minor update to latex formulae

This commit is contained in:
Jukka Aho
2015-11-24 11:45:51 +02:00
parent fe55cb0faa
commit 8a39ae4f94
+2 -3
View File
@@ -17,8 +17,7 @@
"\n",
"Each element is modelled as own \"body\" and they are connected using tie contacts. Segments 5-6 and 9-10 and 6-7 are slave surfaces, so node 6 or 9 is on at least two tie contacts as slave node. Moreover this model has dirichlet boundary $y=0$ at bottom of body 1 and $x=0$ on left. To get the accurate solution one needs to minimize \n",
"\\begin{equation}\n",
"\\frac{15}{2}u_{1}^{4} + 60 u_{1}^{3} + \\frac{15}{4}u_{1}^{2} u_{2}^{2} + 15 u_{1}^{2} u_{2} + 120 u_{1}^{2} + 15 u_{1} u_{2}^{2} + 60 u_{1} u_{2} + \\frac{15}{2}u_{2}^{4} + 60 u_{2}^{3} + 120 u_{2}^{2} + 50 u_{2}\n",
",\n",
"\\frac{15}{2}u_1^4 + 60 u_1^3 + \\frac{15}{4}u_1^2 u_2^2 + 15 u_1^2 u_2 + 120 u_1^2 + 15 u_1 u_2^2 + 60 u_1 u_2 + \\frac{15}{2}u_2^4 + 60 u_2^3 + 120 u_2^2 + 50 u_2,\n",
"\\end{equation}\n",
"which gives approximate $u_1 = 0.0634862$ and $u_2 = -0.277183$ for the displacement of upper right corner.\n",
"[Wolfram](http://www.wolframalpha.com/input/?i=local+minimum+15*x^4%2F2+%2B+60*x^3+%2B+15*x^2*y^2%2F4+%2B+15*x^2*y+%2B+120*x^2+%2B+15*x*y^2+%2B+60*x*y+%2B+15*y^4%2F2+%2B+60*y^3+%2B+120*y^2+%2B+50*y)."
@@ -385,7 +384,7 @@
],
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