Detailed Description

A 8-nodes Hexahedron Element.

Hex:
              6
        7-----------6
       /:          /|
      / :         / |
    7/  :        /5 |
    / 11:       /   | 10
   /    : 4    /    |
  4-----------5     |
  |     :     | 2   |
  |     3.....|.....2
  |    .      |    /
8 |   .       |9  /
  | 3.        |  / 1
  | .         | /
  |.          |/
  0-----------1
        0

Definition at line 46 of file HexRule8.h.

#include <HexRule8.h>

Inheritance diagram for MeshLib::HexRule8:

[legend]

Collaboration diagram for MeshLib::HexRule8:

[legend]

Public Types
using	EdgeReturn = MeshLib::LinearEdgeReturn
	Returns the i-th edge of the element. More...

Static Public Member Functions
static const Element *	getFace (const Element *e, unsigned i)
	Returns the i-th face of the element. More...

static bool	isPntInElement (Node const const nodes, MathLib::Point3d const &pnt, double eps)

static ElementErrorCode	validate (const Element *e)

static unsigned	identifyFace (Node const const , Node const *nodes[3])
	Returns the ID of a face given an array of nodes. More...

static double	computeVolume (Node const const _nodes)
	Calculates the volume of a convex hexahedron by partitioning it into six tetrahedra. More...

Static Public Member Functions inherited from MeshLib::CellRule
static bool	testElementNodeOrder (Element const &e)

Static Public Attributes
static const unsigned	n_base_nodes = 8u
	Constant: The number of base nodes for this element. More...

static const unsigned	n_all_nodes = 8u
	Constant: The number of all nodes for this element. More...

static const MeshElemType	mesh_elem_type = MeshElemType::HEXAHEDRON
	Constant: The geometric type of the element. More...

static const CellType	cell_type = CellType::HEX8
	Constant: The FEM type of the element. More...

static const unsigned	n_faces = 6
	Constant: The number of faces. More...

static const unsigned	n_edges = 12
	Constant: The number of edges. More...

static const unsigned	n_neighbors = 6
	Constant: The number of neighbors. More...

static const unsigned	face_nodes [6][4]
	Constant: Local node index table for faces. More...

static const unsigned	edge_nodes [12][2]
	Constant: Local node index table for edge. More...

Static Public Attributes inherited from MeshLib::CellRule
static const unsigned	dimension = 3u
	Constant: Dimension of this mesh element. More...

Member Typedef Documentation

◆ EdgeReturn

using MeshLib::HexRule8::EdgeReturn = MeshLib::LinearEdgeReturn

Returns the i-th edge of the element.

Definition at line 77 of file HexRule8.h.

Member Function Documentation

◆ computeVolume()

double MeshLib::HexRule8::computeVolume ( Node const *const * _nodes )

static

Calculates the volume of a convex hexahedron by partitioning it into six tetrahedra.

Definition at line 62 of file HexRule8.cpp.

 {
     return MathLib::calcTetrahedronVolume(
                *_nodes[4], *_nodes[7], *_nodes[5], *_nodes[0]) +
            MathLib::calcTetrahedronVolume(
                *_nodes[5], *_nodes[3], *_nodes[1], *_nodes[0]) +
            MathLib::calcTetrahedronVolume(
                *_nodes[5], *_nodes[7], *_nodes[3], *_nodes[0]) +
            MathLib::calcTetrahedronVolume(
                *_nodes[5], *_nodes[7], *_nodes[6], *_nodes[2]) +
            MathLib::calcTetrahedronVolume(
                *_nodes[1], *_nodes[3], *_nodes[5], *_nodes[2]) +
            MathLib::calcTetrahedronVolume(
                *_nodes[3], *_nodes[7], *_nodes[5], *_nodes[2]);
 }

References MathLib::calcTetrahedronVolume().

◆ getFace()

const Element * MeshLib::HexRule8::getFace	(	const Element *	e,
		unsigned	i
	)

static

Returns the i-th face of the element.

Definition at line 47 of file HexRule8.cpp.

 {
     if (i < n_faces)
     {
         std::array<Node*, 4> nodes{};
         for (unsigned j = 0; j < 4; j++)
         {
             nodes[j] = const_cast<Node*>(e->getNode(face_nodes[i][j]));
         }
         return new Quad(nodes, e->getID());
     }
     ERR("Error in MeshLib::Element::getFace() - Index {:d} does not exist.", i);
     return nullptr;
 }

References ERR(), face_nodes, MeshLib::Element::getID(), MeshLib::Element::getNode(), and n_faces.

◆ identifyFace()

unsigned MeshLib::HexRule8::identifyFace	(	Node const const	_nodes,
		Node const *	nodes[3]
	)

static

Returns the ID of a face given an array of nodes.

Definition at line 96 of file HexRule8.cpp.

 {
     for (unsigned i = 0; i < 6; i++)
     {
         unsigned flag(0);
         for (unsigned j = 0; j < 4; j++)
         {
             for (unsigned k = 0; k < 3; k++)
             {
                 if (_nodes[face_nodes[i][j]] == nodes[k])
                 {
                     flag++;
                 }
             }
         }
         if (flag == 3)
         {
             return i;
         }
     }
     return std::numeric_limits<unsigned>::max();
 }

References face_nodes.

◆ isPntInElement()

bool MeshLib::HexRule8::isPntInElement	(	Node const const	nodes,
		MathLib::Point3d const &	pnt,
		double	eps
	)

static

Checks if a point is inside the element.

Parameters

pnt	a 3D MathLib::Point3d object
eps	tolerance for numerical algorithm used or computing the property

Returns: true if the point is not outside the element, false otherwise

Parameters

nodes the nodes of the element.

Definition at line 78 of file HexRule8.cpp.

 {
     return (MathLib::isPointInTetrahedron(
                 pnt, *nodes[4], *nodes[7], *nodes[5], *nodes[0], eps) ||
             MathLib::isPointInTetrahedron(
                 pnt, *nodes[5], *nodes[3], *nodes[1], *nodes[0], eps) ||
             MathLib::isPointInTetrahedron(
                 pnt, *nodes[5], *nodes[7], *nodes[3], *nodes[0], eps) ||
             MathLib::isPointInTetrahedron(
                 pnt, *nodes[5], *nodes[7], *nodes[6], *nodes[2], eps) ||
             MathLib::isPointInTetrahedron(
                 pnt, *nodes[1], *nodes[3], *nodes[5], *nodes[2], eps) ||
             MathLib::isPointInTetrahedron(
                 pnt, *nodes[3], *nodes[7], *nodes[5], *nodes[2], eps));
 }

References MathLib::isPointInTetrahedron().

◆ validate()

ElementErrorCode MeshLib::HexRule8::validate ( const Element * e )

static

Tests if the element is geometrically valid.

Definition at line 119 of file HexRule8.cpp.

 {
     ElementErrorCode error_code;
     error_code[ElementErrorFlag::ZeroVolume] = hasZeroVolume(*e);
  
     for (unsigned i = 0; i < 6; ++i)
     {
         if (error_code.all())
         {
             break;
         }
  
         const MeshLib::Element* quad(e->getFace(i));
         error_code |= quad->validate();
         delete quad;
     }
     error_code[ElementErrorFlag::NodeOrder] = !e->testElementNodeOrder();
     return error_code;
 }

References MeshLib::Element::getFace(), MeshLib::hasZeroVolume(), NodeOrder, MeshLib::Element::testElementNodeOrder(), MeshLib::Element::validate(), and ZeroVolume.

Member Data Documentation

◆ cell_type

const CellType MeshLib::HexRule8::cell_type = CellType::HEX8

static

Constant: The FEM type of the element.

Definition at line 59 of file HexRule8.h.

◆ edge_nodes

const unsigned MeshLib::HexRule8::edge_nodes

static

Initial value:

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

Constant: Local node index table for edge.

Definition at line 74 of file HexRule8.h.

◆ face_nodes

const unsigned MeshLib::HexRule8::face_nodes

static

Initial value:

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

Constant: Local node index table for faces.

Definition at line 71 of file HexRule8.h.

Referenced by getFace(), and identifyFace().

◆ mesh_elem_type

const MeshElemType MeshLib::HexRule8::mesh_elem_type = MeshElemType::HEXAHEDRON

static

Constant: The geometric type of the element.

Definition at line 56 of file HexRule8.h.

◆ n_all_nodes

const unsigned MeshLib::HexRule8::n_all_nodes = 8u

static

Constant: The number of all nodes for this element.

Definition at line 53 of file HexRule8.h.

◆ n_base_nodes

const unsigned MeshLib::HexRule8::n_base_nodes = 8u

static

Constant: The number of base nodes for this element.

Definition at line 50 of file HexRule8.h.

◆ n_edges

const unsigned MeshLib::HexRule8::n_edges = 12

static

Constant: The number of edges.

Definition at line 65 of file HexRule8.h.

◆ n_faces

const unsigned MeshLib::HexRule8::n_faces = 6

static

Constant: The number of faces.

Definition at line 62 of file HexRule8.h.

Referenced by MeshLib::HexRule20::getFace(), and getFace().

◆ n_neighbors

const unsigned MeshLib::HexRule8::n_neighbors = 6

static

Constant: The number of neighbors.

Definition at line 68 of file HexRule8.h.

The documentation for this class was generated from the following files:

MeshLib/Elements/HexRule8.h
MeshLib/Elements/HexRule8.cpp

Detailed Description

Public Types

Static Public Member Functions

Static Public Attributes

Member Typedef Documentation

◆ EdgeReturn

Member Function Documentation

◆ computeVolume()

◆ getFace()

◆ identifyFace()

◆ isPntInElement()

◆ validate()

Member Data Documentation

◆ cell_type

◆ edge_nodes

◆ face_nodes

◆ mesh_elem_type

◆ n_all_nodes

◆ n_base_nodes

◆ n_edges

◆ n_faces

◆ n_neighbors