Reference documentation for deal.II version 8.5.1
Functions
LocalIntegrators::Elasticity Namespace Reference
Integrators

Local integrators related to elasticity problems. More...

Functions

template<int dim>
void cell_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double factor=1.)
 
template<int dim, typename number >
void cell_residual (Vector< number > &result, const FEValuesBase< dim > &fe, const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &input, double factor=1.)
 
template<int dim>
void nitsche_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, double penalty, double factor=1.)
 
template<int dim>
void nitsche_tangential_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, double penalty, double factor=1.)
 
template<int dim, typename number >
void nitsche_residual (Vector< number > &result, const FEValuesBase< dim > &fe, const VectorSlice< const std::vector< std::vector< double > > > &input, const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &Dinput, const VectorSlice< const std::vector< std::vector< double > > > &data, double penalty, double factor=1.)
 
template<int dim, typename number >
void nitsche_tangential_residual (Vector< number > &result, const FEValuesBase< dim > &fe, const VectorSlice< const std::vector< std::vector< double > > > &input, const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &Dinput, const VectorSlice< const std::vector< std::vector< double > > > &data, double penalty, double factor=1.)
 
template<int dim, typename number >
void nitsche_residual_homogeneous (Vector< number > &result, const FEValuesBase< dim > &fe, const VectorSlice< const std::vector< std::vector< double > > > &input, const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &Dinput, double penalty, double factor=1.)
 
template<int dim>
void ip_matrix (FullMatrix< double > &M11, FullMatrix< double > &M12, FullMatrix< double > &M21, FullMatrix< double > &M22, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, const double pen, const double int_factor=1., const double ext_factor=-1.)
 
template<int dim, typename number >
void ip_residual (Vector< number > &result1, Vector< number > &result2, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, const VectorSlice< const std::vector< std::vector< double > > > &input1, const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &Dinput1, const VectorSlice< const std::vector< std::vector< double > > > &input2, const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &Dinput2, double pen, double int_factor=1., double ext_factor=-1.)
 

Detailed Description

Local integrators related to elasticity problems.

Author
Guido Kanschat
Date
2010

Function Documentation

◆ cell_matrix()

template<int dim>
void LocalIntegrators::Elasticity::cell_matrix ( FullMatrix< double > &  M,
const FEValuesBase< dim > &  fe,
const double  factor = 1. 
)
inline

The linear elasticity operator in weak form, namely double contraction of symmetric gradients.

\[ \int_Z \varepsilon(u): \varepsilon(v)\,dx \]

Definition at line 48 of file elasticity.h.

◆ cell_residual()

template<int dim, typename number >
void LocalIntegrators::Elasticity::cell_residual ( Vector< number > &  result,
const FEValuesBase< dim > &  fe,
const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &  input,
double  factor = 1. 
)
inline

Vector-valued residual operator for linear elasticity in weak form

\[ - \int_Z \varepsilon(u): \varepsilon(v) \,dx \]

Definition at line 80 of file elasticity.h.

◆ nitsche_matrix()

template<int dim>
void LocalIntegrators::Elasticity::nitsche_matrix ( FullMatrix< double > &  M,
const FEValuesBase< dim > &  fe,
double  penalty,
double  factor = 1. 
)
inline

The matrix for the weak boundary condition of Nitsche type for linear elasticity:

\[ \int_F \Bigl(\gamma u \cdot v - n^T \epsilon(u) v - u \epsilon(v) n\Bigr)\;ds. \]

Definition at line 115 of file elasticity.h.

◆ nitsche_tangential_matrix()

template<int dim>
void LocalIntegrators::Elasticity::nitsche_tangential_matrix ( FullMatrix< double > &  M,
const FEValuesBase< dim > &  fe,
double  penalty,
double  factor = 1. 
)
inline

The matrix for the weak boundary condition of Nitsche type for the tangential displacement in linear elasticity:

\[ \int_F \Bigl(\gamma u_\tau \cdot v_\tau - n^T \epsilon(u_\tau) v_\tau - u_\tau^T \epsilon(v_\tau) n\Bigr)\;ds. \]

Definition at line 160 of file elasticity.h.

◆ nitsche_residual()

template<int dim, typename number >
void LocalIntegrators::Elasticity::nitsche_residual ( Vector< number > &  result,
const FEValuesBase< dim > &  fe,
const VectorSlice< const std::vector< std::vector< double > > > &  input,
const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &  Dinput,
const VectorSlice< const std::vector< std::vector< double > > > &  data,
double  penalty,
double  factor = 1. 
)

Weak boundary condition for the elasticity operator by Nitsche, namely on the face F the vector

\[ \int_F \Bigl(\gamma (u-g) \cdot v - n^T \epsilon(u) v - (u-g) \epsilon(v) n^T\Bigr)\;ds. \]

Here, u is the finite element function whose values and gradient are given in the arguments input and Dinput, respectively. g is the inhomogeneous boundary value in the argument data. $n$ is the outer normal vector and $\gamma$ is the usual penalty parameter.

Author
Guido Kanschat
Date
2013

Definition at line 231 of file elasticity.h.

◆ nitsche_tangential_residual()

template<int dim, typename number >
void LocalIntegrators::Elasticity::nitsche_tangential_residual ( Vector< number > &  result,
const FEValuesBase< dim > &  fe,
const VectorSlice< const std::vector< std::vector< double > > > &  input,
const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &  Dinput,
const VectorSlice< const std::vector< std::vector< double > > > &  data,
double  penalty,
double  factor = 1. 
)
inline

The weak boundary condition of Nitsche type for the tangential displacement in linear elasticity:

\[ \int_F \Bigl(\gamma (u_\tau-g_\tau) \cdot v_\tau - n^T \epsilon(u_\tau) v - (u_\tau-g_\tau) \epsilon(v_\tau) n\Bigr)\;ds. \]

Definition at line 279 of file elasticity.h.

◆ nitsche_residual_homogeneous()

template<int dim, typename number >
void LocalIntegrators::Elasticity::nitsche_residual_homogeneous ( Vector< number > &  result,
const FEValuesBase< dim > &  fe,
const VectorSlice< const std::vector< std::vector< double > > > &  input,
const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &  Dinput,
double  penalty,
double  factor = 1. 
)

Homogeneous weak boundary condition for the elasticity operator by Nitsche, namely on the face F the vector

\[ \int_F \Bigl(\gamma u \cdot v - n^T \epsilon(u) v - u \epsilon(v) n^T\Bigr)\;ds. \]

Here, u is the finite element function whose values and gradient are given in the arguments input and Dinput, respectively. $n$ is the outer normal vector and $\gamma$ is the usual penalty parameter.

Author
Guido Kanschat
Date
2013

Definition at line 354 of file elasticity.h.

◆ ip_matrix()

template<int dim>
void LocalIntegrators::Elasticity::ip_matrix ( FullMatrix< double > &  M11,
FullMatrix< double > &  M12,
FullMatrix< double > &  M21,
FullMatrix< double > &  M22,
const FEValuesBase< dim > &  fe1,
const FEValuesBase< dim > &  fe2,
const double  pen,
const double  int_factor = 1.,
const double  ext_factor = -1. 
)
inline

The interior penalty flux for symmetric gradients.

Definition at line 396 of file elasticity.h.

◆ ip_residual()

template<int dim, typename number >
void LocalIntegrators::Elasticity::ip_residual ( Vector< number > &  result1,
Vector< number > &  result2,
const FEValuesBase< dim > &  fe1,
const FEValuesBase< dim > &  fe2,
const VectorSlice< const std::vector< std::vector< double > > > &  input1,
const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &  Dinput1,
const VectorSlice< const std::vector< std::vector< double > > > &  input2,
const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &  Dinput2,
double  pen,
double  int_factor = 1.,
double  ext_factor = -1. 
)

Elasticity residual term for the symmetric interior penalty method.

Author
Guido Kanschat
Date
2013

Definition at line 476 of file elasticity.h.

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