quadrilateral_2d_4.h

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//    |  /           |
//    ' /   __| _` | __|  _ \   __|
//    . \  |   (   | |   (   |\__ `
//   _|\_\_|  \__,_|\__|\___/ ____/
//                   Multi-Physics
//
//  License:         BSD License
//                   Kratos default license: kratos/license.txt
//
//  Main authors:    Riccardo Rossi
//                   Janosch Stascheit
//                   Felix Nagel
//  contributors:    Hoang Giang Bui
//                   Josep Maria Carbonell
//
 
#pragma once
 
// System includes
 
// External includes
 
// Project includes
#include "geometries/line_2d_2.h"
#include "geometries/triangle_2d_3.h"
#include "utilities/integration_utilities.h"
#include "integration/quadrilateral_gauss_legendre_integration_points.h"
#include "integration/quadrilateral_collocation_integration_points.h"
 
namespace Kratos
{
 
 
 
 
 
template<class TPointType> class Quadrilateral2D4
    : public Geometry<TPointType>
{
public:
 
    typedef Geometry<TPointType> BaseType;
 
    typedef Line2D2<TPointType> EdgeType;
 
    KRATOS_CLASS_POINTER_DEFINITION( Quadrilateral2D4 );
 
    typedef GeometryData::IntegrationMethod IntegrationMethod;
 
    typedef typename BaseType::GeometriesArrayType GeometriesArrayType;
 
    typedef TPointType PointType;
 
    typedef typename BaseType::IndexType IndexType;
 
    typedef typename BaseType::SizeType SizeType;
 
    typedef  typename BaseType::PointsArrayType PointsArrayType;
 
    typedef typename BaseType::CoordinatesArrayType CoordinatesArrayType;
 
    typedef typename BaseType::IntegrationPointType IntegrationPointType;
 
    typedef typename BaseType::IntegrationPointsArrayType IntegrationPointsArrayType;
 
    typedef typename BaseType::IntegrationPointsContainerType IntegrationPointsContainerType;
 
    typedef typename BaseType::ShapeFunctionsValuesContainerType ShapeFunctionsValuesContainerType;
 
    typedef typename BaseType::ShapeFunctionsLocalGradientsContainerType ShapeFunctionsLocalGradientsContainerType;
 
    typedef typename BaseType::JacobiansType JacobiansType;
 
    typedef typename BaseType::ShapeFunctionsGradientsType ShapeFunctionsGradientsType;
 
    typedef typename BaseType::ShapeFunctionsSecondDerivativesType
    ShapeFunctionsSecondDerivativesType;
 
    typedef typename BaseType::ShapeFunctionsThirdDerivativesType
    ShapeFunctionsThirdDerivativesType;
 
    typedef typename BaseType::NormalType NormalType;
 
 
//     Quadrilateral2D4( const PointType& FirstPoint,
//                       const PointType& SecondPoint,
//                       const PointType& ThirdPoint,
//                       const PointType& FourthPoint )
//         : BaseType( PointsArrayType(), &msGeometryData )
//     {
//         this->Points().push_back( typename PointType::Pointer( new PointType( FirstPoint ) ) );
//         this->Points().push_back( typename PointType::Pointer( new PointType( SecondPoint ) ) );
//         this->Points().push_back( typename PointType::Pointer( new PointType( ThirdPoint ) ) );
//         this->Points().push_back( typename PointType::Pointer( new PointType( FourthPoint ) ) );
//     }
 
    Quadrilateral2D4( typename PointType::Pointer pFirstPoint,
                      typename PointType::Pointer pSecondPoint,
                      typename PointType::Pointer pThirdPoint,
                      typename PointType::Pointer pFourthPoint )
        : BaseType( PointsArrayType(), &msGeometryData )
    {
        this->Points().push_back( pFirstPoint );
        this->Points().push_back( pSecondPoint );
        this->Points().push_back( pThirdPoint );
        this->Points().push_back( pFourthPoint );
    }
 
    explicit Quadrilateral2D4( const PointsArrayType& rThisPoints )
        : BaseType( rThisPoints, &msGeometryData )
    {
        if ( this->PointsNumber() != 4 )
            KRATOS_ERROR << "Invalid points number. Expected 4, given " << this->PointsNumber() << std::endl;
    }
 
    explicit Quadrilateral2D4(
        const IndexType GeometryId,
        const PointsArrayType& rThisPoints
    ) : BaseType(GeometryId, rThisPoints, &msGeometryData)
    {
        KRATOS_ERROR_IF( this->PointsNumber() != 4 ) << "Invalid points number. Expected 4, given " << this->PointsNumber() << std::endl;
    }
 
    explicit Quadrilateral2D4(
        const std::string& rGeometryName,
        const PointsArrayType& rThisPoints
    ) : BaseType(rGeometryName, rThisPoints, &msGeometryData)
    {
        KRATOS_ERROR_IF(this->PointsNumber() != 4) << "Invalid points number. Expected 4, given " << this->PointsNumber() << std::endl;
    }
 
    Quadrilateral2D4( Quadrilateral2D4 const& rOther )
        : BaseType( rOther )
    {
    }
 
    template<class TOtherPointType> explicit Quadrilateral2D4( Quadrilateral2D4<TOtherPointType> const& rOther )
        : BaseType( rOther )
    {
    }
 
    ~Quadrilateral2D4() override {}
 
    GeometryData::KratosGeometryFamily GetGeometryFamily() const override
    {
        return GeometryData::KratosGeometryFamily::Kratos_Quadrilateral;
    }
 
    GeometryData::KratosGeometryType GetGeometryType() const override
    {
        return GeometryData::KratosGeometryType::Kratos_Quadrilateral2D4;
    }
 
 
    Quadrilateral2D4& operator=( const Quadrilateral2D4& rOther )
    {
        BaseType::operator=( rOther );
        return *this;
    }
 
    template<class TOtherPointType>
    Quadrilateral2D4& operator=( Quadrilateral2D4<TOtherPointType> const & rOther )
    {
        BaseType::operator=( rOther );
        return *this;
    }
 
 
    typename BaseType::Pointer Create(
        const IndexType NewGeometryId,
        PointsArrayType const& rThisPoints
        ) const override
    {
        return typename BaseType::Pointer( new Quadrilateral2D4( NewGeometryId, rThisPoints ) );
    }
 
    typename BaseType::Pointer Create(
        const IndexType NewGeometryId,
        const BaseType& rGeometry
    ) const override
    {
        auto p_geometry = typename BaseType::Pointer( new Quadrilateral2D4( NewGeometryId, rGeometry.Points() ) );
        p_geometry->SetData(rGeometry.GetData());
        return p_geometry;
    }
 
    SizeType PointsNumberInDirection(IndexType LocalDirectionIndex) const override
    {
        if ((LocalDirectionIndex == 0) || (LocalDirectionIndex == 1)) {
            return 2;
        }
        KRATOS_ERROR << "Possible direction index reaches from 0-1. Given direction index: "
            << LocalDirectionIndex << std::endl;
    }
 
    Matrix& PointsLocalCoordinates( Matrix& rResult ) const override
    {
        if (rResult.size1() != 4 || rResult.size2() != 2)
            rResult.resize(4, 2, false);
        rResult(0, 0) = -1.0;
        rResult(0, 1) = -1.0;
        rResult(1, 0) = 1.0;
        rResult(1, 1) = -1.0;
        rResult(2, 0) = 1.0;
        rResult(2, 1) = 1.0;
        rResult(3, 0) = -1.0;
        rResult(3, 1) = 1.0;
        return rResult;
    }
 
 
    double Length() const override
    {
        //return sqrt(fabs( DeterminantOfJacobian(PointType())));
        double length = 0.000;
        length = sqrt( fabs( Area() ) );
        return length;
 
    }
 
    double Area() const override
    {
        return IntegrationUtilities::ComputeArea2DGeometry(*this);
    }
 
    double Volume() const override
    {
        KRATOS_WARNING("Quadrilateral2D4") << "Method not well defined. Replace with DomainSize() instead. This method preserves current behaviour but will be changed in June 2023 (returning error instead)" << std::endl;
        return Area();
        // TODO: Replace in June 2023
        // KRATOS_ERROR << "Quadrilateral2D4:: Method not well defined. Replace with DomainSize() instead." << std::endl;
        // return 0.0;
    }
 
    double DomainSize() const override
    {
        return Area();
    }
 
    bool IsInside(
        const CoordinatesArrayType& rPoint,
        CoordinatesArrayType& rResult,
        const double Tolerance = std::numeric_limits<double>::epsilon()
        ) const override
    {
        this->PointLocalCoordinates( rResult, rPoint );
 
        if ( std::abs(rResult[0]) <= (1.0+Tolerance) )
        {
            if ( std::abs(rResult[1]) <= (1.0+Tolerance) )
            {
                return true;
            }
        }
 
        return false;
    }
 
 
    SizeType EdgesNumber() const override
    {
        return 4;
    }
 
    GeometriesArrayType GenerateEdges() const override
    {
        GeometriesArrayType edges = GeometriesArrayType();
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 0 ), this->pGetPoint( 1 ) ) );
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 1 ), this->pGetPoint( 2 ) ) );
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 2 ), this->pGetPoint( 3 ) ) );
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 3 ), this->pGetPoint( 0 ) ) );
        return edges;
    }
 
    bool HasIntersection( const Point& rLowPoint, const Point& rHighPoint ) const override
    {
        Triangle2D3<PointType> triangle_0 (this->pGetPoint( 0 ),
                                           this->pGetPoint( 1 ),
                                           this->pGetPoint( 2 )
        );
        Triangle2D3<PointType> triangle_1 (this->pGetPoint( 2 ),
                                           this->pGetPoint( 3 ),
                                           this->pGetPoint( 0 )
        );
 
        if      ( triangle_0.HasIntersection(rLowPoint, rHighPoint) ) return true;
        else if ( triangle_1.HasIntersection(rLowPoint, rHighPoint) ) return true;
        else return false;
    }
 
 
    double ShapeFunctionValue( IndexType ShapeFunctionIndex,
                                       const CoordinatesArrayType& rPoint ) const override
    {
        switch ( ShapeFunctionIndex )
        {
        case 0:
            return( 0.25*( 1.0 - rPoint[0] )*( 1.0 - rPoint[1] ) );
        case 1:
            return( 0.25*( 1.0 + rPoint[0] )*( 1.0 - rPoint[1] ) );
        case 2:
            return( 0.25*( 1.0 + rPoint[0] )*( 1.0 + rPoint[1] ) );
        case 3:
            return( 0.25*( 1.0 - rPoint[0] )*( 1.0 + rPoint[1] ) );
        default:
            KRATOS_ERROR << "Wrong index of shape function!" << *this << std::endl;
        }
 
        return 0;
    }
 
    Vector& ShapeFunctionsValues (Vector &rResult, const CoordinatesArrayType& rCoordinates) const override
    {
      if(rResult.size() != 4) rResult.resize(4,false);
      rResult[0] =  0.25*( 1.0 - rCoordinates[0] )*( 1.0 - rCoordinates[1] );
      rResult[1] =  0.25*( 1.0 + rCoordinates[0] )*( 1.0 - rCoordinates[1] );
      rResult[2] =  0.25*( 1.0 + rCoordinates[0] )*( 1.0 + rCoordinates[1] );
      rResult[3] =  0.25*( 1.0 - rCoordinates[0] )*( 1.0 + rCoordinates[1] );
 
        return rResult;
    }
 
 
 
 
    std::string Info() const override
    {
        return "2 dimensional quadrilateral with four nodes in 2D space";
    }
 
    void PrintInfo( std::ostream& rOStream ) const override
    {
        rOStream << "2 dimensional quadrilateral with four nodes in 2D space";
    }
 
    void PrintData( std::ostream& rOStream ) const override
    {
        // Base Geometry class PrintData call
        BaseType::PrintData( rOStream );
        std::cout << std::endl;
 
        // If the geometry has valid points, calculate and output its data
        if (this->AllPointsAreValid()) {
            Matrix jacobian;
            this->Jacobian( jacobian, PointType() );
            rOStream << "    Jacobian in the origin\t : " << jacobian;
        }
    }
 
    virtual ShapeFunctionsGradientsType ShapeFunctionsLocalGradients(
        IntegrationMethod ThisMethod )
    {
        ShapeFunctionsGradientsType localGradients
            = CalculateShapeFunctionsIntegrationPointsLocalGradients( ThisMethod );
        const int integration_points_number
            = msGeometryData.IntegrationPointsNumber( ThisMethod );
        ShapeFunctionsGradientsType Result( integration_points_number );
 
        for ( int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            Result[pnt] = localGradients[pnt];
        }
 
        return Result;
    }
 
    virtual ShapeFunctionsGradientsType ShapeFunctionsLocalGradients()
    {
        IntegrationMethod ThisMethod = msGeometryData.DefaultIntegrationMethod();
        ShapeFunctionsGradientsType localGradients
            = CalculateShapeFunctionsIntegrationPointsLocalGradients( ThisMethod );
        const int integration_points_number
            = msGeometryData.IntegrationPointsNumber( ThisMethod );
        ShapeFunctionsGradientsType Result( integration_points_number );
 
        for ( int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            Result[pnt] = localGradients[pnt];
        }
 
        return Result;
    }
 
    Matrix& ShapeFunctionsLocalGradients( Matrix& rResult,
            const CoordinatesArrayType& rPoint ) const override
    {
        rResult.resize( 4, 2 , false);
        noalias( rResult ) = ZeroMatrix( 4, 2 );
        rResult( 0, 0 ) = -0.25 * ( 1.0 - rPoint[1] );
        rResult( 0, 1 ) = -0.25 * ( 1.0 - rPoint[0] );
        rResult( 1, 0 ) =  0.25 * ( 1.0 - rPoint[1] );
        rResult( 1, 1 ) = -0.25 * ( 1.0 + rPoint[0] );
        rResult( 2, 0 ) =  0.25 * ( 1.0 + rPoint[1] );
        rResult( 2, 1 ) =  0.25 * ( 1.0 + rPoint[0] );
        rResult( 3, 0 ) = -0.25 * ( 1.0 + rPoint[1] );
        rResult( 3, 1 ) =  0.25 * ( 1.0 - rPoint[0] );
        return rResult;
    }
 
 
 
    virtual Matrix& ShapeFunctionsGradients( Matrix& rResult, PointType& rPoint )
    {
        rResult.resize( 4, 2 , false);
        rResult( 0, 0 ) = -0.25 * ( 1.0 - rPoint.Y() );
        rResult( 0, 1 ) = -0.25 * ( 1.0 - rPoint.X() );
        rResult( 1, 0 ) =  0.25 * ( 1.0 - rPoint.Y() );
        rResult( 1, 1 ) = -0.25 * ( 1.0 + rPoint.X() );
        rResult( 2, 0 ) =  0.25 * ( 1.0 + rPoint.Y() );
        rResult( 2, 1 ) =  0.25 * ( 1.0 + rPoint.X() );
        rResult( 3, 0 ) = -0.25 * ( 1.0 + rPoint.Y() );
        rResult( 3, 1 ) =  0.25 * ( 1.0 - rPoint.X() );
        return rResult;
    }
 
    ShapeFunctionsSecondDerivativesType& ShapeFunctionsSecondDerivatives( ShapeFunctionsSecondDerivativesType& rResult, const CoordinatesArrayType& rPoint ) const override
    {
        if ( rResult.size() != this->PointsNumber() )
        {
            // KLUDGE: While there is a bug in
            // ublas vector resize, I have to put this beside resizing!!
            ShapeFunctionsGradientsType temp( this->PointsNumber() );
            rResult.swap( temp );
        }
 
        rResult[0].resize( 2, 2 , false);
        rResult[1].resize( 2, 2 , false);
        rResult[2].resize( 2, 2 , false);
        rResult[3].resize( 2, 2 , false);
 
        rResult[0]( 0, 0 ) = 0.0;
        rResult[0]( 0, 1 ) = 0.25;
        rResult[0]( 1, 0 ) = 0.25;
        rResult[0]( 1, 1 ) = 0.0;
 
        rResult[1]( 0, 0 ) =  0.0;
        rResult[1]( 0, 1 ) = -0.25;
        rResult[1]( 1, 0 ) = -0.25;
        rResult[1]( 1, 1 ) =  0.0;
 
        rResult[2]( 0, 0 ) = 0.0;
        rResult[2]( 0, 1 ) = 0.25;
        rResult[2]( 1, 0 ) = 0.25;
        rResult[2]( 1, 1 ) = 0.0;
 
        rResult[3]( 0, 0 ) =  0.0;
        rResult[3]( 0, 1 ) = -0.25;
        rResult[3]( 1, 0 ) = -0.25;
        rResult[3]( 1, 1 ) =  0.0;
 
        return rResult;
    }
 
    ShapeFunctionsThirdDerivativesType& ShapeFunctionsThirdDerivatives( ShapeFunctionsThirdDerivativesType& rResult, const CoordinatesArrayType& rPoint ) const override
    {
        if ( rResult.size() != this->PointsNumber() )
        {
            // KLUDGE: While there is a bug in
            // ublas vector resize, I have to put this beside resizing!!
//                 ShapeFunctionsGradientsType
            ShapeFunctionsThirdDerivativesType temp( this->PointsNumber() );
            rResult.swap( temp );
        }
 
        for ( IndexType i = 0; i < rResult.size(); i++ )
        {
            DenseVector<Matrix> temp( this->PointsNumber() );
            rResult[i].swap( temp );
        }
 
        for ( unsigned int i = 0; i < this->PointsNumber(); i++ )
        {
            for ( unsigned int j = 0; j < 2; j++ )
            {
                rResult[i][j].resize( 2, 2 , false);
                noalias( rResult[i][j] ) = ZeroMatrix( 2, 2 );
            }
        }
 
//             rResult(0,0).resize( 2, 2);
//             rResult(0,1).resize( 2, 2);
//             rResult(1,0).resize( 2, 2);
//             rResult(1,1).resize( 2, 2);
//             rResult(2,0).resize( 2, 2);
//             rResult(2,1).resize( 2, 2);
//             rResult(3,0).resize( 2, 2);
//             rResult(3,0).resize( 2, 2);
 
        for ( int i = 0; i < 4; i++ )
        {
            rResult[i][0]( 0, 0 ) = 0.0;
            rResult[i][0]( 0, 1 ) = 0.0;
            rResult[i][0]( 1, 0 ) = 0.0;
            rResult[i][0]( 1, 1 ) = 0.0;
            rResult[i][1]( 0, 0 ) = 0.0;
            rResult[i][1]( 0, 1 ) = 0.0;
            rResult[i][1]( 1, 0 ) = 0.0;
            rResult[i][1]( 1, 1 ) = 0.0;
        }
 
        return rResult;
    }
 
 
 
protected:
private:
 
    static const GeometryData msGeometryData;
 
    static const GeometryDimension msGeometryDimension;
 
 
 
 
    friend class Serializer;
 
    void save( Serializer& rSerializer ) const override
    {
        KRATOS_SERIALIZE_SAVE_BASE_CLASS( rSerializer, BaseType );
    }
 
    void load( Serializer& rSerializer ) override
    {
        KRATOS_SERIALIZE_LOAD_BASE_CLASS( rSerializer, BaseType );
    }
 
    Quadrilateral2D4(): BaseType( PointsArrayType(), &msGeometryData ) {}
 
 
 
 
 
    static Matrix CalculateShapeFunctionsIntegrationPointsValues(
        typename BaseType::IntegrationMethod ThisMethod )
    {
        IntegrationPointsContainerType all_integration_points =
            AllIntegrationPoints();
        IntegrationPointsArrayType integration_points = all_integration_points[static_cast<int>(ThisMethod)];
        //number of integration points
        const int integration_points_number = integration_points.size();
        //number of nodes in current geometry
        const int points_number = 4;
        //setting up return matrix
        Matrix shape_function_values( integration_points_number, points_number );
        //loop over all integration points
 
        for ( int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            shape_function_values( pnt, 0 ) =
                0.25 * ( 1.0 - integration_points[pnt].X() )
                * ( 1.0 - integration_points[pnt].Y() );
            shape_function_values( pnt, 1 ) =
                0.25 * ( 1.0 + integration_points[pnt].X() )
                * ( 1.0 - integration_points[pnt].Y() );
            shape_function_values( pnt, 2 ) =
                0.25 * ( 1.0 + integration_points[pnt].X() )
                * ( 1.0 + integration_points[pnt].Y() );
            shape_function_values( pnt, 3 ) =
                0.25 * ( 1.0 - integration_points[pnt].X() )
                * ( 1.0 + integration_points[pnt].Y() );
        }
 
        return shape_function_values;
    }
 
    static ShapeFunctionsGradientsType
    CalculateShapeFunctionsIntegrationPointsLocalGradients(
        typename BaseType::IntegrationMethod ThisMethod )
    {
        IntegrationPointsContainerType all_integration_points =
            AllIntegrationPoints();
        IntegrationPointsArrayType integration_points = all_integration_points[static_cast<int>(ThisMethod)];
        //number of integration points
        const int integration_points_number = integration_points.size();
        ShapeFunctionsGradientsType d_shape_f_values( integration_points_number );
        //initialising container
        //std::fill(d_shape_f_values.begin(), d_shape_f_values.end(), Matrix(4,2));
        //loop over all integration points
 
        for ( int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            Matrix result( 4, 2 );
            result( 0, 0 ) = -0.25 * ( 1.0 - integration_points[pnt].Y() );
            result( 0, 1 ) = -0.25 * ( 1.0 - integration_points[pnt].X() );
            result( 1, 0 ) = 0.25 * ( 1.0 - integration_points[pnt].Y() );
            result( 1, 1 ) = -0.25 * ( 1.0 + integration_points[pnt].X() );
            result( 2, 0 ) = 0.25 * ( 1.0 + integration_points[pnt].Y() );
            result( 2, 1 ) = 0.25 * ( 1.0 + integration_points[pnt].X() );
            result( 3, 0 ) = -0.25 * ( 1.0 + integration_points[pnt].Y() );
            result( 3, 1 ) = 0.25 * ( 1.0 - integration_points[pnt].X() );
            d_shape_f_values[pnt] = result;
        }
 
        return d_shape_f_values;
    }
 
    static const IntegrationPointsContainerType AllIntegrationPoints()
    {
        IntegrationPointsContainerType integration_points =
        {
            {
                Quadrature < QuadrilateralGaussLegendreIntegrationPoints1,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralGaussLegendreIntegrationPoints2,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralGaussLegendreIntegrationPoints3,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralGaussLegendreIntegrationPoints4,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralGaussLegendreIntegrationPoints5,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralCollocationIntegrationPoints1,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralCollocationIntegrationPoints2,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralCollocationIntegrationPoints3,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralCollocationIntegrationPoints4,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralCollocationIntegrationPoints5,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints()
            }
        };
        return integration_points;
    }
 
    static const ShapeFunctionsValuesContainerType AllShapeFunctionsValues()
    {
        ShapeFunctionsValuesContainerType shape_functions_values =
        {
            {
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_1 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_2 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_3 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_4 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_5 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_1 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_2 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_3 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_4 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_5 )
            }
        };
        return shape_functions_values;
    }
 
    static const ShapeFunctionsLocalGradientsContainerType
    AllShapeFunctionsLocalGradients()
    {
        ShapeFunctionsLocalGradientsContainerType shape_functions_local_gradients =
        {
            {
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_1 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_2 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_3 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_4 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_5 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_1 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_2 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_3 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_4 ),
                Quadrilateral2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_5 ),
            }
        };
        return shape_functions_local_gradients;
    }
 
 
 
 
 
 
    template<class TOtherPointType> friend class Quadrilateral2D4;
 
 
 
}; // Class Geometry
 
 
 
 
template<class TPointType> inline std::istream& operator >> (
    std::istream& rIStream,
    Quadrilateral2D4<TPointType>& rThis );
template<class TPointType> inline std::ostream& operator << (
    std::ostream& rOStream,
    const Quadrilateral2D4<TPointType>& rThis )
{
    rThis.PrintInfo( rOStream );
    rOStream << std::endl;
    rThis.PrintData( rOStream );
    return rOStream;
}
 
 
template<class TPointType> const
GeometryData Quadrilateral2D4<TPointType>::msGeometryData(
    &msGeometryDimension,
    GeometryData::IntegrationMethod::GI_GAUSS_2,
    Quadrilateral2D4<TPointType>::AllIntegrationPoints(),
    Quadrilateral2D4<TPointType>::AllShapeFunctionsValues(),
    AllShapeFunctionsLocalGradients()
);
 
template<class TPointType> const
GeometryDimension Quadrilateral2D4<TPointType>::msGeometryDimension(2, 2);
 
}// namespace Kratos.