ForceDirField Class Reference

Traction field based on a given force resultant and orientation. More...

#include <TractionField.h>

Inheritance diagram for ForceDirField:

Collaboration diagram for ForceDirField:

Public Member Functions
	ForceDirField (const ScalarFunc *f, const Vec3Func *d, const RealFunc *s, const Vec3 &Xaxis=Vec3(Real(1), Real(0), Real(0)), const Vec3 &Zaxis=Vec3(Real(0), Real(0), Real(1)), const Vec3 &Xorig=Vec3(), bool v=false)
	The constructor initializes the function pointers. More...
	ForceDirField (const ScalarFunc *f, const ScalarFunc *a, char x, const RealFunc *s, const Vec3 &Xaxis=Vec3(Real(1), Real(0), Real(0)), const Vec3 &Zaxis=Vec3(Real(0), Real(0), Real(1)), const Vec3 &Xorig=Vec3())
	Alternative constructor for single-axis rotation. More...
virtual	~ForceDirField ()
	The destructor frees the force functions.
virtual bool	isZero () const
	Returns whether the function is identically zero or not.
Public Member Functions inherited from TractionFunc
virtual bool	isNormalPressure () const
	Returns whether the traction is always normal to the face or not.
virtual Vec3	timeDerivative (const Vec3 &, const Vec3 &) const
	Returns the time-derivative of the function.
Public Member Functions inherited from utl::Function2< Vec3, Vec3 >
virtual	~Function2 ()
	Empty destructor.
Vec3	operator() (const Vec3 &x, const Vec3 &y) const
	Operator returning the function value for the given arguments.

Protected Member Functions
virtual Vec3	evaluate (const Vec3 &x, const Vec3 &) const
	Evaluates the traction field function at the specified point. More...
Protected Member Functions inherited from utl::Function2< Vec3, Vec3 >
	Function2 ()
	The constructor is protected to allow sub-class instances only.

Private Types
typedef utl::Function< Real, Vec3 >	Vec3Func
	Convenience type.

Private Attributes
Vec3	X0
	Local origin.
Tensor	Tlg
	Local-to-global transformation.
const ScalarFunc *	force
	Force resultant magnitude.
const ScalarFunc *	angle
	Force angle about rotAxis.
const Vec3Func *	fdir
	Force direction/angles.
const RealFunc *	shape
	Shape function for force distribution.
bool	dirVec
	If true, fdir is the force direction vector.
char	rotAxis
	Which local axis the angle is referring to.

Additional Inherited Members
Public Types inherited from utl::Function2< Vec3, Vec3 >
typedef Vec3	Input
	Input type.
typedef Vec3	Output
	Output type.

Detailed Description

Traction field based on a given force resultant and orientation.

This class defines an explicit traction field function based on a time-dependent force magnitude function, a time-dependent vector-valued function (fdir) giving either the force direction as a unit vector or the three rotation angles (roll, pitch and yaw) about the local coordinate axes. Finally, a spatial shape function is used to describe the distribution of the force resultant over the loaded face.

The global force is acting along the Y-axis of the local coordinate system, which is defined by the specified origin X0 and the local-to-global transformation Tlg. This local coordinate system is then assigned a time-dependent rotation as given by fdir. The traction value at a given global point X and time t is therefore computed as

\[ {\bf t}({\bf X},t) = {\bf T}_{lg}\left\{f(t)S({\bf x}(t)){\bf d}(t)\right\} \]

where \(f(t)\) denotes the value for the force magnitude function, \(S({\bf x}(t))\) is the shape function value at the local point x and time t, and \({\bf d}(t)\) is the time-dependent force direction vector of unit length. The local, time-dependent coordinates x are computed from the global coordinate X through

\[ {\bf x}(t) = {\bf T}_{rot}(t)\left\{({\bf X}-{\bf X}_0){\bf T}_{lg}\right\} \]

where \({\bf T}_{rot}(t)\) is the time-dependent rotation matrix derived from either the vector-valued function fdir, or the scalar-valued function angle and the rotAxis parameter. The Local force direction vector \({\bf d}(t)\) is then taken as the second column of this transformation matrix (i.e., the Y-axis).

Constructor & Destructor Documentation

ForceDirField() [1/2]

ForceDirField::ForceDirField ( const ScalarFunc *  f, const Vec3Func *  d, const RealFunc *  s, const Vec3 &  Xaxis = Vec3(Real(1),Real(0),Real(0)), const Vec3 &  Zaxis = Vec3(Real(0),Real(0),Real(1)), const Vec3 &  Xorig = Vec3(), bool  v = false  )

inline

The constructor initializes the function pointers.

Parameters

[in]	f	The scalar function defining the force magnitude
[in]	d	The direction/angles the force is acting in
[in]	s	Shape function defining the force distribution
[in]	Xaxis	Local X-axis direction
[in]	Zaxis	Local Z-axis direction
[in]	Xorig	Origin of the local coordinate system
[in]	v	If true, fdir is the force direction vector

ForceDirField() [2/2]

ForceDirField::ForceDirField ( const ScalarFunc *  f, const ScalarFunc *  a, char  x, const RealFunc *  s, const Vec3 &  Xaxis = Vec3(Real(1),Real(0),Real(0)), const Vec3 &  Zaxis = Vec3(Real(0),Real(0),Real(1)), const Vec3 &  Xorig = Vec3()  )

inline

Alternative constructor for single-axis rotation.

Parameters

[in]	f	The scalar function defining the force magnitude
[in]	a	The scalar function defining the force angle
[in]	x	Which local axis the angle is referring to
[in]	s	Shape function defining the force distribution
[in]	Xaxis	Local X-axis direction
[in]	Zaxis	Local Z-axis direction
[in]	Xorig	Origin of the local coordinate system

Member Function Documentation

evaluate()

Vec3 ForceDirField::evaluate ( const Vec3 &  x, const Vec3 &    ) const

protectedvirtual

Evaluates the traction field function at the specified point.

Parameters

[in]

x

Global coordinates of evaluation point

Implements utl::Function2< Vec3, Vec3 >.

References angle, dirVec, fdir, force, Real, rotAxis, shape, Vec4::t, Tlg, Vec3::x, X0, Vec3::y, and Vec3::z.

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

• src/Utility/TractionField.h
• src/Utility/TractionField.C