Global_Parameters Namespace Reference

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)

## 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 = E*Nu/(1.0+Nu)/(1.0-2.0*Nu)
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

 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 100 of file cylinder.cc.

References Lambda, Mu, and Omega_sq.

 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 87 of file cylinder.cc.

References Lambda, and Mu.

 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 182 of file cylinder.cc.

References exact_solution_th().

 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 198 of file cylinder.cc.

References exact_solution_th().

 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 190 of file cylinder.cc.

References exact_solution_th().

 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 158 of file cylinder.cc.

References exact_solution_th().

 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 174 of file cylinder.cc.

References exact_solution_th().

 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 166 of file cylinder.cc.

References exact_solution_th().

 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 207 of file cylinder.cc.

 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 120 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().

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

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

Definition at line 134 of file cylinder.cc.

References exact_solution_th().

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

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

Definition at line 150 of file cylinder.cc.

References exact_solution_th().

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

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

Definition at line 142 of file cylinder.cc.

References exact_solution_th().

## Variable Documentation

 double Global_Parameters::E = 1.0

Define the non-dimensional Young's modulus.

Definition at line 53 of file cylinder.cc.

 double Global_Parameters::Lambda = E*Nu/(1.0+Nu)/(1.0-2.0*Nu)

Lame parameters.

Definition at line 56 of file cylinder.cc.

Referenced by body_force(), and boundary_traction().

 double Global_Parameters::Lr = 1.0

Length of domain in r direction.

Definition at line 69 of file cylinder.cc.

 double Global_Parameters::Lz = 2.0

Length of domain in z-direction.

Definition at line 72 of file cylinder.cc.

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

Definition at line 57 of file cylinder.cc.

Referenced by body_force(), and boundary_traction().

 unsigned Global_Parameters::Nr = 5

Number of elements in r-direction.

Definition at line 63 of file cylinder.cc.

 double Global_Parameters::Nu = 0.3

Define Poisson's ratio Nu.

Definition at line 50 of file cylinder.cc.

 unsigned Global_Parameters::Nz = 10

Number of elements in z-direction.

Definition at line 66 of file cylinder.cc.

 double Global_Parameters::Omega_sq = 0.5

Square of the frequency of the time dependence.

Definition at line 60 of file cylinder.cc.

 double Global_Parameters::Rmax = Rmin+Lr

Set up max r coordinate.

Definition at line 81 of file cylinder.cc.

 double Global_Parameters::Rmin = 0.1

Set up min r coordinate.

Definition at line 75 of file cylinder.cc.

 double Global_Parameters::Zmax = Zmin+Lz

Set up max z coordinate.

Definition at line 84 of file cylinder.cc.

 double Global_Parameters::Zmin = 0.3

Set up min z coordinate.

Definition at line 78 of file cylinder.cc.