Namespace for global parameters. More...

Functions
void	boundary_traction (const double &time, const Vector< double > &x, const Vector< double > &n, Vector< double > &result)
	The traction function at r=Rmin: (t_r, t_z, t_theta) More...

void	body_force (const double &time, const Vector< double > &x, Vector< double > &result)
	The body force function; returns vector of doubles in the order (b_r, b_z, b_theta) More...

void	exact_solution_th (const Vector< double > &x, Vector< double > &u)
	Helper function - spatial components of the exact solution in a vector. This is necessary because we need to multiply this by different things to obtain the velocity and acceleration 0: u_r, 1: u_z, 2: u_theta. More...

double	u_r (const double &time, const Vector< double > &x)
	Calculate the time dependent form of the r-component of displacement. More...

double	u_z (const double &time, const Vector< double > &x)
	Calculate the time dependent form of the z-component of displacement. More...

double	u_theta (const double &time, const Vector< double > &x)
	Calculate the time dependent form of the theta-component of displacement. More...

double	d_u_r_dt (const double &time, const Vector< double > &x)
	Calculate the time dependent form of the r-component of velocity. More...

double	d_u_z_dt (const double &time, const Vector< double > &x)
	Calculate the time dependent form of the z-component of velocity. More...

double	d_u_theta_dt (const double &time, const Vector< double > &x)
	Calculate the time dependent form of the theta-component of velocity. More...

double	d2_u_r_dt2 (const double &time, const Vector< double > &x)
	Calculate the time dependent form of the r-component of acceleration. More...

double	d2_u_z_dt2 (const double &time, const Vector< double > &x)
	Calculate the time dependent form of the z-component of acceleration. More...

double	d2_u_theta_dt2 (const double &time, const Vector< double > &x)
	Calculate the time dependent form of the theta-component of acceleration. More...

void	exact_solution (const double &time, const Vector< double > &x, Vector< double > &u)
	The exact solution in a vector: 0: u_r, 1: u_z, 2: u_theta and their 1st and 2nd derivs. More...

Variables
double	Nu = 0.3
	Define Poisson's ratio Nu. More...

double	E = 1.0
	Define the non-dimensional Young's modulus. More...

double	Lambda = ENu/(1.0+Nu)/(1.0-2.0Nu)
	Lame parameters. More...

double	Mu = E/2.0/(1.0+Nu)

double	Omega_sq = 0.5
	Square of the frequency of the time dependence. More...

unsigned	Nr = 5
	Number of elements in r-direction. More...

unsigned	Nz = 10
	Number of elements in z-direction. More...

double	Lr = 1.0
	Length of domain in r direction. More...

double	Lz = 2.0
	Length of domain in z-direction. More...

double	Rmin = 0.1
	Set up min r coordinate. More...

double	Zmin = 0.3
	Set up min z coordinate. More...

double	Rmax = Rmin+Lr
	Set up max r coordinate. More...

double	Zmax = Zmin+Lz
	Set up max z coordinate. More...

Detailed Description

Namespace for global parameters.

Function Documentation

◆ body_force()

void Global_Parameters::body_force	(	const double &	time,
		const Vector< double > &	x,
		Vector< double > &	result
	)

The body force function; returns vector of doubles in the order (b_r, b_z, b_theta)

Definition at line 96 of file cylinder.cc.

References Lambda, Mu, and Omega_sq.

Referenced by AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::AxisymmetricLinearElasticityProblem().

◆ boundary_traction()

void Global_Parameters::boundary_traction	(	const double &	time,
		const Vector< double > &	x,
		const Vector< double > &	n,
		Vector< double > &	result
	)

The traction function at r=Rmin: (t_r, t_z, t_theta)

Definition at line 83 of file cylinder.cc.

References Lambda, and Mu.

Referenced by AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::AxisymmetricLinearElasticityProblem().

◆ d2_u_r_dt2()

double Global_Parameters::d2_u_r_dt2	(	const double &	time,
		const Vector< double > &	x
	)

Calculate the time dependent form of the r-component of acceleration.

Definition at line 178 of file cylinder.cc.

References exact_solution_th().

Referenced by exact_solution(), AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_boundary_conditions(), and AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_initial_conditions().

◆ d2_u_theta_dt2()

double Global_Parameters::d2_u_theta_dt2	(	const double &	time,
		const Vector< double > &	x
	)

Calculate the time dependent form of the theta-component of acceleration.

Definition at line 194 of file cylinder.cc.

References exact_solution_th().

Referenced by exact_solution(), AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_boundary_conditions(), and AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_initial_conditions().

◆ d2_u_z_dt2()

double Global_Parameters::d2_u_z_dt2	(	const double &	time,
		const Vector< double > &	x
	)

Calculate the time dependent form of the z-component of acceleration.

Definition at line 186 of file cylinder.cc.

References exact_solution_th().

Referenced by exact_solution(), AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_boundary_conditions(), and AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_initial_conditions().

◆ d_u_r_dt()

double Global_Parameters::d_u_r_dt	(	const double &	time,
		const Vector< double > &	x
	)

Calculate the time dependent form of the r-component of velocity.

Definition at line 154 of file cylinder.cc.

References exact_solution_th().

Referenced by exact_solution(), AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_boundary_conditions(), and AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_initial_conditions().

◆ d_u_theta_dt()

double Global_Parameters::d_u_theta_dt	(	const double &	time,
		const Vector< double > &	x
	)

Calculate the time dependent form of the theta-component of velocity.

Definition at line 170 of file cylinder.cc.

References exact_solution_th().

Referenced by exact_solution(), AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_boundary_conditions(), and AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_initial_conditions().

◆ d_u_z_dt()

double Global_Parameters::d_u_z_dt	(	const double &	time,
		const Vector< double > &	x
	)

Calculate the time dependent form of the z-component of velocity.

Definition at line 162 of file cylinder.cc.

References exact_solution_th().

Referenced by exact_solution(), AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_boundary_conditions(), and AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_initial_conditions().

◆ exact_solution()

void Global_Parameters::exact_solution	(	const double &	time,
		const Vector< double > &	x,
		Vector< double > &	u
	)

The exact solution in a vector: 0: u_r, 1: u_z, 2: u_theta and their 1st and 2nd derivs.

Definition at line 203 of file cylinder.cc.

References d2_u_r_dt2(), d2_u_theta_dt2(), d2_u_z_dt2(), d_u_r_dt(), d_u_theta_dt(), d_u_z_dt(), u_r(), u_theta(), and u_z().

Referenced by AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::doc_solution(), and AxisymmetricLinearElasticityProblem< ELEMENT, TIMESTEPPER >::set_boundary_conditions().

◆ exact_solution_th()

void Global_Parameters::exact_solution_th	(	const Vector< double > &	x,
		Vector< double > &	u
	)

Helper function - spatial components of the exact solution in a vector. This is necessary because we need to multiply this by different things to obtain the velocity and acceleration 0: u_r, 1: u_z, 2: u_theta.

Definition at line 116 of file cylinder.cc.

Referenced by d2_u_r_dt2(), d2_u_theta_dt2(), d2_u_z_dt2(), d_u_r_dt(), d_u_theta_dt(), d_u_z_dt(), u_r(), u_theta(), and u_z().