Struct ae108::elements::Minimal

template <std::size_t Size_, std::size_t Dimension_, std::size_t DegreesOfFreedom_>

ClassList > ae108 > elements > Minimal

A minimal example of an element. Note that only the energy is defined.

• #include <Minimal.h>

Public Types

Type	Name
typedef Minimal< Size_, Dimension_, DegreesOfFreedom_ >	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 tensor::Tensor< Value, NumVerts, DegreesOfFreedom >	NodalDisplacements The displacements per node.
typedef double	Real
typedef std::size_t	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 Real	Time
typedef double	Value

Public Static Attributes

Type	Name
const Size	DegreesOfFreedom = Dimension\_ Number of degrees of freedom.
const Size	Dimension = Dimension\_ The dimension of physical space.
const Size	NumVerts = 1 Number of element nodes / shape functions.

Public Functions

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

Public Types Documentation

typedef Element

using ae108::elements::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::Element =  Minimal<Size_, Dimension_, DegreesOfFreedom_>;

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typedef Energy

using ae108::elements::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::Energy =  Real;

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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::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::Forces =  NodalDisplacements;

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typedef NodalDisplacements

The displacements per node.

using ae108::elements::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::NodalDisplacements =  tensor::Tensor<Value, NumVerts, DegreesOfFreedom>;

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typedef Real

using ae108::elements::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::Real =  double;

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typedef Size

using ae108::elements::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::Size =  std::size_t;

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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::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::StiffnessMatrix =  Eigen::Matrix<Value, NumVerts * DegreesOfFreedom, NumVerts * DegreesOfFreedom, Eigen::RowMajor>;

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typedef Time

using ae108::elements::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::Time =  Real;

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typedef Value

using ae108::elements::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::Value =  double;

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Public Static Attributes Documentation

variable DegreesOfFreedom

Number of degrees of freedom.

const Size ae108::elements::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::DegreesOfFreedom;

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variable Dimension

The dimension of physical space.

const Size ae108::elements::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::Dimension;

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variable NumVerts

Number of element nodes / shape functions.

const Size ae108::elements::Minimal< Size_, Dimension_, DegreesOfFreedom_ >::NumVerts;

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Public Functions Documentation

function computeEnergy

Computes the energy for the given displacements.

inline Energy ae108::elements::Minimal::computeEnergy (
    const NodalDisplacements &,
    const Time &
) noexcept const

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function computeForces

Computes the forces for the given displacements.

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

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function computeStiffnessMatrix

Computes the stiffness matrix for the given displacements.

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

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