TAPsFEMHexahedron.hpp

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/******************************************************************************
TAPsFEMHexahedron.hpp
******************************************************************************/
/******************************************************************************
SUKITTI PUNAK   (12/30/2009)
UPDATE          (07/01/2010)
******************************************************************************/
#ifndef TAPs_FEM_HEXAHEDRON_HPP
#define TAPs_FEM_HEXAHEDRON_HPP

#include "TAPsFEMElement.hpp"

//  Node Numbering Convention
//
//       7---------------6        ^ z / zeta
//      /|              /|        |
//     / |             / |        |    / y / eta
//    /  |            /  |        |   /
//   /   |           /   |        |  /
//  4---------------5    |        | /
//  |    |          |    |        |/          x / xi
//  |    3----------|----2        +------------->
//  |   /           |   /
//  |  /            |  /
//  | /             | /
//  |/              |/
//  0---------------1

BEGIN_NAMESPACE_TAPs__FEM
//=============================================================================
// Forward declaration
template <typename T> class MeshHexahedra;

template <typename T>
class Hexahedron : public Element<T> {
//=============================================================================
    friend  class MeshHexahedra<T>;
public:
    // Member Functions -------------------------------------------------------
    friend std::ostream & operator<< ( std::ostream &output, Hexahedron<T> const &obj )
    {
        output << obj.StrInfo();
        return output;
    }
    //-------------------------------------------------------------------------
    Hexahedron ( 
        std::vector< Vector3<T> > * deformedNodes,      
        std::vector< Vector3<T> > * undeformedNodes,    
        T YoungModulus,     
        T PoissionRatio,    
        unsigned int globalNode0,   
        unsigned int globalNode1,   
        unsigned int globalNode2,   
        unsigned int globalNode3,   
        unsigned int globalNode4,   
        unsigned int globalNode5,   
        unsigned int globalNode6,   
        unsigned int globalNode7    
    );
    //Hexahedron ( Hexahedron<T> const &orig );
    virtual ~Hexahedron ();
    //-------------------------------------------------------------------------
    virtual std::string StrInfo () const;
    //-------------------------------------------------------------------------
    //Hexahedron<T> & operator= ( Hexahedron<T> const &orig );

    //-------------------------------------------------------------------------
    // Get/Set Functions

    inline Matrix3x3<T> const & GetStiffnessMatrix ( unsigned int n, unsigned int m ) const;

    //-------------------------------------------------------------------------
    // Operations

    virtual inline Vector3<T> * const DeformedNode ( unsigned int i );

    virtual inline Vector3<T> * const UndeformedNode ( unsigned int i );

    inline Vector3<T> ComputeDeformedPositionBasedOnCoordinates ( T xi, T eta, T zeta );

    inline Vector3<T> ComputeUndeformedPositionBasedOnCoordinates ( T xi, T eta, T zeta );

    int EstimateParametricCoords ( 
        T x, T y, T z,          
        T &xi, T &eta, T &zeta  
    );

    //---------------------------------------------------------------
    // Inherited from FEMElement class
    //---------------------------------------------------------------
    inline void SetNode ( unsigned int i, unsigned int globalNodeNumber );

    //inline virtual void ResetToDeformedState ();

    inline virtual void ResetToUndeformedState ();

    inline virtual T    CalDeformedVolume () const;

    inline virtual T    CalUndeformedVolume ();

    virtual void UpdateStrainDisplacementMatrixElements ();

    virtual void UpdateStiffnessMatrixElements ();

    inline unsigned int GetGlobalNodeNumberFromLocalNode ( unsigned int i ) const
    {
        assert( 0 <= i && i <= 7 );
        return ids[i];
    }
    //---------------------------------------------------------------


    //---------------------------------------------------------------
    // Static Member Functions

    static inline void InterpolateShapeFunctions (
        T xi,           
        T eta,          
        T zeta,         
        T weights[8]    
    );

    static inline void InterpolateShapeFunctionDerivatives (
        T xi,           
        T eta,          
        T zeta,         
        T derivs[24]    
    );

    //-------------------------------------------
    // 1-point Gauss quadrature rule
    static void UpdateShapeFnsPartialDerivatives_1PtGuassRule ();
    //-------------------------------------------
    // 2-point Gauss quadrature rule
    static void UpdateShapeFnsPartialDerivatives_2PtGuassRule ();

    //-------------------------------------------------------------------------
    // Data Members -----------------------------------------------------------
//=============================================================================
protected:
    // Member Functions -------------------------------------------------------

    // Data Members -----------------------------------------------------------

    unsigned int    ids[8]; 

    // Element's properties
    //T b[8];   //!< element of strain-displacement matrix (B) with is partial diff by x
    //T c[8];   //!< element of strain-displacement matrix (B) with is partial diff by y
    //T d[8];   //!< element of strain-displacement matrix (B) with is partial diff by z

    // Stiffness matrix
    // The hexahedron stiffness matrix is a 24x24 matrix which can be broken into 8x8 of 3x3 matrices
    Matrix3x3<T>    Ke[8][8];   

//=============================================================================
private:
    // Member Functions -------------------------------------------------------

    static void CalAndStoreShapeFnsPartialDerivatives ( T store[], int ptNumber, T xi, T eta, T zeta );

    inline Matrix3x3<T> CalJacobian ( 
        T GaussStore[],     
        int GaussPtNumber   
    );

    virtual void UpdateStiffnessMatrixElements_1PtGauss ();

    virtual void UpdateStiffnessMatrixElements_2PtGauss ();


    // Data Members -----------------------------------------------------------

    static bool g_Is1PtGaussPointInit;  
    static bool g_Is2PtGaussPointInit;  
    //-------------------------------------------
    // 1-point Gauss quadrature rule
    static T g_1PtGauss_Der[8*3];   
    //Matrix3x3<T>  m_1ptGauss_JMatrices[1];    //!< Jacobian matrices for 1-point Gauss quadrature rule
    //-------------------------------------------
    // 2-point Gauss quadrature rule --> 8 pts for 3D
    static T g_2PtGauss_Der[8*3*8]; 
    //Matrix3x3<T>  m_2ptGauss_JMatrices[8];    //!< Jacobian matrices for 1-point Gauss quadrature rule

    // For finding an approximated parametric coordinates from a global coordinates
    static const int MAX_ITERATION; 
    static const T ERROR_THRESHOLD; 
    static const T NEG_BOUND;       
    static const T POS_BOUND;   
    static const T DIVERGENCE_THRESHOLD;    

//=============================================================================

#if defined(__gl_h_) || defined(__GL_H__)
public:
    virtual void Draw ();

    virtual void DrawUndeformedMesh ();

    virtual void DrawDeformedMesh ();
#endif

//=============================================================================
}; // END CLASS Hexahedron
//=============================================================================
END_NAMESPACE_TAPs__FEM
//-----------------------------------------------------------------------------
#include "TAPsFEMHexahedron.cpp"

// Include definition if TAPs_USE_EXPORT is not defined
//#if !defined( TAPs_USE_EXPORT )
//  #include "TAPsFEMHexahedron.cpp"
//#endif
//-----------------------------------------------------------------------------
#endif
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