update docs

Author: claudioperez

docs/api/library/Circle.rst

@@ -6,3 +6,4 @@ Circle
 .. autoclass:: xsection.library.Circle
    :members:
    :undoc-members:
+

docs/examples/introduction.ipynb

@@ -10,7 +10,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "311f3710",
    "metadata": {},
    "outputs": [],
@@ -30,7 +30,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "id": "0e6b98be",
    "metadata": {},
    "outputs": [
@@ -1162,7 +1162,7 @@
        "</script>\n"
       ],
       "text/plain": [
-       "<veux.frame.FrameArtist at 0x127483da0>"
+       "<veux.frame.FrameArtist at 0x11cd9e150>"
       ]
      },
      "execution_count": 2,
@@ -1190,15 +1190,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "id": "888cda4d",
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "17280.000000000007\n"
+      "0.3191620166230887\n"
      ]
     }
    ],
@@ -1226,20 +1226,20 @@
      "text": [
       "\n",
       "  Block                              x            y           z           yz\n",
-      "  [nn]    Area                    360.0   , \n",
+      "  [nn]    Area                   0.8699   , \n",
       "  [nm]    Centroid                  0.0          0.0,        0.0\n",
-      "  [nw|v]                            0.0 | -1.959e-15,  1.501e-14\n",
+      "  [nw|v]                            0.0 |  1.506e-16, -3.913e-15\n",
       "\n",
-      "  [mm]    Flexural moments    2.403e+04    1.728e+04,   6.75e+03,  4.299e-13\n",
-      "  [mv|w]                     -7.344e+03 |      0.176,      1.329\n",
+      "  [mm]    Flexural moments       0.4333       0.3192,     0.1141, -3.773e-17\n",
+      "  [mv|w]                        -0.4136 | -4.749e-15, -1.128e-17\n",
       "\n",
       "\n",
-      "  [ww]    Warping constant     6.61e+04  (  6.61e+04 at S.C.)\n",
-      "  [vv]    Bishear             7.344e+03\n",
+      "  [ww]    Warping constant      0.04725  (   0.04725 at S.C.)\n",
+      "  [vv]    Bishear                0.4136\n",
       "\n",
       "\n",
-      "          Shear center              0.0    1.019e-05,  0.0001968\n",
-      "          Torsion constant    1.669e+04\n",
+      "          Shear center              0.0          0.0,        0.0\n",
+      "          Torsion constant      0.01971\n",
       "        \n"
      ]
     }
@@ -1266,31 +1266,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 5,
    "id": "a6cd50d9",
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "\n",
-      "  Block                              x            y           z           yz\n",
-      "  [nn]    Area                    360.0   , \n",
-      "  [nm]    Centroid                  0.0          0.0,        0.0\n",
-      "  [nw|v]                            0.0 | -1.959e-15,  1.501e-14\n",
-      "\n",
-      "  [mm]    Flexural moments    2.403e+04    1.728e+04,   6.75e+03,  4.299e-13\n",
-      "  [mv|w]                     -7.344e+03 |      0.176,      1.329\n",
-      "\n",
-      "\n",
-      "  [ww]    Warping constant     6.61e+04  (  6.61e+04 at S.C.)\n",
-      "  [vv]    Bishear             7.344e+03\n",
-      "\n",
-      "\n",
-      "          Shear center              0.0    1.019e-05,  0.0001968\n",
-      "          Torsion constant    1.669e+04\n",
-      "        \n"
+      "  Iy : 1.728e+04\n",
+      "  Iz : 6750\n",
+      "   A : 360\n",
+      "  Ay : 302.1\n",
+      "  Az : 300.9\n",
+      "   J : 1.669e+04\n",
+      " Iyz : -4.157e-13\n"
      ]
     },
     {
@@ -2421,10 +2411,10 @@
        "</script>\n"
       ],
       "text/plain": [
-       "<veux.frame.FrameArtist at 0x1275a7a10>"
+       "<veux.frame.FrameArtist at 0x11cfe6f60>"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2451,7 +2441,7 @@
     "        ])\n",
     "\n",
     "\n",
-    "print(shape.summary())\n",
+    "print(shape.elastic.summary())\n",
     "\n",
     "artist = veux.create_artist(shape.model) #veux.model.FiberModel(shape.create_fibers()))\n",
     "# artist.draw_samples()\n",

docs/index.rst

@@ -8,6 +8,7 @@ xsection
    :caption: Contents:
 
    api/index
-   theory/index
    examples/index
 
+..
+   theory/index

docs/theory/elasticity.md

@@ -6,3 +6,11 @@ $$
 \boldsymbol{S}=\lambda \mathbf{1} \operatorname{tr} \boldsymbol{E}+2 \mu \boldsymbol{E}
 $$
 
+## Flexural Constants
+
+The elastic flexural constants `cmm` represent the sections moment
+resistance to curvature, defined tensorially by the expression:
+
+$$
+\texttt{cmm} = \int -\boldsymbol{r}^{\times}\boldsymbol{r}^{\times}\,\mathrm{d}A
+$$