oomph::TimeHarmonicElasticityTensor Class Reference

#include <time_harmonic_elasticity_tensor.h>

Inheritance diagram for oomph::TimeHarmonicElasticityTensor:

Public Member Functions
virtual	~TimeHarmonicElasticityTensor ()
	Empty virtual Destructor. More...
double	operator() (const unsigned &i, const unsigned &j, const unsigned &k, const unsigned &l) const

Protected Member Functions
virtual double	independent_component (const unsigned &i) const
void	range_check (const unsigned &i, const unsigned &j, const unsigned &k, const unsigned &l) const
	TimeHarmonicElasticityTensor ()
	Empty Constructor. More...

Static Private Attributes
static const unsigned	Index [3][3][3][3]

Detailed Description

A base class that represents the fourth-rank elasticity tensor \(E_{ijkl}\) defined such that

\[\tau_{ij} = E_{ijkl} e_{kl},\]

where \(e_{ij}\) is the infinitessimal (Cauchy) strain tensor and \(\tau_{ij}\) is the stress tensor. The symmetries of the tensor are such that

\[E_{ijkl} = E_{jikl} = E_{ijlk} = E_{klij}\]

and thus there are relatively few independent components. These symmetries are included in the definition of the object so that non-physical symmetries cannot be accidentally imposed.

Constructor & Destructor Documentation

TimeHarmonicElasticityTensor()

oomph::TimeHarmonicElasticityTensor::TimeHarmonicElasticityTensor ( )

inlineprotected

Empty Constructor.

{}

~TimeHarmonicElasticityTensor()

virtual oomph::TimeHarmonicElasticityTensor::~TimeHarmonicElasticityTensor ( )

inlinevirtual

Empty virtual Destructor.

{}

Member Function Documentation

independent_component()

virtual double oomph::TimeHarmonicElasticityTensor::independent_component ( const unsigned &  i ) const

inlineprotectedvirtual

Member function that returns the i-th independent component of the elasticity tensor

Reimplemented in oomph::TimeHarmonicIsotropicElasticityTensor.

    {
      return 0.0;
    }

Referenced by operator()().

operator()()

double oomph::TimeHarmonicElasticityTensor::operator() ( const unsigned &  i, const unsigned &  j, const unsigned &  k, const unsigned &  l  ) const

inline

Return the appropriate independent component via the index translation scheme (const version).

    {
      // Range check
#ifdef PARANOID
      range_check(i, j, k, l);
#endif
      return independent_component(Index[i][j][k][l]);
    }

References i, independent_component(), Index, j, k, and range_check().

range_check()

void oomph::TimeHarmonicElasticityTensor::range_check ( const unsigned &  i, const unsigned &  j, const unsigned &  k, const unsigned &  l  ) const

inlineprotected

Helper range checking function (Note that this only captures over-runs in 3D but errors are likely to be caught in evaluation of the stress and strain tensors anyway...)

    {
      if ((i > 2) || (j > 2) || (k > 2) || (l > 2))
      {
        std::ostringstream error_message;
        if (i > 2)
        {
          error_message << "Range Error : Index 1 " << i
                        << " is not in the range (0,2)";
        }
        if (j > 2)
        {
          error_message << "Range Error : Index 2 " << j
                        << " is not in the range (0,2)";
        }
 
        if (k > 2)
        {
          error_message << "Range Error : Index 2 " << k
                        << " is not in the range (0,2)";
        }
 
        if (l > 2)
        {
          error_message << "Range Error : Index 4 " << l
                        << " is not in the range (0,2)";
        }
 
        // Throw the error
        throw OomphLibError(error_message.str(),
                            OOMPH_CURRENT_FUNCTION,
                            OOMPH_EXCEPTION_LOCATION);
      }
    }

References i, j, k, OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

Referenced by operator()().

Member Data Documentation

Index

const unsigned oomph::TimeHarmonicElasticityTensor::Index

staticprivate

Initial value:

= {
    {{{0, 1, 6}, {1, 2, 7}, {6, 7, 8}},
     {{1, 3, 9}, {3, 4, 10}, {9, 10, 11}},
     {{6, 9, 12}, {9, 13, 14}, {12, 14, 15}}},
 
    {{{1, 3, 9}, {3, 4, 10}, {9, 10, 11}},
     {{2, 4, 13}, {4, 5, 16}, {13, 16, 17}},
     {{7, 10, 14}, {10, 16, 18}, {14, 18, 19}}},
 
    {{{6, 9, 12}, {9, 13, 14}, {12, 14, 15}},
     {{7, 10, 14}, {10, 16, 18}, {14, 18, 19}},
     {{8, 11, 15}, {11, 17, 19}, {15, 19, 20}}}}

Translation table from the four indices to the corresponding independent component

Translation scheme that takes account of the symmetries of the tensor. The independent coefficients are related to the coefficients of the elasticity tensor as follows: /

\[\begin{array}{cc} 0 & E_{1111} \\ 1 & E_{1112} \\ 2 & E_{1122} \\ 3 & E_{1212} \\ 4 & E_{1222} \\ 5 & E_{2222} \\ 6 & E_{1113} \\ 7 & E_{1123} \\ 8 & E_{1133} \\ 9 & E_{1213} \\ 10 & E_{1223} \\ 11 & E_{1233} \\ 12 & E_{1313} \\ 13 & E_{1322} \\ 14 & E_{1323} \\ 15 & E_{1333} \\ 16 & E_{2223} \\ 17 & E_{2233} \\ 18 & E_{2323} \\ 19 & E_{2333} \\ 20 & E_{3333} \end{array}\]

/

Referenced by operator()().

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

• time_harmonic_elasticity_tensor.h
• time_harmonic_elasticity_tensor.cc