From: pelteret Date: Thu, 29 Dec 2011 22:13:12 +0000 (+0000) Subject: Step-44: Fixed a couple of documentation compilation errors. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=4c34b9ccde159da42198d171f943d0438264025d;p=dealii-svn.git Step-44: Fixed a couple of documentation compilation errors. git-svn-id: https://svn.dealii.org/trunk@24866 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-44/step-44.cc b/deal.II/examples/step-44/step-44.cc index 8efafa55dd..591243c571 100644 --- a/deal.II/examples/step-44/step-44.cc +++ b/deal.II/examples/step-44/step-44.cc @@ -11,6 +11,7 @@ /* further information on this license. */ // @sect3{Include files} + // We start by including all the necessary // deal.II header files and some C++ related // ones. They have been discussed in detail @@ -157,7 +158,7 @@ void Geometry::parse_parameters (ParameterHandler &prm) prm.leave_subsection(); } -// @sect{Materials} +// @sect4{Materials} // Store the shear modulus and Lame constant // for the Neo-Hookean material struct Materials @@ -249,9 +250,9 @@ void LinearSolver::parse_parameters (ParameterHandler &prm) prm.leave_subsection(); } -// Nonlinear solver +// @sect4{Nonlinear solver} // Define the tolerances and maximum number of iterations for the -// Newton-Raphson nono-linear solver. +// Newton-Raphson nonlinear solver. struct NonlinearSolver { unsigned int max_iterations_NR; @@ -333,7 +334,7 @@ void Time::parse_parameters (ParameterHandler &prm) prm.leave_subsection(); } -// sect4{All parameters} +// @sect4{All parameters} // Finally we consolidate all of the above structures into // a single container that holds all of our run-time selections. struct AllParameters @@ -388,9 +389,9 @@ void AllParameters::parse_parameters (ParameterHandler &prm) // in a seperate namespace for convenience. namespace AdditionalTools { -// Define an operation that takes two tensors \f$ \mathbf{A} \f$ and -// \f$ \mathbf{B} \f$ such that their outer-product -// \f$ \mathbf{A} \bar{\otimes} \mathbf{B} \Rightarrow C_{ijkl} = A_{ik} B_{jl} \f$ +// Define an operation that takes two tensors $ \mathbf{A} $ and +// $ \mathbf{B} $ such that their outer-product +// $ \mathbf{A} \bar{\otimes} \mathbf{B} \Rightarrow C_{ijkl} = A_{ik} B_{jl} $ template SymmetricTensor<4,dim> outer_product_T23 (const SymmetricTensor<2,dim> & A, const SymmetricTensor<2,dim> & B) @@ -413,7 +414,7 @@ SymmetricTensor<4,dim> outer_product_T23 (const SymmetricTensor<2,dim> & A, // The \a extract_submatrix function takes specific entries from a \a matrix, // and copies them to a \a sub_matrix. The copied entries are defined by the // first two parameters which hold the row and column entries to be extracted. -// The \a matrix is automatically resized to size \f$ r \times c \f$. +// The \a matrix is automatically resized to size $ r \times c $. template void extract_submatrix(const std::vector< unsigned int > &row_index_set, const std::vector< unsigned int > &column_index_set, @@ -530,20 +531,19 @@ private: // with constant properties throughout. This class defines // the behaviour of this material. Neo-Hookean materials // can be described by a strain-energy function (SEF) -// \f$ \phi = \phi_{B} + \phi_{V} \f$ +// $ \phi = \phi_{B} + \phi_{V} $ // where the bulk deformation is given by -// \f$ \phi_{B} = C_{1} \left( I_{1} - 3 \right) \f$ -// where \f$ C_{1} - \frac{\mu}{2} \f$ and $I_{1}$ is the first +// $ \phi_{B} = C_{1} \left( I_{1} - 3 \right) $ +// where $ C_{1} - \frac{\mu}{2} $ and $I_{1}$ is the first // invariant of the left- or right- Cauchy deformation tensors. // In this example the SEF that governs the volumetric // response is defined as -// \f$ \phi_{V} = \kappa \left( \frac{1}{2} \left( \theta^{2} - 1 \right) - ln \left( \theta \right) \right) \f$ +// $ \phi_{V} = \kappa \left( \frac{1}{2} \left( \theta^{2} - 1 \right) - ln \left( \theta \right) \right) $ // where $\kappa$ is the bulk modulus. template class Material_NH { public: - /// \brief Class constructor Material_NH (const double & lambda, const double & mu) : @@ -555,7 +555,7 @@ public: // The Kirchhoff stress tensor is required in the formulation // used in this work. This is obtained from the SEF by - // \f$ \mathbf{T} = \mathbf{F} \frac{\partial \hat{\phi}}{\partial \mathbf{C}} \mathbf{F}^{T} = \frac{\partial \phi}{\partial \mathbf{B}} \mathbf{B} \f$ + // $ \mathbf{T} = \mathbf{F} \frac{\partial \hat{\phi}}{\partial \mathbf{C}} \mathbf{F}^{T} = \frac{\partial \phi}{\partial \mathbf{B}} \mathbf{B} $ SymmetricTensor<2, dim> get_T (const double & J, const SymmetricTensor <2, dim> & B) { @@ -564,9 +564,9 @@ public: } // The tangent matrix for this material is also calculated from the SEF by - // \f$ JC_{ijkl} = F_{iA} F_{jB} H_{ABCD} F_{kC} F_{lD}\f$ + // $ JC_{ijkl} = F_{iA} F_{jB} H_{ABCD} F_{kC} F_{lD}$ // with - // \f$ \mathbf{H} = \frac{\partial^{2} \hat{\phi}}{\partial \mathbf{C} \partial \mathbf{C}} \f$ + // $ \mathbf{H} = \frac{\partial^{2} \hat{\phi}}{\partial \mathbf{C} \partial \mathbf{C}} $ SymmetricTensor<4, dim> get_JC (const double & J, const SymmetricTensor <2, dim> & B) { @@ -607,32 +607,32 @@ template SymmetricTensor<4, dim> const Material_NH::II = Symmetr // We introduce the multiplicative decomposition of the // deformation gradient into a volume-preserving and volume // changing component: -// \f$ \mathbf{F} = \hat{\mathbf{F}} \bar{\mathbf{F}} \f$ +// $ \mathbf{F} = \hat{\mathbf{F}} \bar{\mathbf{F}} $ // where the volumetric part is -// \f$ \hat{\mathbf{F}} = J^{\frac{1}{3}} \mathbf{I} \f$ +// $ \hat{\mathbf{F}} = J^{\frac{1}{3}} \mathbf{I} $ // and the isochoric part is given by -// \f$ \bar{\mathbf{F}} = J^{-\frac{1}{3}} \mathbf{F} \f$ +// $ \bar{\mathbf{F}} = J^{-\frac{1}{3}} \mathbf{F} $ // . From this, the deviatoric left Cauchy-Green deformation // tensor can be defined as -// \f$ \bar{\mathbf{B}} = \bar{\mathbf{F}} \bar{\mathbf{F}}^{T} = J^{-\frac{2}{3}} \mathbf{F} \mathbf{F}^{T} \f$ +// $ \bar{\mathbf{B}} = \bar{\mathbf{F}} \bar{\mathbf{F}}^{T} = J^{-\frac{2}{3}} \mathbf{F} \mathbf{F}^{T} $ // // Here we also introduce an additive volumetric-deviatoric split // in the material reponse. We can express the governing SEF as -// \f$ \phi = \phi_{V} + \phi_{I} \f$ +// $ \phi = \phi_{V} + \phi_{I} $ // with the result that the Kirchhoff stress is additively // decomposed into -// \f$ \mathbf{\tau} = \mathbf{\tau}_{V} + \mathbf{\tau}_{I} \f$ +// $ \mathbf{\tau} = \mathbf{\tau}_{V} + \mathbf{\tau}_{I} $ // as is the tangent matrix -// \f$ J\mathbf{C} = J\mathbf{C}_{V} + J\mathbf{C}_{I} \f$. +// $ J\mathbf{C} = J\mathbf{C}_{V} + J\mathbf{C}_{I} $. // // These quantities are calculated as -// \f$ \mathbf{\tau}_{I} = pJ\mathbf{I} \f$ -// \f$ \mathbf{\tau}_{V} = \mathcal{P}:\bar{\mathbf{\tau}} \f$ -// with \f$ \bar{\mathbf{\tau}} = \mathbf{\tau} \vert_{\mathbf{B} = \bar{\mathbf{B}}} \f$ -// and the deviatoric tensor \f$ \mathcal{P} = \mathcal{I} - \mathbf{I} \otimes \mathbf{I} \f$ -// \f$ J\mathbf{C}_{I} = pJ(\mathbf{I} \otimes \mathbf{I} - 2 \mathcal{I}) \f$ -// \f$ J\mathbf{C}_{V} = \frac{2}{3} tr\left(\bar{\mathbf{\tau}}\right) \mathcal{P} - \frac{2}{3} \left(\mathbf{\tau}_{I}\otimes\mathbf{I} + \mathbf{I}\otimes\mathbf{\tau}_{I} \right) + \mathcal{P}:\bar{\mathcal{C}}:\mathcal{P} \f$ -// with \f$ \bar{\mathcal{C}} = \mathcal{C} \vert_{\mathbf{B} = \bar{\mathbf{B}}} \f$ +// $ \mathbf{\tau}_{I} = pJ\mathbf{I} $ +// $ \mathbf{\tau}_{V} = \mathcal{P}:\bar{\mathbf{\tau}} $ +// with $ \bar{\mathbf{\tau}} = \mathbf{\tau} \vert_{\mathbf{B} = \bar{\mathbf{B}}} $ +// and the deviatoric tensor $ \mathcal{P} = \mathcal{I} - \frac{1}{3} \mathbf{I} \otimes \mathbf{I} $ +// $ J\mathbf{C}_{I} = pJ(\mathbf{I} \otimes \mathbf{I} - 2 \mathcal{I}) $ +// $ J\mathbf{C}_{V} = \frac{2}{3} tr\left(\bar{\mathbf{\tau}}\right) \mathcal{P} - \frac{2}{3} \left(\mathbf{\tau}_{I}\otimes\mathbf{I} + \mathbf{I}\otimes\mathbf{\tau}_{I} \right) + \mathcal{P}:\bar{\mathcal{C}}:\mathcal{P} $ +// with $ \bar{\mathcal{C}} = \mathcal{C} \vert_{\mathbf{B} = \bar{\mathbf{B}}} $ template class PointHistory { @@ -677,9 +677,7 @@ public: pressure_n = pressure; dilatation_n = dilatation; - // Now that all the necessary variables are set, we can update the stress tensors - // Stress update can only update the stresses once the - // dilatation has been set as p = p(d). + // Now that all the necessary variables are set, we can update the stress tensors. // Note that T_iso depends on T_bar so it must be calculated afterwards. T_bar = material->get_T (get_J(), get_B_bar()); T_iso = dev_P*get_T_bar(); @@ -816,7 +814,7 @@ private: ScratchData_SC & scratch, PerTaskData_SC & data); void copy_local_to_global_SC (const PerTaskData_SC & data); - /// \brief Apply Dirichlet boundary values + // Apply Dirichlet boundary values void make_constraints (const int & it_nr, ConstraintMatrix & constraints);