1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
|
/*=========================================================================
*
* Copyright Insight Software Consortium
*
* 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
*
* http://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 itkFEMElement2DC0LinearQuadrilateral_h
#define itkFEMElement2DC0LinearQuadrilateral_h
#include "itkFEMElementStd.h"
#include "ITKFEMExport.h"
namespace itk
{
namespace fem
{
/**
* \class Element2DC0LinearQuadrilateral
* \brief 4-noded, linear, C0 continuous finite element in 2D space.
* \ingroup ITKFEM
*
* The ordering of the nodes is counter clockwise. That is the nodes
* should be defined in the following order:
*
* 3 (0,1) 2 (1,1)
* *------------------------*
* | |
* | |
* | |
* | |
* | |
* | |
* *------------------------*
* 0 (0,0) 1 (0,1)
*
* This is an abstract class. Specific concrete implementations of this
* It must be combined with the physics component of the problem.
* This has already been done in the following classes:
*
* \sa Element2DC0LinearQuadrilateralMembrane
* \sa Element2DC0LinearQuadrilateralStrain
* \sa Element2DC0LinearQuadrilateralStress
*/
class ITKFEM_EXPORT Element2DC0LinearQuadrilateral : public ElementStd<4, 2>
{
public:
/** Standard class typedefs. */
typedef Element2DC0LinearQuadrilateral Self;
typedef ElementStd<4, 2> TemplatedParentClass;
typedef TemplatedParentClass Superclass;
typedef SmartPointer<Self> Pointer;
typedef SmartPointer<const Self> ConstPointer;
/** Run-time type information (and related methods). */
itkTypeMacro(Element2DC0LinearQuadrilateral, TemplatedParentClass);
// ////////////////////////////////////////////////////////////////////////
/**
* Methods related to numeric integration
*/
enum { DefaultIntegrationOrder = 2 };
/** Get the Integration point and weight */
virtual void GetIntegrationPointAndWeight(unsigned int i, VectorType & pt, Float & w, unsigned int order) const ITK_OVERRIDE;
/** Get the number of integration points */
virtual unsigned int GetNumberOfIntegrationPoints(unsigned int order) const ITK_OVERRIDE;
// ////////////////////////////////////////////////////////////////////////
/**
* Methods related to the geometry of an element
*/
/** Return the shape functions used to interpolate across the element */
virtual VectorType ShapeFunctions(const VectorType & pt) const ITK_OVERRIDE;
/** Return the shape functions derivatives in the shapeD matrix */
virtual void ShapeFunctionDerivatives(const VectorType & pt, MatrixType & shapeD) const ITK_OVERRIDE;
/** Convert from global to local coordinates */
virtual bool GetLocalFromGlobalCoordinates(const VectorType & globalPt, VectorType & localPt) const ITK_OVERRIDE;
/** Interpolation Functions */
void InterpolationFunctions( const VectorType & pcoords, VectorType & sf) const;
/** Interpolation Derivatives */
void InterpolationDerivs(const VectorType & pcoords, VectorType & derivs) const;
/** Return the determinate of a 2x2 matrix */
Float Determinant2x2(const VectorType & c1, const VectorType & c2) const;
protected:
virtual void PopulateEdgeIds(void) ITK_OVERRIDE;
virtual void PrintSelf(std::ostream& os, Indent indent) const ITK_OVERRIDE;
private:
};
}
} // end namespace itk::fem
#endif // #ifndef itkFEMElement2DC0LinearQuadrilateral_h
|
