Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef > Class Template Reference

Kirchhoff-Love shell finite element class. More...

#include <ikarus/finiteelements/mechanics/kirchhoffloveshell.hh>

Inheritance diagram for Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >:

Classes
struct	KinematicVariables
	A structure representing kinematic variables. More...

Public Types
using	Basis = Basis_
using	FlatBasis = typename Basis::FlatBasis
using	BasePowerFE = PowerBasisFE< FlatBasis >
using	FERequirementType = FERequirements_
using	ResultRequirementsType = ResultRequirements< FERequirementType >
using	LocalView = typename FlatBasis::LocalView
using	Element = typename LocalView::Element
using	Geometry = typename Element::Geometry
using	GridView = typename FlatBasis::GridView
using	Traits = TraitsFromLocalView< LocalView, useEigenRef >
using	LocalBasisType = decltype(std::declval< LocalView >().tree().child(0).finiteElement().localBasis())
using	RootBasis = Basis_::FlatBasis
	Type of the root basis. More...
using	GlobalIndex = typename LocalView::MultiIndex
	Type of the global index. More...
using	GridElement = typename LocalView::Element
	Type of the grid element. More...

Public Member Functions
template<typename VolumeLoad = utils::LoadDefault, typename NeumannBoundaryLoad = utils::LoadDefault>
	KirchhoffLoveShell (const Basis &globalBasis, const typename LocalView::Element &element, double emod, double nu, double thickness, VolumeLoad p_volumeLoad={}, const BoundaryPatch< GridView > *p_neumannBoundary=nullptr, NeumannBoundaryLoad p_neumannBoundaryLoad={})
	Constructor for the KirchhoffLoveShell class. More...
template<typename ScalarType = double>
auto	displacementFunction (const FERequirementType &par, const std::optional< const Eigen::VectorX< ScalarType > > &dx=std::nullopt) const
	Get the displacement function and nodal displacements. More...
double	calculateScalar (const FERequirementType &req) const
	Calculate the scalar value. More...
void	calculateVector (const FERequirementType &req, typename Traits::template VectorType<> force) const
	Calculate the vector associated with the given FERequirementType. More...
void	calculateMatrix (const FERequirementType &req, typename Traits::template MatrixType<> K) const
	Calculate the matrix associated with the given FERequirementType. More...
void	calculateAt (const ResultRequirementsType &req, const Dune::FieldVector< double, Traits::mydim > &local, ResultTypeMap< double > &result) const
	Calculate results at local coordinates. More...
constexpr size_t	size () const
	Get the size of the local view. More...
void	globalFlatIndices (std::vector< GlobalIndex > &globalIndices) const
	Get the global flat indices for the power basis. More...
const GridElement &	gridElement () const
	Get the grid element associated with the local view. More...
const LocalView &	localView () const
	Get the const reference to the local view. More...
LocalView &	localView ()
	Get the reference to the local view. More...

Public Attributes
std::shared_ptr< const Geometry >	geo_
Dune::CachedLocalBasis< std::remove_cvref_t< LocalBasisType > >	localBasis
std::function< Eigen::Vector< double, worldDim >(const Dune::FieldVector< double, worldDim > &, const double &)>	volumeLoad
std::function< Eigen::Vector< double, worldDim >(const Dune::FieldVector< double, worldDim > &, const double &)>	neumannBoundaryLoad
const BoundaryPatch< GridView > *	neumannBoundary
DefaultMembraneStrain	membraneStrain
double	emod_
double	nu_
double	thickness_
size_t	numberOfNodes {0}
int	order {}

Static Public Attributes
static constexpr int	myDim = Traits::mydim
static constexpr int	worldDim = Traits::worlddim
static constexpr int	membraneStrainSize = 3
static constexpr int	bendingStrainSize = 3
static constexpr int	num_children
	Number of children in the powerBasis. More...

Protected Member Functions
auto	computeMaterialAndStrains (const Dune::FieldVector< double, 2 > &gpPos, int gpIndex, const Geometry &geo, const auto &uFunction) const
	Compute material properties and strains at a given integration point. More...
template<typename ScalarType >
void	calculateMatrixImpl (const FERequirementType &par, typename Traits::template MatrixType< ScalarType > K, const std::optional< const Eigen::VectorX< ScalarType > > &dx=std::nullopt) const
template<typename ScalarType >
void	calculateVectorImpl (const FERequirementType &par, typename Traits::template VectorType< ScalarType > force, const std::optional< const Eigen::VectorX< ScalarType > > &dx=std::nullopt) const
template<typename ScalarType >
auto	calculateScalarImpl (const FERequirementType &par, const std::optional< const Eigen::VectorX< ScalarType > > &dx=std::nullopt) const -> ScalarType
template<typename ScalarType >
Eigen::Matrix< ScalarType, 3, 3 >	kgBending (const Eigen::Matrix< ScalarType, 2, 3 > &jcur, const Eigen::Matrix3< ScalarType > &h, const auto &dN, const auto &ddN, const Eigen::Vector3< ScalarType > &a3N, const Eigen::Vector3< ScalarType > &a3, const Eigen::Vector3< ScalarType > &S, int I, int J) const
template<typename ScalarType >
Eigen::Matrix< ScalarType, 3, 3 >	bopBending (const Eigen::Matrix< ScalarType, 2, 3 > &jcur, const Eigen::Matrix3< ScalarType > &h, const auto &dN, const auto &ddN, const int node, const Eigen::Vector3< ScalarType > &a3N, const Eigen::Vector3< ScalarType > &a3) const
Eigen::Matrix< double, 3, 3 >	materialTangent (const Eigen::Matrix< double, 3, 3 > &Aconv) const

Detailed Description

template<typename Basis_, typename FERequirements_ = FERequirements<>, bool useEigenRef = false>
class Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >

This class represents Kirchhoff-Love shell finite elements.

Template Parameters

Basis_	The basis type for the finite element.
FERequirements_	The type representing the requirements for finite element calculations.
useEigenRef	A boolean indicating whether to use Eigen references for efficiency.

Member Typedef Documentation

BasePowerFE

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::BasePowerFE = PowerBasisFE<FlatBasis>

Basis

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::Basis = Basis_

Element

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::Element = typename LocalView::Element

FERequirementType

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::FERequirementType = FERequirements_

FlatBasis

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::FlatBasis = typename Basis::FlatBasis

Geometry

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::Geometry = typename Element::Geometry

GlobalIndex

using Ikarus::PowerBasisFE< Basis_::FlatBasis >::GlobalIndex = typename LocalView::MultiIndex

inherited

GridElement

using Ikarus::PowerBasisFE< Basis_::FlatBasis >::GridElement = typename LocalView::Element

inherited

GridView

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::GridView = typename FlatBasis::GridView

LocalBasisType

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::LocalBasisType = decltype(std::declval<LocalView>().tree().child(0).finiteElement().localBasis())

LocalView

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::LocalView = typename FlatBasis::LocalView

ResultRequirementsType

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::ResultRequirementsType = ResultRequirements<FERequirementType>

RootBasis

using Ikarus::PowerBasisFE< Basis_::FlatBasis >::RootBasis = Basis_::FlatBasis

inherited

Traits

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

using Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::Traits = TraitsFromLocalView<LocalView, useEigenRef>

Constructor & Destructor Documentation

KirchhoffLoveShell()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

template<typename VolumeLoad = utils::LoadDefault, typename NeumannBoundaryLoad = utils::LoadDefault>

Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::KirchhoffLoveShell ( const Basis &  globalBasis, const typename LocalView::Element &  element, double  emod, double  nu, double  thickness, VolumeLoad  p_volumeLoad = {}, const BoundaryPatch< GridView > *  p_neumannBoundary = nullptr, NeumannBoundaryLoad  p_neumannBoundaryLoad = {}  )

inline

Initializes the KirchhoffLoveShell instance with the given parameters.

Template Parameters

VolumeLoad	The type representing the volume load function.
NeumannBoundaryLoad	The type representing the Neumann boundary load function.

Parameters

globalBasis	The global basis for the finite element.
element	The local element to bind.
emod	Young's modulus of the material.
nu	Poisson's ratio of the material.
thickness	Thickness of the shell.
p_volumeLoad	The volume load function (optional, default is utils::LoadDefault).
p_neumannBoundary	The Neumann boundary patch (optional, default is nullptr).
p_neumannBoundaryLoad	The Neumann boundary load function (optional, default is LoadDefault).

Member Function Documentation

bopBending()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

template<typename ScalarType >

Eigen::Matrix< ScalarType, 3, 3 > Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::bopBending ( const Eigen::Matrix< ScalarType, 2, 3 > &  jcur, const Eigen::Matrix3< ScalarType > &  h, const auto &  dN, const auto &  ddN, const int  node, const Eigen::Vector3< ScalarType > &  a3N, const Eigen::Vector3< ScalarType > &  a3  ) const

inlineprotected

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calculateAt()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

void Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::calculateAt ( const ResultRequirementsType &  req, const Dune::FieldVector< double, Traits::mydim > &  local, ResultTypeMap< double > &  result  ) const

inline

Calculates the results at the specified local coordinates based on the given requirements and stores them in the result container.

Parameters

req	The result requirements.
local	The local coordinates at which results are to be calculated.
result	The result container to store the calculated values.

calculateMatrix()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

void Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::calculateMatrix ( const FERequirementType &  req, typename Traits::template MatrixType<>  K  ) const

inline

Template Parameters

ScalarType

The scalar type for the calculation.

Parameters

req	The FERequirementType object specifying the requirements for the calculation.
K	The matrix to store the calculated result.

calculateMatrixImpl()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

template<typename ScalarType >

void Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::calculateMatrixImpl ( const FERequirementType &  par, typename Traits::template MatrixType< ScalarType >  K, const std::optional< const Eigen::VectorX< ScalarType > > &  dx = std::nullopt  ) const

inlineprotected

calculateScalar()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

double Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::calculateScalar ( const FERequirementType &  req ) const

inline

Calculates the scalar value based on the given FERequirements.

Parameters

req	The FERequirements.

Returns

The calculated scalar value.

calculateScalarImpl()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

template<typename ScalarType >

auto Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::calculateScalarImpl ( const FERequirementType &  par, const std::optional< const Eigen::VectorX< ScalarType > > &  dx = std::nullopt  ) const -> ScalarType

inlineprotected

calculateVector()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

void Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::calculateVector ( const FERequirementType &  req, typename Traits::template VectorType<>  force  ) const

inline

Template Parameters

ScalarType

The scalar type for the calculation.

Parameters

req	The FERequirementType object specifying the requirements for the calculation.
force	The vector to store the calculated result.

calculateVectorImpl()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

template<typename ScalarType >

void Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::calculateVectorImpl ( const FERequirementType &  par, typename Traits::template VectorType< ScalarType >  force, const std::optional< const Eigen::VectorX< ScalarType > > &  dx = std::nullopt  ) const

inlineprotected

computeMaterialAndStrains()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

auto Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::computeMaterialAndStrains ( const Dune::FieldVector< double, 2 > &  gpPos, int  gpIndex, const Geometry &  geo, const auto &  uFunction  ) const

inlineprotected

Parameters

gpPos	The position of the integration point.
gpIndex	The index of the integration point.
geo	The geometry object providing position and derivatives.
uFunction	The function representing the displacement field.

Template Parameters

gpPos	The type of the integration point position.
gpIndex	The type of the integration point index.
geo	The type of the geometry object.
uFunction	The type of the displacement field function.

Returns

A tuple containing the material tangent, membrane strain, bending, Jacobian matrix of the reference position, Jacobian matrix of the current position, Hessian matrix of the current position, Hessian matrix of the reference position, normal vector, and normalized normal vector at the given integration point.

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displacementFunction()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

template<typename ScalarType = double>

auto Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::displacementFunction ( const FERequirementType &  par, const std::optional< const Eigen::VectorX< ScalarType > > &  dx = std::nullopt  ) const

inline

Retrieves the displacement function and nodal displacements based on the given FERequirements.

Template Parameters

ScalarType

The scalar type used for calculations.

Parameters

par	The FERequirements.
dx	Optional additional displacement vector.

Returns

The displacement function.

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globalFlatIndices()

void Ikarus::PowerBasisFE< Basis_::FlatBasis >::globalFlatIndices ( std::vector< GlobalIndex > &  globalIndices ) const

inlineinherited

The global indices are collected in a FlatInterLeaved order. I.e. x_0, y_0, z_0, ..., x_n, y_n, z_n

Parameters

globalIndices

Output vector to store global indices.

gridElement()

const GridElement & Ikarus::PowerBasisFE< Basis_::FlatBasis >::gridElement ( ) const

inlineinherited

Returns

The grid element.

kgBending()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

template<typename ScalarType >

Eigen::Matrix< ScalarType, 3, 3 > Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::kgBending ( const Eigen::Matrix< ScalarType, 2, 3 > &  jcur, const Eigen::Matrix3< ScalarType > &  h, const auto &  dN, const auto &  ddN, const Eigen::Vector3< ScalarType > &  a3N, const Eigen::Vector3< ScalarType > &  a3, const Eigen::Vector3< ScalarType > &  S, int  I, int  J  ) const

inlineprotected

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localView() [1/2]

LocalView & Ikarus::PowerBasisFE< Basis_::FlatBasis >::localView ( )

inlineinherited

Returns

The reference to the local view.

localView() [2/2]

const LocalView & Ikarus::PowerBasisFE< Basis_::FlatBasis >::localView ( ) const

inlineinherited

Returns

The const reference to the local view.

materialTangent()

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

Eigen::Matrix< double, 3, 3 > Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::materialTangent ( const Eigen::Matrix< double, 3, 3 > &  Aconv ) const

inlineprotected

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size()

constexpr size_t Ikarus::PowerBasisFE< Basis_::FlatBasis >::size ( ) const

inlineconstexprinherited

Returns

The size of the local view.

Member Data Documentation

bendingStrainSize

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

constexpr int Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::bendingStrainSize = 3

staticconstexpr

emod_

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

double Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::emod_

geo_

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

std::shared_ptr<const Geometry> Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::geo_

localBasis

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

Dune::CachedLocalBasis<std::remove_cvref_t<LocalBasisType> > Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::localBasis

membraneStrain

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

DefaultMembraneStrain Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::membraneStrain

membraneStrainSize

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

constexpr int Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::membraneStrainSize = 3

staticconstexpr

myDim

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

constexpr int Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::myDim = Traits::mydim

staticconstexpr

neumannBoundary

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

const BoundaryPatch<GridView>* Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::neumannBoundary

neumannBoundaryLoad

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

std::function<Eigen::Vector<double, worldDim>(const Dune::FieldVector<double, worldDim>&, const double&)> Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::neumannBoundaryLoad

nu_

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

double Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::nu_

num_children

constexpr int Ikarus::PowerBasisFE< Basis_::FlatBasis >::num_children

staticconstexprinherited

numberOfNodes

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

size_t Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::numberOfNodes {0}

order

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

int Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::order {}

thickness_

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

double Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::thickness_

volumeLoad

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

std::function<Eigen::Vector<double, worldDim>(const Dune::FieldVector<double, worldDim>&, const double&)> Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::volumeLoad

worldDim

template<typename Basis_ , typename FERequirements_ = FERequirements<>, bool useEigenRef = false>

constexpr int Ikarus::KirchhoffLoveShell< Basis_, FERequirements_, useEigenRef >::worldDim = Traits::worlddim

staticconstexpr

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

• finiteelements/mechanics/kirchhoffloveshell.hh