From: Wolfgang Bangerth Date: Fri, 12 Jun 2015 00:25:56 +0000 (-0500) Subject: Fix some formulas. X-Git-Tag: v8.3.0-rc1~116^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=283193618fd9c767831635d99605e6cf0e791978;p=dealii.git Fix some formulas. We use things like $\sigma \cdot n$ in a number of places, but common notation would denote the product between a tensor and a vector without the cdot. This fixes #928. --- diff --git a/examples/step-42/doc/intro.dox b/examples/step-42/doc/intro.dox index 4137876e70..1befb2a5f9 100644 --- a/examples/step-42/doc/intro.dox +++ b/examples/step-42/doc/intro.dox @@ -58,10 +58,10 @@ The classical formulation of the problem possesses the following form: \varepsilon^p:(\tau - \sigma) &\geq 0\quad\forall\tau\text{ with }\mathcal{F}(\tau)\leq 0 & &\quad\text{in } \Omega,\\ \mathbf u &= 0 & &\quad\text{on }\Gamma_D,\\ - \sigma \cdot \mathbf n - [\mathbf n \cdot(\sigma \cdot \mathbf n)]\mathbf n &= 0, - \quad \mathbf n \cdot (\sigma \cdot + \sigma \mathbf n - [\mathbf n \cdot(\sigma \mathbf n)]\mathbf n &= 0, + \quad \mathbf n \cdot (\sigma \mathbf n) \leq 0 & &\quad\text{on }\Gamma_C,\\ - (\mathbf n \cdot (\sigma \cdot + (\mathbf n \cdot (\sigma \mathbf n))(\mathbf n \cdot \mathbf u - g) &= 0,\quad \mathbf n \cdot \mathbf u - g \leq 0 & &\quad\text{on } \Gamma_C. @f} @@ -92,10 +92,10 @@ and $|\cdot|$ denotes the Frobenius norm. Further equations describe a fixed, zero displacement on $\Gamma_D$ and that on the surface $\Gamma_C=\partial\Omega\backslash\Gamma_D$ where contact may appear, the normal -force $\sigma_n=\mathbf n \cdot (\sigma(\mathbf u) \cdot +force $\sigma_n=\mathbf n \cdot (\sigma(\mathbf u) \mathbf n)$ exerted by the obstacle is inward (no "pull" by the obstacle on our -body) and with zero tangential component $\mathbf \sigma_t= \sigma \cdot \mathbf n - \mathbf \sigma_n \mathbf n -= \sigma \cdot \mathbf n - [\mathbf n \cdot(\sigma \cdot \mathbf n)]\mathbf n$. +body) and with zero tangential component $\mathbf \sigma_t= \sigma \mathbf n - \mathbf \sigma_n \mathbf n += \sigma \mathbf n - [\mathbf n \cdot(\sigma \mathbf n)]\mathbf n$. The last condition is again a complementarity condition that implies that on $\Gamma_C$, the normal force can only be nonzero if the body is in contact with the obstacle; the