Virtual class for creating a section object. More...

#include <Section.hpp>

Inheritance diagram for Section:

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Collaboration diagram for Section:

Public Member Functions
	Section (std::string name)
	Creates a Section to be specified at a Gauss-point in an Element. More...

virtual	~Section ()=0
	Destroys this Section object. More...

virtual std::unique_ptr< Section >	CopySection ()=0
	Clone the selected Section. More...

virtual Eigen::VectorXd	GetStrain ()=0
	Returns the resultant (generalised) strain vector over the section. More...

virtual Eigen::VectorXd	GetStress ()=0
	Returns the resultant (generalised) stress vector over the section. More...

virtual Eigen::MatrixXd	GetDensity ()=0
	Access the section density matrix. More...

virtual Eigen::MatrixXd	GetTangentStiffness ()=0
	Returns the section stiffness matrix. More...

virtual Eigen::MatrixXd	GetInitialTangentStiffness ()=0
	Returns the section initial stiffness matrix. More...

virtual Eigen::VectorXd	GetStrainAt (double x3=0, double x2=0)=0
	Returns the section strain at given position. More...

virtual Eigen::VectorXd	GetStressAt (double x3=0, double x2=0)=0
	Returns the section stress at given position. More...

virtual void	CommitState ()=0
	Perform converged section state update. More...

virtual void	ReverseState ()=0
	Reverse the section states to previous converged state. More...

virtual void	InitialState ()=0
	Brings the section states to its initial state. More...

virtual void	UpdateState (Eigen::VectorXd strain, unsigned int cond=0)=0
	Update the section state for this iteration. More...

std::string	GetName ()
	Gets Section name. More...

Protected Member Functions
Eigen::MatrixXd	GetLineRotationMatrix (double theta)
	Gets Local Axis Rotation for Line Section according to provided angle. More...

Eigen::MatrixXd	GetAreaRotationMatrix (double Theta)
	Gets Local Axis Rotation for Area Section according to provided angle. More...

Eigen::MatrixXd	GetLineTranslationMatrix (double h, double b, double zc, double yc, unsigned int ip)
	Gets centroid translation axis for Line Section according to insertion point. More...

void	InsertionPointCoordinates (double &x3, double &x2, double h, double b, double zc, double yc, unsigned int ip)
	Gets the coordinate according to insertion point. More...

Eigen::MatrixXd	ComputeLineLocalAxes (double h, double b, double zcm, double ycm, double angle, unsigned int ip)
	Transforms generalised strain/stresses from Element to Section local coordinate. More...

Private Attributes
std::string	Name
	Section Name. More...

Detailed Description

Virtual class for creating a section object.

See also: Mesh.hpp

Constructor & Destructor Documentation

◆ Section()

Section::Section ( std::string name )

Creates a Section to be specified at a Gauss-point in an Element.

Parameters

name	Name of the derived class.

See also: Section::Name.

◆ ~Section()

virtual Section::~Section ( )

pure virtual

Destroys this Section object.

Member Function Documentation

◆ CommitState()

virtual void Section::CommitState ( )

pure virtual

Perform converged section state update.

Note: This function sets the trail stress and strain as converged.

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ ComputeLineLocalAxes()

Eigen::MatrixXd Section::ComputeLineLocalAxes	(	double	h,
		double	b,
		double	zcm,
		double	ycm,
		double	angle,
		unsigned int	ip
	)

protected

Transforms generalised strain/stresses from Element to Section local coordinate.

Parameters

h	The total height of the section.
b	The total width of the section.
zcm	Position of the section axis along x3-axis.
ycm	Position of the section axis along x2-axis.
ip	The insertion point where the section axes are located.

Returns: The section translation matrix according to ip.

Note: More details can be found at Insertion Point.

◆ CopySection()

virtual std::unique_ptr<Section> Section::CopySection ( )

pure virtual

Clone the selected Section.

Returns: A Section pointer to the derived class.

See also: Section.

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ GetAreaRotationMatrix()

Eigen::MatrixXd Section::GetAreaRotationMatrix ( double Theta )

protected

Gets Local Axis Rotation for Area Section according to provided angle.

Parameters

theta The angle of rotation about x3-axis.

Returns: The section rotation matrix in theta degrees.

Note: More details can be found at Local Axes.

◆ GetDensity()

virtual Eigen::MatrixXd Section::GetDensity ( )

pure virtual

Access the section density matrix.

Returns: The section density matrix.

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ GetInitialTangentStiffness()

virtual Eigen::MatrixXd Section::GetInitialTangentStiffness ( )

pure virtual

Returns the section initial stiffness matrix.

Returns: Matrix with the initial section tangent stiffness matrix.

Note: The initial tangent stiffness matrix is computed when the generalized strain vector is zero.

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ GetLineRotationMatrix()

Eigen::MatrixXd Section::GetLineRotationMatrix ( double theta )

protected

Gets Local Axis Rotation for Line Section according to provided angle.

Parameters

theta The angle of rotation about x1-axis.

Returns: The section rotation matrix in theta degrees.

Note: More details can be found at Local Axes.

◆ GetLineTranslationMatrix()

Eigen::MatrixXd Section::GetLineTranslationMatrix	(	double	h,
		double	b,
		double	zc,
		double	yc,
		unsigned int	ip
	)

protected

Gets centroid translation axis for Line Section according to insertion point.

Parameters

h	The total height of the section.
b	The total width of the section.
zc	Position of the section axis along x3-axis.
yc	Position of the section axis along x2-axis.
ip	The insertion point where the section axes are located.

Returns: The section translation matrix according to ip.

Note: More details can be found at Insertion Point.

◆ GetName()

std::string Section::GetName ( )

Gets Section name.

See also: Section::Name.

◆ GetStrain()

virtual Eigen::VectorXd Section::GetStrain ( )

pure virtual

Returns the resultant (generalised) strain vector over the section.

Returns: Vector with the resultant strain components.

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ GetStrainAt()

virtual Eigen::VectorXd Section::GetStrainAt	(	double	x3 = `0`,
		double	x2 = `0`
	)

pure virtual

Returns the section strain at given position.

Parameters

x3	Position on the x3-axis where the strain is evaluated.
x2	Position on the x2-axis where the strain is evaluated.

Returns: Vector with the strain components at coordinate (x3,x2).

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ GetStress()

virtual Eigen::VectorXd Section::GetStress ( )

pure virtual

Returns the resultant (generalised) stress vector over the section.

Returns: Vector with the resultant stress components.

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ GetStressAt()

virtual Eigen::VectorXd Section::GetStressAt	(	double	x3 = `0`,
		double	x2 = `0`
	)

pure virtual

Returns the section stress at given position.

Parameters

x3	Position on the x3-axis where the stress is evaluated.
x2	Position on the x2-axis where the stress is evaluated.

Returns: Vector with the stress components at coordinate (x3,x2).

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ GetTangentStiffness()

virtual Eigen::MatrixXd Section::GetTangentStiffness ( )

pure virtual

Returns the section stiffness matrix.

Returns: Matrix with the section consistent tangent stiffness matrix.

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ InitialState()

virtual void Section::InitialState ( )

pure virtual

Brings the section states to its initial state.

Note: This function returns the material states to the beginning.

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ InsertionPointCoordinates()

void Section::InsertionPointCoordinates	(	double &	x3,
		double &	x2,
		double	h,
		double	b,
		double	zc,
		double	yc,
		unsigned int	ip
	)

protected

Gets the coordinate according to insertion point.

Parameters

x3	The coordinate along the 3-axis.
x2	The coordinate along the 2-axis.
h	The total height of the section.
b	The total width of the section.
zc	Position of the section axis along x3-axis.
yc	Position of the section axis along x2-axis.
ip	The insertion point where the section axes are located.

Returns: The section translation matrix according to ip.

Note: More details can be found at Insertion Point.

◆ ReverseState()

virtual void Section::ReverseState ( )

pure virtual

Reverse the section states to previous converged state.

Note: This function returns the material states to previous converged states.

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

◆ UpdateState()

virtual void Section::UpdateState	(	Eigen::VectorXd	strain,
		unsigned int	cond = `0`
	)

pure virtual

Update the section state for this iteration.

Parameters

strain	Vector with the strain components at this Gauss-point.
cond	If the the elastic/plastic material components will be updated.

Note: This function computes the strain and tanget stiffness matrix once the trial strain converged.

Implemented in Fib3DLineSection, Lin2DAngle, Lin2DChannel, Lin2DRectangularTube, Lin2DTee, Lin2DWideFlange, Lin3DAngle, Lin3DChannel, Lin3DRectangularTube, Lin3DTee, Lin3DWideFlange, Lin2DRectangular, Lin3DCircularTube, Lin3DRectangular, Lin2DCircular, Lin2DCircularTube, Lin2DUserDefined, Lin3DCircular, Lin3DUserDefined, and Lin3DThinArea.

Member Data Documentation

◆ Name

std::string Section::Name

private

Section Name.

Public Member Functions

Protected Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Section()

◆ ~Section()

Member Function Documentation

◆ CommitState()

◆ ComputeLineLocalAxes()

◆ CopySection()

◆ GetAreaRotationMatrix()

◆ GetDensity()

◆ GetInitialTangentStiffness()

◆ GetLineRotationMatrix()

◆ GetLineTranslationMatrix()

◆ GetName()

◆ GetStrain()

◆ GetStrainAt()

◆ GetStress()

◆ GetStressAt()

◆ GetTangentStiffness()

◆ InitialState()

◆ InsertionPointCoordinates()

◆ ReverseState()

◆ UpdateState()

Member Data Documentation

◆ Name