GeneralizedAlpha Class Reference

A GeneralizedAlpha class defines a solver using GeneralizedAlpha algorithm. More...

#include <GeneralizedAlpha.h>

Inheritance diagram for GeneralizedAlpha:

Collaboration diagram for GeneralizedAlpha:

Public Member Functions
	GeneralizedAlpha (unsigned, double)
	GeneralizedAlpha (unsigned, double, double)
void	assemble_resistance () override
void	assemble_matrix () override
int	process_load () override
int	process_constraint () override
int	process_load_resistance () override
int	process_constraint_resistance () override
int	update_trial_status () override
void	update_parameter (double) override
void	update_compatibility () const override
	update acceleration and velocity for zero displacement increment More...
vec	from_incre_velocity (const vec &, const uvec &) override
vec	from_incre_acceleration (const vec &, const uvec &) override
void	print () override
Public Member Functions inherited from Integrator
	Integrator (unsigned=0)
	Integrator (const Integrator &)=delete
	Integrator (Integrator &&)=delete
Integrator &	operator= (const Integrator &)=delete
Integrator &	operator= (Integrator &&)=delete
	~Integrator () override
void	set_domain (const weak_ptr< DomainBase > &)
const weak_ptr< DomainBase > &	get_domain () const
virtual int	initialize ()
void	set_time_step_switch (bool)
bool	allow_to_change_time_step () const
virtual int	process_criterion ()
virtual int	process_modifier ()
void	record () const
virtual vec	get_force_residual ()
virtual vec	get_displacement_residual ()
virtual vec	get_auxiliary_residual ()
virtual sp_mat	get_reference_load ()
virtual sp_mat	get_auxiliary_stiffness ()
virtual void	update_load ()
virtual void	update_constraint ()
virtual void	update_trial_load_factor (double)
virtual void	update_trial_load_factor (const vec &)
virtual void	update_trial_displacement (const vec &)
void	update_trial_time (double)
void	update_incre_time (double)
virtual int	update_incre_status ()
virtual int	update_internal (const mat &)
mat	solve (const mat &)
mat	solve (const sp_mat &)
mat	solve (mat &&)
mat	solve (sp_mat &&)
virtual int	solve (mat &, const mat &)
virtual int	solve (mat &, const sp_mat &)
virtual int	solve (mat &, mat &&)
virtual int	solve (mat &, sp_mat &&)
virtual void	erase_machine_error () const
virtual void	stage_and_commit_status ()
virtual void	stage_status ()
virtual void	commit_status ()
virtual void	clear_status ()
virtual void	reset_status ()
vec	from_total_velocity (const vec &, const uvec &)
vec	from_total_acceleration (const vec &, const uvec &)
vec	from_incre_velocity (double, const uvec &)
vec	from_incre_acceleration (double, const uvec &)
vec	from_total_velocity (double, const uvec &)
vec	from_total_acceleration (double, const uvec &)
Public Member Functions inherited from Tag
	Tag (unsigned=0)
	Tag (const Tag &)=default
	Tag (Tag &&)=default
Tag &	operator= (const Tag &)=delete
Tag &	operator= (Tag &&)=delete
virtual	~Tag ()=default
void	set_tag (unsigned) const
unsigned	get_tag () const
void	enable ()
void	disable ()
void	guard ()
void	unguard ()
bool	is_active () const
bool	is_guarded () const

Detailed Description

A GeneralizedAlpha class defines a solver using GeneralizedAlpha algorithm.

Unlike Newmark method, in which the equilibrium is satisfied at the end of current time step, i.e., \(t=t_0+\Delta{}t\), the generalized- \(\alpha\) approach applies it at somewhere in current step, i.e., \(t=t_0+\Delta{}t-\alpha\), similar to the generalized midpoint concept.

doi: 10.1115/1.2900803

Author

tlc

Date

21/10/2017

Version

0.1.0

Constructor & Destructor Documentation

GeneralizedAlpha() [1/2]

GeneralizedAlpha::GeneralizedAlpha	(	unsigned	T,
		double	R
	)

GeneralizedAlpha() [2/2]

GeneralizedAlpha::GeneralizedAlpha	(	unsigned	T,
		double	AF,
		double	AM
	)

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Member Function Documentation

assemble_matrix()

void GeneralizedAlpha::assemble_matrix ( )

overridevirtual

Assemble the global effective matrix A in AX=B. For FEM applications, it is often a linear combination of stiffness, mass, damping and geometry matrices.

Reimplemented from Integrator.

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assemble_resistance()

void GeneralizedAlpha::assemble_resistance ( )

overridevirtual

Reimplemented from Integrator.

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from_incre_acceleration()

vec GeneralizedAlpha::from_incre_acceleration ( const vec &  , const uvec &  encoding  )

overridevirtual

When external loads are applied, they can be applied in forms of displacement/velocity/acceleration. The time integration methods, by default, form effective stiffness matrices in displacement domain. That is, in AX=B, A is the effective stiffness matrix and X is the displacement increment. Thus, loads in velocity/acceleration must be converted to displacement. This cannot be done arbitrarily due to compatibility issues. This method takes acceleration increment and converts it to displacement increment.

Reimplemented from Integrator.

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from_incre_velocity()

vec GeneralizedAlpha::from_incre_velocity ( const vec &  , const uvec &  encoding  )

overridevirtual

When external loads are applied, they can be applied in forms of displacement/velocity/acceleration. The time integration methods, by default, form effective stiffness matrices in displacement domain. That is, in AX=B, A is the effective stiffness matrix and X is the displacement increment. Thus, loads in velocity/acceleration must be converted to displacement. This cannot be done arbitrarily due to compatibility issues. This method takes velocity increment and converts it to displacement increment.

Reimplemented from Integrator.

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print()

void GeneralizedAlpha::print ( )

overridevirtual

Reimplemented from Tag.

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process_constraint()

int GeneralizedAlpha::process_constraint ( )

overridevirtual

The main task of this method is to apply constraints (of various forms implemented in various methods). Combinations of different types need to be considered: 1) homogeneous, 2) inhomogeneous, 3) linear, 4) nonlinear. Combinations of different methods need to be considered: 1) penalty, 2) multiplier. On exit, the global stiffness matrix should be updated, the global residual vector should be updated.

Reimplemented from Integrator.

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process_constraint_resistance()

int GeneralizedAlpha::process_constraint_resistance ( )

overridevirtual

This method is similar to process_constraint(), but it only updates the global residual vector. The global stiffness matrix is not touched as in some solving schemes, the global stiffness matrix is only assembled and factorised once at the beginning. Subsequent iterations do not assemble the global stiffness matrix again and reuse the factorised matrix. In this case, the factorised matrix cannot be modified.

Reimplemented from Integrator.

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process_load()

int GeneralizedAlpha::process_load ( )

overridevirtual

Reimplemented from Integrator.

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process_load_resistance()

int GeneralizedAlpha::process_load_resistance ( )

overridevirtual

Reimplemented from Integrator.

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update_compatibility()

void GeneralizedAlpha::update_compatibility ( ) const

overridevirtual

update acceleration and velocity for zero displacement increment

Reimplemented from Integrator.

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update_parameter()

void GeneralizedAlpha::update_parameter ( double  )

overridevirtual

When tim step changes, some parameters may need to be updated.

Reimplemented from Integrator.

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update_trial_status()

int GeneralizedAlpha::update_trial_status ( )

overridevirtual

Reimplemented from Integrator.

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

• Solver/Integrator/GeneralizedAlpha.h
• Solver/Integrator/GeneralizedAlpha.cpp