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32
playground/geometry.ipynb
View File

@ -8,30 +8,14 @@
},
"source": [
"# Geometry parameters\n",
"## Face centered structure\n",
"\n",
"\n",
"$ \\theta_{min} = 0.01 $\n",
"\n",
"$ \\theta_{max} = 0.13 $\n",
"\n",
"$ L = 1 $\n",
"\n",
"$ r_0 = L \\sqrt{2} / 4 $\n",
"\n",
"Spheres radius:\n",
"\n",
"$ r = r_0 / (1 - \\theta) $\n",
"\n",
"Fillets radius:\n",
"\n",
"$ C_1 = 0.3, C_2 = 0.2 $\n",
"\n",
"$ C_f = C_1 + (C_2 - C_1) (\\theta_{max} - \\theta_{min}) / (\\theta - \\theta_{min}) $\n",
"\n",
"$ \\delta = 0.012 $\n",
"\n",
"$ r_{fillets} = \\delta - C_f (r - r_0) $"
"| Parameter | simple | faceCentered | bodyCentered |\n",
"| --------- | ------ | ------------ | ------------ |\n",
"| $\\theta$ | [0.1, 0.28] | [0.1, 0.13] | [0.1, 0.18] |\n",
"| $r_0$ | 1 | 1 | 1 |\n",
"| $L$ | $2 r_0$ | $4 r_0 / \\sqrt{2}$ | $4 r_0 / \\sqrt{3}$ |\n",
"| $r$ | $r_0 / (1 - \\theta)$ | $r_0 / (1 - \\theta)$ | $r_0 / (1 - \\theta)$ |\n",
"| $r_{fillets}$ | $r_0 (\\sqrt{2} - 1 / (1 - \\theta))$ | $r_0 (2 \\sqrt{3} / 3 - 1 / (1 - \\theta))$ | - |"
]
},
{
@ -156,7 +140,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.6"
"version": "3.10.0"
}
},
"nbformat": 4,

23
playground/untitled.tex Normal file
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@ -0,0 +1,23 @@
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}
\draw[semithick] (0, 0) circle (1);
\draw[semithick] (2, 0) circle (1);
\draw[semithick] (1, 1.73205) circle (1);
\draw[dashed,color=gray] (0,0) arc (-90:90:0.5 and 1.5);% right half of the left ellipse
\draw[semithick] (0,0) -- (4,1);% bottom line
\draw[semithick] (0,3) -- (4,2);% top line
\draw[semithick] (0,0) arc (270:90:0.5 and 1.5);% left half of the left ellipse
\draw[semithick] (4,1.5) ellipse (0.166 and 0.5);% right ellipse
\draw (-1,1.5) node {$\varnothing d_1$};
\draw (3.3,1.5) node {$\varnothing d_2$};
\draw[|-,semithick] (0,-0.5) -- (4,-0.5);
\draw[|->,semithick] (4,-0.5) -- (4.5,-0.5);
\draw (0,-1) node {$x=0$};
\draw (4,-1) node {$x=l$};
\end{tikzpicture}
\end{document}