Element traits for 8-node trilinear hexahedron (Hex8) More...

#include <Hex8.hpp>

Collaboration diagram for DNDS::Geom::Elem::ElementTraits< Hex8 >:

Static Public Member Functions
static constexpr ElemType	GetFaceType (t_index)
	Get the element type of a face.

Static Public Attributes
static constexpr ElemType	elemType = Hex8

static constexpr int	dim = 3

static constexpr int	order = 1

static constexpr int	numVertices = 8

static constexpr int	numNodes = 8

static constexpr int	numFaces = 6

static constexpr ParamSpace	paramSpace = HexSpace

static constexpr t_real	paramSpaceVol = 8.0

static constexpr std::array< t_real, 3 *8 >	standardCoords
	Standard coordinates of nodes in parametric space.

static constexpr std::array< std::array< t_index, 10 >, 6 >	faceNodes
	Node indices for each face (bilinear quad)

static constexpr ElemType	elevatedType = Hex27
	Element type after order elevation (O1 -> O2) Hex8 elevates to Hex27 (27-node triquadratic hex)

static constexpr int	numElevNodes = 19
	Number of additional nodes created during elevation.

static constexpr std::array< tElevSpan, 19 >	elevSpans
	Elevation spans define new node connections.

static constexpr std::array< ElemType, 19 >	elevNodeSpanTypes
	Element type of each elevation span.

static constexpr int	vtkCellType = 12
	VTK cell type identifier (12 = VTK_HEXAHEDRON)

static constexpr std::array< int, 8 >	vtkNodeOrder = {0, 1, 2, 3, 4, 5, 6, 7}
	VTK node ordering map.

Detailed Description

Element traits for 8-node trilinear hexahedron (Hex8)

Hex8 is the simplest 3D hexahedral element, commonly used for:

Structured hexahedral meshes
Boundary-fitted grids
Isoparametric mapping of complex geometries

Geometry:

Reference hex: xi, eta, zeta in [-1, 1]
8 nodes at the corners of the reference cube
Parametric space volume = 8.0

Faces:

6 faces, each is a Quad4 element

Definition at line 182 of file Hex8.hpp.

Member Function Documentation

◆ GetFaceType()

static constexpr ElemType DNDS::Geom::Elem::ElementTraits< Hex8 >::GetFaceType ( t_index )

inlinestaticconstexpr

Get the element type of a face.

Returns: Quad4 (all faces of hex are bilinear quads)

Definition at line 229 of file Hex8.hpp.

Member Data Documentation

◆ dim

constexpr int DNDS::Geom::Elem::ElementTraits< Hex8 >::dim = 3

staticconstexpr

Definition at line 189 of file Hex8.hpp.

◆ elemType

constexpr ElemType DNDS::Geom::Elem::ElementTraits< Hex8 >::elemType = Hex8

staticconstexpr

Definition at line 188 of file Hex8.hpp.

◆ elevatedType

constexpr ElemType DNDS::Geom::Elem::ElementTraits< Hex8 >::elevatedType = Hex27

staticconstexpr

Element type after order elevation (O1 -> O2) Hex8 elevates to Hex27 (27-node triquadratic hex)

Definition at line 257 of file Hex8.hpp.

◆ elevNodeSpanTypes

constexpr std::array<ElemType, 19> DNDS::Geom::Elem::ElementTraits< Hex8 >::elevNodeSpanTypes

staticconstexpr

Initial value:

= {
            Line2, Line2, Line2, Line2,    
            Line2, Line2, Line2, Line2,    
            Line2, Line2, Line2, Line2,    
            Quad4, Quad4, Quad4, Quad4, Quad4, Quad4,  
            Hex8}

Element type of each elevation span.

Definition at line 285 of file Hex8.hpp.

◆ elevSpans

constexpr std::array<tElevSpan, 19> DNDS::Geom::Elem::ElementTraits< Hex8 >::elevSpans

staticconstexpr

Initial value:

= {{
            
            {0, 1}, {1, 2}, {2, 3}, {3, 0},
            
            {0, 4}, {1, 5}, {2, 6}, {3, 7},
            
            {4, 5}, {5, 6}, {6, 7}, {7, 4},
            
            {0, 3, 2, 1}, {0, 1, 5, 4},
            {1, 2, 6, 5}, {2, 3, 7, 6},
            {0, 4, 7, 3}, {4, 5, 6, 7},
            
            {0, 1, 2, 3, 4, 5, 6, 7}}}

Elevation spans define new node connections.

Elevation creates 19 new nodes: Spans 0-11: edge midpoints (12 edges) Spans 12-17: face centers (6 faces) Span 18: body center (all 8 vertices)

Definition at line 270 of file Hex8.hpp.

◆ faceNodes

constexpr std::array<std::array<t_index, 10>, 6> DNDS::Geom::Elem::ElementTraits< Hex8 >::faceNodes

staticconstexpr

Initial value:

= {{
            {0, 3, 2, 1},    
            {0, 1, 5, 4},    
            {1, 2, 6, 5},    
            {2, 3, 7, 6},    
            {0, 4, 7, 3},    
            {4, 5, 6, 7}}}

Node indices for each face (bilinear quad)

Face 0: bottom face (z=-1, nodes 0-3-2-1) - note reversed for outward normal Face 1: back face (y=-1, nodes 0-1-5-4) Face 2: right face (x=+1, nodes 1-2-6-5) Face 3: front face (y=+1, nodes 2-3-7-6) Face 4: left face (x=-1, nodes 3-0-4-7) Face 5: top face (z=+1, nodes 4-5-6-7)

Definition at line 241 of file Hex8.hpp.

◆ numElevNodes

constexpr int DNDS::Geom::Elem::ElementTraits< Hex8 >::numElevNodes = 19

staticconstexpr

Number of additional nodes created during elevation.

Definition at line 260 of file Hex8.hpp.

◆ numFaces

constexpr int DNDS::Geom::Elem::ElementTraits< Hex8 >::numFaces = 6

staticconstexpr

Definition at line 193 of file Hex8.hpp.

◆ numNodes

constexpr int DNDS::Geom::Elem::ElementTraits< Hex8 >::numNodes = 8

staticconstexpr

Definition at line 192 of file Hex8.hpp.

◆ numVertices

constexpr int DNDS::Geom::Elem::ElementTraits< Hex8 >::numVertices = 8

staticconstexpr

Definition at line 191 of file Hex8.hpp.

◆ order

constexpr int DNDS::Geom::Elem::ElementTraits< Hex8 >::order = 1

staticconstexpr

Definition at line 190 of file Hex8.hpp.

◆ paramSpace

constexpr ParamSpace DNDS::Geom::Elem::ElementTraits< Hex8 >::paramSpace = HexSpace

staticconstexpr

Definition at line 194 of file Hex8.hpp.

◆ paramSpaceVol

constexpr t_real DNDS::Geom::Elem::ElementTraits< Hex8 >::paramSpaceVol = 8.0

staticconstexpr

Definition at line 195 of file Hex8.hpp.

◆ standardCoords

constexpr std::array<t_real, 3 * 8> DNDS::Geom::Elem::ElementTraits< Hex8 >::standardCoords

staticconstexpr

Initial value:

= {
            -1, -1, -1,   
             1, -1, -1,   
             1,  1, -1,   
            -1,  1, -1,   
            -1, -1,  1,   
             1, -1,  1,   
             1,  1,  1,   
            -1,  1,  1}

Standard coordinates of nodes in parametric space.

Reference cube [-1,1]^3 with nodes at corners. Standard ordering: bottom face (z=-1) counter-clockwise, then top face (z=+1) counter-clockwise.

Node 0-3: bottom face (z = -1) Node 4-7: top face (z = +1)

Definition at line 211 of file Hex8.hpp.

◆ vtkCellType

constexpr int DNDS::Geom::Elem::ElementTraits< Hex8 >::vtkCellType = 12

staticconstexpr

VTK cell type identifier (12 = VTK_HEXAHEDRON)

Definition at line 297 of file Hex8.hpp.

◆ vtkNodeOrder

constexpr std::array<int, 8> DNDS::Geom::Elem::ElementTraits< Hex8 >::vtkNodeOrder = {0, 1, 2, 3, 4, 5, 6, 7}

staticconstexpr

VTK node ordering map.

VTK uses the same ordering as DNDS for Hex8: VTK nodes 0-7 = corner nodes 0-7

Definition at line 305 of file Hex8.hpp.

The documentation for this struct was generated from the following file:

/home/runner/work/DNDSR/DNDSR/src/Geom/Elements/Hex8.hpp

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ GetFaceType()

Member Data Documentation

◆ dim

◆ elemType

◆ elevatedType

◆ elevNodeSpanTypes

◆ elevSpans

◆ faceNodes

◆ numElevNodes

◆ numFaces

◆ numNodes

◆ numVertices

◆ order

◆ paramSpace

◆ paramSpaceVol

◆ standardCoords

◆ vtkCellType

◆ vtkNodeOrder