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

#include <Newmark.h>

Inheritance diagram for Newmark:

Collaboration diagram for Newmark:

Public Member Functions
	Newmark (unsigned=0, double=.25, double=.5)

void	assemble_resistance () override

void	assemble_matrix () override

int	update_trial_status () override

void	update_parameter (double) override

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 ImplicitIntegrator
constexpr IntegratorType	type () const override

bool	time_independent_matrix () const override

	Integrator (unsigned=0)

	Integrator (const Integrator &)=delete

	Integrator (Integrator &&)=delete

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=default

void	set_domain (const weak_ptr< DomainBase > &)

shared_ptr< DomainBase >	get_domain () const

virtual int	initialize ()

virtual constexpr IntegratorType	type () const

void	set_time_step_switch (bool)

bool	allow_to_change_time_step () const

void	set_matrix_assembled_switch (bool)

bool	matrix_is_assembled () const

virtual bool	has_corrector () const

virtual bool	time_independent_matrix () const

virtual int	process_load ()

virtual int	process_constraint ()

virtual int	process_criterion ()

virtual int	process_modifier ()

virtual int	process_load_resistance ()

virtual int	process_constraint_resistance ()

void	record () const

virtual void	assemble_resistance ()

virtual void	assemble_matrix ()

virtual vec	get_force_residual ()

virtual vec	get_displacement_residual ()

virtual vec	get_auxiliary_residual ()

virtual sp_mat	get_reference_load ()

virtual const vec &	get_trial_displacement () const

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_from_ninja ()

virtual void	update_trial_time (double)

virtual void	update_incre_time (double)

virtual int	update_trial_status ()

virtual int	correct_trial_status ()

virtual int	sync_status (bool)

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 (vec &) const

void	stage_and_commit_status ()

virtual void	stage_status ()

virtual void	commit_status ()

virtual void	clear_status ()

virtual void	reset_status ()

virtual void	update_parameter (double)

virtual vec	from_incre_velocity (const vec &, const uvec &)

virtual vec	from_incre_acceleration (const vec &, const uvec &)

virtual vec	from_total_velocity (const vec &, const uvec &)

virtual 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

virtual void	print ()

Protected Attributes
double	C0 = 0.

double	C1 = 0.

double	C2 = 0.

double	C3 = 0.

double	C4 = 0.

double	C5 = 0.

Detailed Description

A Newmark class defines a solver using Newmark algorithm.

Newmark algorithm is unconditionally stable if

\begin{gather}\alpha\geq\dfrac{1}{4}\left(\dfrac{1}{2}+\beta\right)^2,\qquad\beta\geq\dfrac{1}{2}\end{gather}

.

There are several choices for solver parameters.

Constant Acceleration:

\begin{gather}\alpha=\dfrac{1}{4},\qquad\beta=\dfrac{1}{2}\end{gather}

.

Linear Acceleration:

\begin{gather}\alpha=\dfrac{1}{6},\qquad\beta=\dfrac{1}{2}\end{gather}

.

Author: tlc

Date: 25/08/2017

Version: 0.1.1

Constructor & Destructor Documentation

◆ Newmark()

Newmark::Newmark	(	unsigned	T = `0`,
		double	A = `.25`,
		double	B = `.5`
	)

explicit

Member Function Documentation

◆ assemble_matrix()

void Newmark::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.

Reimplemented in NonviscousNewmark, and WilsonPenzienNewmark.

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◆ assemble_resistance()

void Newmark::assemble_resistance ( )

overridevirtual

Reimplemented from Integrator.

Reimplemented in NonviscousNewmark, RayleighNewmark, and WilsonPenzienNewmark.

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◆ from_incre_acceleration()

vec Newmark::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 TOTAL displacement.

Reimplemented from Integrator.

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◆ from_incre_velocity()

vec Newmark::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 TOTAL displacement.

Reimplemented from Integrator.

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◆ print()

void Newmark::print ( )

overridevirtual

Reimplemented from Tag.

Reimplemented in NonviscousNewmark, and WilsonPenzienNewmark.

◆ update_parameter()

void Newmark::update_parameter ( double )

overridevirtual

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

Reimplemented from Integrator.

Reimplemented in NonviscousNewmark.

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◆ update_trial_status()

int Newmark::update_trial_status ( )

overridevirtual

Reimplemented from Integrator.

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Member Data Documentation

◆ C0

double Newmark::C0 = 0.

protected

◆ C1

double Newmark::C1 = 0.

protected

◆ C2

double Newmark::C2 = 0.

protected

◆ C3

double Newmark::C3 = 0.

protected

◆ C4

double Newmark::C4 = 0.

protected

◆ C5

double Newmark::C5 = 0.

protected

parameters

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

Solver/Integrator/Newmark.h
Solver/Integrator/Newmark.cpp

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Newmark()

Member Function Documentation

◆ assemble_matrix()

◆ assemble_resistance()

◆ from_incre_acceleration()

◆ from_incre_velocity()

◆ print()

◆ update_parameter()

◆ update_trial_status()

Member Data Documentation

◆ C0

◆ C1

◆ C2

◆ C3

◆ C4

◆ C5