61 lines
1.6 KiB
Plaintext
61 lines
1.6 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "c94a76d4-15cb-4628-980e-644c24119b55",
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"metadata": {
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"tags": []
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},
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"source": [
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"# Geometry parameters\n",
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"\n",
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"## Simple structure\n",
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"\n",
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"$$ \\theta \\in \\left[ 0.01, 0.28 \\right] $$\n",
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"$$ r_0 = 1 $$\n",
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"$$ L = 2 r_0 $$\n",
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"$$ r = \\frac{r_0}{1 - \\theta} $$\n",
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"$$ r_{fillet} = r_0 \\left (\\sqrt{2} - \\frac{1}{1 - \\theta} \\right) $$\n",
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"\n",
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"## Face centered structure\n",
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"\n",
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"$$ \\theta \\in \\left[ 0.01, 0.13 \\right] $$\n",
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"$$ r_0 = 1 $$\n",
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"$$ L = \\frac{4 r_0}{\\sqrt{2}} $$\n",
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"$$ r = \\frac{r_0}{1 - \\theta} $$\n",
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"$$ r_{fillet} = r_0 \\left( \\frac{2 \\sqrt{3}}{3} - \\frac{1}{1 - \\theta} \\right) $$\n",
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"\n",
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"## Body centered structure\n",
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"\n",
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"$$ \\theta \\in \\left[ 0.01, 0.18 \\right] $$\n",
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"$$ r_0 = 1 $$\n",
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"$$ L = \\frac{4 r_0}{\\sqrt{3}} $$\n",
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"$$ r = \\frac{r_0}{1 - \\theta} $$\n",
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"$$ r_{fillet} = r_0 \\left( \\frac{\\sqrt{2}}{\\sqrt{1 - \\cos \\left(\\pi - 2 \\arccos \\left(\\sqrt{\\frac{2}{3}} \\right) \\right)}} - \n",
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" \\frac{1}{1 - \\theta} \\right) $$\n"
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]
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}
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"version": "3.10.0"
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