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/*=========================================================================
*
* Copyright NumFOCUS
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* https://www.apache.org/licenses/LICENSE-2.0.txt
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*=========================================================================*/
#ifndef itkFEMElement2DC0QuadraticTriangular_h
#define itkFEMElement2DC0QuadraticTriangular_h
#include "itkFEMElementStd.h"
#include "ITKFEMExport.h"
namespace itk
{
namespace fem
{
/**
* \class Element2DC0QuadraticTriangular
* \ingroup ITKFEM
* \brief 6-noded, quadratic, C0 continuous finite element in 2D space
* that defines a triangle.
*
* The ordering of the nodes is counter clockwise. That is the nodes
* should be defined in the following order:
*
* (0,1)
* 2
* *
* |\
* | \
* | \
*(0,0.5) 5 * * 4 (0.5, 0.5)
* | \
* | \
* *-----*-----*
* 0 3 1
* (0,0) (0,0.5) (0,1)
*
* This class defines the geometry of the FE problem.
* It must be combined with the physics component of the problem.
* This has already been done in the following classes:
*
* \sa Element2DC0QuadraticTriangularStrain
* \sa Element2DC0QuadraticTriangularStress
*/
class ITKFEM_EXPORT Element2DC0QuadraticTriangular : public ElementStd<6, 2>
{
public:
/** Standard class type aliases. */
using Self = Element2DC0QuadraticTriangular;
using TemplatedParentClass = ElementStd<6, 2>;
using Superclass = TemplatedParentClass;
using Pointer = SmartPointer<Self>;
using ConstPointer = SmartPointer<const Self>;
/** \see LightObject::GetNameOfClass() */
itkOverrideGetNameOfClassMacro(Element2DC0QuadraticTriangular);
// ////////////////////////////////////////////////////////////////////////
/**
* Methods related to numeric integration
*/
enum
{
DefaultIntegrationOrder = 2
};
/** Get the Integration point and weight */
void
GetIntegrationPointAndWeight(unsigned int i, VectorType & pt, Float & w, unsigned int order) const override;
/** Get the number of integration points */
unsigned int
GetNumberOfIntegrationPoints(unsigned int order) const override;
// ////////////////////////////////////////////////////////////////////////
/**
* Methods related to the geometry of an element
*/
/** Return the shape functions used to interpolate across the element */
VectorType
ShapeFunctions(const VectorType & pt) const override;
/** Return the shape functions derivatives in the shapeD matrix */
void
ShapeFunctionDerivatives(const VectorType & pt, MatrixType & shapeD) const override;
/** Convert from global to local coordinates */
bool
GetLocalFromGlobalCoordinates(const VectorType & GlobalPt, VectorType & LocalPt) const override;
// Since the Jacobian is not quadratic, we need to provide our
// own implementation of calculating the determinant and inverse.
Float
JacobianDeterminant(const VectorType & pt, const MatrixType * pJ = nullptr) const override;
/** Compute the inverse of the Jacobian matrix */
void
JacobianInverse(const VectorType & pt, MatrixType & invJ, const MatrixType * pJ = nullptr) const override;
protected:
void
PrintSelf(std::ostream & os, Indent indent) const override;
void
PopulateEdgeIds() override;
};
} // end namespace fem
} // end namespace itk
#endif // itkFEMElement2DC0QuadraticTriangular_h
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