after first running the geometric and warping analysis)."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ca25a4a4",
+   "id": "e0be003c-b341-42aa-babc-9659bcf84e95",
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "sec.calculate_geometric_properties()\n",
+    "sec.calculate_warping_properties()\n",
+    "stress = sec.calculate_stress(mzz=10e6)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "af740576-9c70-4cd0-9d7d-df2fb2abd412",
+   "metadata": {},
+   "source": [
+    "## Generate Plot\n",
+    "\n",
+    "We are going to generate a plot of the geometry, mesh, centroids and stress. In the first plot, we will setup the parameters of the entire figure. We make sure we set `render=False` to prevent the plot from displaying before we are finished. In the subsequent plots we pass the axis we would like to display the plot on."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ff4d819e-45c7-4a73-92c5-9f40f8656327",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "# plot the geometry\n",
+    "ax = geom.plot_geometry(\n",
+    "    labels=[],\n",
+    "    nrows=2,\n",
+    "    ncols=2,\n",
+    "    figsize=(12, 7),\n",
+    "    render=False,\n",
+    ")\n",
+    "\n",
+    "# get the figure object from the first plot\n",
+    "fig = ax.get_figure()\n",
+    "\n",
+    "# plot the mesh\n",
+    "sec.plot_mesh(materials=False, ax=fig.axes[1])\n",
+    "\n",
+    "# plot the centroids\n",
+    "sec.plot_centroids(ax=fig.axes[2])\n",
+    "\n",
+    "# plot the torsion stress\n",
+    "stress.plot_stress(\n",
+    "    stress=\"mzz_zxy\",\n",
+    "    normalize=False,\n",
+    "    ax=fig.axes[3],\n",
+    ")\n",
+    "\n",
+    "# finally display the plot\n",
+    "plt.show()"
+   ]
   }
  ],
  "metadata": {

docs/examples/advanced/rectangle_torsion.ipynb

@@ -8,13 +8,102 @@
     "# Torsion Constant of a Rectangle"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "4dc5e9c9-cfde-413c-8d7d-ff4cab4e8fe3",
+   "metadata": {},
+   "source": [
+    "This example shows how `sectionproperties` can be used as part of a script to conduct multiple analyses. In this example, we examine how the torsion constant varies with the aspect ratio of a rectangle section."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a918ccf-a17d-4813-8557-990ca96d904a",
+   "metadata": {},
+   "source": [
+    "## Setup Analysis Parameters"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a7ce67c7-f227-4756-83e8-1ffec6590ee0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "# list of aspect ratios to analyse (10^0 = 1 to 10^1.301 = 20)\n",
+    "# logspace used to concentrate data near aspect ratio = 1\n",
+    "aspect_ratios = np.logspace(0, 1.301, 50)\n",
+    "torsion_constants = []  # list of torsion constant results\n",
+    "area = 1  # cross-section area\n",
+    "n = 100  # approximate number of finite elements in each analysis"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e03ba7bb-2971-4f92-a0f3-317a8bd52adf",
+   "metadata": {},
+   "source": [
+    "## Analysis Loop"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e485da27",
+   "id": "7984f360-8928-4b1c-a528-819ceca24b17",
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "from sectionproperties.pre.library import rectangular_section\n",
+    "from sectionproperties.analysis.section import Section\n",
+    "\n",
+    "for ar in aspect_ratios:\n",
+    "    # calculate rectangle dimensions\n",
+    "    d = np.sqrt(ar)\n",
+    "    b = 1 / d\n",
+    "    geom = rectangular_section(d=d, b=b)\n",
+    "\n",
+    "    # create mesh and Section object\n",
+    "    ms = d * b / n\n",
+    "    geom.create_mesh(mesh_sizes=[ms])\n",
+    "    sec = Section(geometry=geom)\n",
+    "\n",
+    "    # perform analysis\n",
+    "    sec.calculate_frame_properties()\n",
+    "\n",
+    "    # save the torsion constant\n",
+    "    torsion_constants.append(sec.get_j())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "222959a8-bab9-44a5-9f4f-67e62ab238e4",
+   "metadata": {},
+   "source": [
+    "## Plot Results"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "79bcd59d-254d-4fd2-b6c1-99bdb17f3ad2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "_, ax = plt.subplots()\n",
+    "ax.plot(aspect_ratios, torsion_constants, \"k-\")\n",
+    "ax.set_xlim(0, 21)\n",
+    "ax.set_ylim(0, 0.15)\n",
+    "ax.set_xlabel(\"Aspect Ratio [d/b]\")\n",
+    "ax.set_ylabel(\"Torsion Constant [J]\")\n",
+    "ax.set_title(\"Rectangular Section Torsion Constant\")\n",
+    "ax.grid()\n",
+    "plt.show()"
+   ]
   }
  ],
  "metadata": {