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docs/benchmarks/linear elasticity/plate-with-hole.md

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@@ -14,10 +14,11 @@ $$
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\sigma_{r\theta} &= -\frac{p}{2}\left(1-\frac{a^2}{r^2}\right)\left(1+\frac{3a^2}{r^2}\right)\sin(2\theta)
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\end{aligned}
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$$
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In order to transform this into a practical benchmark, we consider a rectangular subdomain
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of the infinite plate around the hole. The boundary conditions of the subdomain are determined
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from the analytical solution. The example is further reduced by only simulating one quarter
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of the rectangular domain and assuming symmetry conditions at the edges. Let $\Omega =[0,l]^2 \setminus\left\{(x,y) \mid \sqrt{x^2+y^2}<a \right\}$ be the domain of the benchmark example, then the PDE is given by
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of the rectangular domain and assuming symmetry conditions at the edges. Let $\Omega =[0,l]^2 \setminus\{(x,y) | \sqrt{x^2+y^2}<a \}$ be the domain of the benchmark example, then the PDE is given by
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$$
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\begin{aligned}
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\boldsymbol{\sigma}(\boldsymbol{\varepsilon}) &= \frac{E}{1-\nu^2}\left((1-\nu)\boldsymbol{\varepsilon} + \nu \mathrm{tr}\boldsymbol{\varepsilon}\boldsymbol I_2\right) && \text{Plane stress law}\\
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\boldsymbol u_y &=0 & y=0& \text{Dirichlet BC}\\
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\boldsymbol u_x &=0 & x=0& \text{Dirichlet BC}\\
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boldsymbol{n}
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\end{aligned}
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$$
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$$

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