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Struct ae108::elements::CoreElement

template <class MaterialModel_, class Integrator_, class ValueType_, class RealType_>

ClassList > ae108 > elements > CoreElement

An element that computes energy, forces, and stiffness matrix using a material model and an integrator.

  • #include <CoreElement.h>

Public Types

Type Name
typedef CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ > Element
typedef Real Energy
typedef NodalDisplacements Forces
The forces equal to $d_{ij} E$. Here, d_ij refers to the derivative with respect to jth degree of freedom of the ith node.
typedef Integrator_ Integrator
typedef MaterialModel_ MaterialModel
typedef tensor::Tensor< Value, NumVerts, DegreesOfFreedom > NodalDisplacements
The displacements per node.
typedef RealType_ Real
typedef Eigen::Map< Eigen::Matrix< Value, NumVerts, NumVerts, Eigen::RowMajor >, 0, Eigen::Stride< Eigen::Index{NumVerts *DegreesOfFreedom *DegreesOfFreedom}, Eigen::Index{DegreesOfFreedom}> > ResultSlice
typedef typename Integrator_::size_type Size
typedef Eigen::Matrix< Value, NumVerts *DegreesOfFreedom, NumVerts *DegreesOfFreedom, Eigen::RowMajor > StiffnessMatrix
The stiffness matrix equal to $d_{ij} d_{kl} E$. Here, d_ij refers to the derivative with respect to jth degree of freedom of the ith node.
typedef std::conditional_t< DegreesOfFreedom==0||sizeof(typename MaterialModel::TangentMatrix)==DegreesOfFreedom *MaterialModel::dimension() *DegreesOfFreedom *MaterialModel::dimension() *sizeof(typename MaterialModel::value_type), Eigen::Map< const Eigen::Matrix< typename MaterialModel::value_type, MaterialModel::dimension(), MaterialModel::dimension(), Eigen::RowMajor >, 0, Eigen::Stride< Eigen::Index{MaterialModel::dimension() *Dimension}, Eigen::Index{1}> >, void > TangentSlice
typedef Real Time
typedef ValueType_ Value

Public Attributes

Type Name
Integrator integrator
The instance of the class used to integrate entities (e.g. energy).
MaterialModel model
The instance of the model used to compute entities at integration points (e.g. energy).

Public Static Attributes

Type Name
const Size DegreesOfFreedom = /* multi line expression */
Number of degrees of freedom.
const Size Dimension = Integrator\_::dimension()
const Size NumVerts = Integrator\_::size()
Number of element nodes / shape functions.

Public Functions

Type Name
StiffnessMatrix computeConsistentMassMatrix () noexcept const
Energy computeEnergy (const NodalDisplacements & u, const Time & time) noexcept const
Computes the energy for the given displacements.
Forces computeForces (const NodalDisplacements & u, const Time & time) noexcept const
Computes the forces for the given displacements.
StiffnessMatrix computeLumpedMassMatrix () noexcept const
StiffnessMatrix computeStiffnessMatrix (const NodalDisplacements & u, const Time & time) noexcept const
Computes the stiffness matrix for the given displacements.

Public Types Documentation

typedef Element

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::Element =  CoreElement<MaterialModel_, Integrator_, ValueType_, RealType_>;

typedef Energy

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::Energy =  Real;

typedef Forces

The forces equal to $d_{ij} E$. Here, d_ij refers to the derivative with respect to jth degree of freedom of the ith node. 

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::Forces =  NodalDisplacements;

typedef Integrator

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::Integrator =  Integrator_;

typedef MaterialModel

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::MaterialModel =  MaterialModel_;

typedef NodalDisplacements

The displacements per node. 

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::NodalDisplacements =  tensor::Tensor<Value, NumVerts, DegreesOfFreedom>;

typedef Real

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::Real =  RealType_;

typedef ResultSlice

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::ResultSlice =  Eigen::Map<Eigen::Matrix<Value, NumVerts, NumVerts, Eigen::RowMajor>, 0, Eigen::Stride<Eigen::Index{NumVerts * DegreesOfFreedom * DegreesOfFreedom}, Eigen::Index{DegreesOfFreedom}> >;

typedef Size

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::Size =  typename Integrator_::size_type;

typedef StiffnessMatrix

The stiffness matrix equal to $d_{ij} d_{kl} E$. Here, d_ij refers to the derivative with respect to jth degree of freedom of the ith node. 

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::StiffnessMatrix =  Eigen::Matrix<Value, NumVerts * DegreesOfFreedom, NumVerts * DegreesOfFreedom, Eigen::RowMajor>;

typedef TangentSlice

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::TangentSlice =  std::conditional_t< DegreesOfFreedom == 0 || sizeof(typename MaterialModel::TangentMatrix) == DegreesOfFreedom * MaterialModel::dimension() * DegreesOfFreedom * MaterialModel::dimension() * sizeof(typename MaterialModel::value_type), Eigen::Map< const Eigen::Matrix<typename MaterialModel::value_type, MaterialModel::dimension(), MaterialModel::dimension(), Eigen::RowMajor>, 0, Eigen::Stride<Eigen::Index{MaterialModel::dimension() * Dimension}, Eigen::Index{1}> >, void>;

typedef Time

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::Time =  Real;

typedef Value

using ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::Value =  ValueType_;

Public Attributes Documentation

variable integrator

The instance of the class used to integrate entities (e.g. energy). 

Integrator ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::integrator;

variable model

The instance of the model used to compute entities at integration points (e.g. energy). 

MaterialModel ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::model;

Public Static Attributes Documentation

variable DegreesOfFreedom

Number of degrees of freedom. 

const Size ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::DegreesOfFreedom;

variable Dimension

const Size ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::Dimension;

variable NumVerts

Number of element nodes / shape functions. 

const Size ae108::elements::CoreElement< MaterialModel_, Integrator_, ValueType_, RealType_ >::NumVerts;

Public Functions Documentation

function computeConsistentMassMatrix

inline StiffnessMatrix ae108::elements::CoreElement::computeConsistentMassMatrix () noexcept const

function computeEnergy

Computes the energy for the given displacements. 

inline Energy ae108::elements::CoreElement::computeEnergy (
    const NodalDisplacements & u,
    const Time & time
) noexcept const

function computeForces

Computes the forces for the given displacements. 

inline Forces ae108::elements::CoreElement::computeForces (
    const NodalDisplacements & u,
    const Time & time
) noexcept const

function computeLumpedMassMatrix

inline StiffnessMatrix ae108::elements::CoreElement::computeLumpedMassMatrix () noexcept const

function computeStiffnessMatrix

Computes the stiffness matrix for the given displacements. 

inline StiffnessMatrix ae108::elements::CoreElement::computeStiffnessMatrix (
    const NodalDisplacements & u,
    const Time & time
) noexcept const

The documentation for this class was generated from the following file elements/src/include/ae108/elements/CoreElement.h