Struct ae108::elements::TimoshenkoBeamElement

template <std::size_t Dimension_, class ValueType_, class RealType_>

ClassList > ae108 > elements > TimoshenkoBeamElement

Implementation of the closed-form Timoshenko beam element as presented in Cook et. al (2002), "Concepts and applications of Finite Element Analysis", 4th ed., pp.24-32.

• #include <TimoshenkoBeamElement.h>

Public Types

Type	Name
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 RealType_	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 ValueType_	Value

Public Attributes

Type	Name
TimoshenkoBeamElement::StiffnessMatrix	stiffness_matrix

Public Static Attributes

Type	Name
const Size	DegreesOfFreedom = ([**Dimension**](structae108_1_1elements_1_1TimoshenkoBeamElement.md#variable-dimension) \* ([**Dimension**](structae108_1_1elements_1_1TimoshenkoBeamElement.md#variable-dimension) + 1)) / 2 Number of degrees of freedom.
const Size	Dimension = Dimension\_ The dimension of physical space.
const Size	NumVerts = 2 Number of element nodes / shape functions.

Public Functions

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

Public Types Documentation

typedef Energy

using ae108::elements::TimoshenkoBeamElement< Dimension_, 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::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::Forces =  NodalDisplacements;

---

typedef NodalDisplacements

The displacements per node.

using ae108::elements::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::NodalDisplacements =  tensor::Tensor<Value, NumVerts, DegreesOfFreedom>;

---

typedef Real

using ae108::elements::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::Real =  RealType_;

---

typedef Size

using ae108::elements::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::Size =  std::size_t;

---

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::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::StiffnessMatrix =  Eigen::Matrix<Value, NumVerts * DegreesOfFreedom, NumVerts * DegreesOfFreedom, Eigen::RowMajor>;

---

typedef Time

using ae108::elements::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::Time =  Real;

---

typedef Value

using ae108::elements::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::Value =  ValueType_;

---

Public Attributes Documentation

variable stiffness_matrix

TimoshenkoBeamElement::StiffnessMatrix ae108::elements::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::stiffness_matrix;

---

Public Static Attributes Documentation

variable DegreesOfFreedom

Number of degrees of freedom.

const Size ae108::elements::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::DegreesOfFreedom;

---

variable Dimension

The dimension of physical space.

const Size ae108::elements::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::Dimension;

---

variable NumVerts

Number of element nodes / shape functions.

const Size ae108::elements::TimoshenkoBeamElement< Dimension_, ValueType_, RealType_ >::NumVerts;

---

Public Functions Documentation

function computeEnergy

Computes the energy for the given displacements.

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

---

function computeForces

Computes the forces for the given displacements.

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

---

function computeStiffnessMatrix

Computes the stiffness matrix for the given displacements.

inline StiffnessMatrix ae108::elements::TimoshenkoBeamElement::computeStiffnessMatrix (
    const NodalDisplacements &,
    const Time &
) noexcept const

---

---

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