Elasticity::FirstOrderSystem< Dim > Struct Template Reference

The linear elasticity equation formulated as a set of coupled first-order PDEs. More...

#include <FirstOrderSystem.hpp>

Public Types
using	primal_fields = tmpl::list<Tags::Displacement<Dim>>
using	primal_fluxes = tmpl::list<Tags::MinusStress<Dim>>
using	background_fields = tmpl::list<>
using	inv_metric_tag = void
using	fluxes_computer = Fluxes<Dim>
using	sources_computer = void
using	boundary_conditions_base
using	modify_boundary_data = void

Static Public Attributes
static constexpr size_t	volume_dim = Dim

Detailed Description

template<size_t Dim>
struct Elasticity::FirstOrderSystem< Dim >

The linear elasticity equation formulated as a set of coupled first-order PDEs.

This system formulates the elasticity equation (see Elasticity):

\begin{align*}\nabla_i T^{ij} = f_\mathrm{ext}^j \\ T^{ij} = -Y^{ijkl} \nabla_{(k} \xi_{l)} \end{align*}

The system can be formulated in terms of these fluxes and sources (see elliptic::protocols::FirstOrderSystem):

\begin{align*}F^{ij} &= -T^{ij} = Y^{ijkl} \nabla_{(k} \xi_{l)} \\ S^j &= 0 \\ f^j &= f_\mathrm{ext}^j \text{.} \end{align*}

Member Typedef Documentation

boundary_conditions_base

template<size_t Dim>

using Elasticity::FirstOrderSystem< Dim >::boundary_conditions_base

Initial value:

 
      elliptic::BoundaryConditions::BoundaryCondition<Dim>

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The documentation for this struct was generated from the following file:

• src/Elliptic/Systems/Elasticity/FirstOrderSystem.hpp