FEMDocumentation`
FEMDocumentation`

HexahedronElement

HexahedronElement[{{i11,,i18},,{in1,,in8}}]

represents n linear hexahedron elements ek with incidents {ik1,ik8}.

HexahedronElement[{{i11,,i120},,{in1,,in20}}]

represents n quadratic hexahedron elements ek with incidents {ik1,,ik20}.

HexahedronElement[{e1,,en},{m1,,mn}]

represents n hexahedron elements ek and n integer markers mk.

Details and OptionsDetails
  • HexahedronElement is used to represent hexahedron mesh elements in ElementMesh.
  • HexahedronElement can be used as an input to ToElementMesh or ToBoundaryMesh.
  • Incidents ikj are integers that index an array of spatial coordinates. The coordinates referenced by ek={ik1,} are the nodes of the k^(th) triangle.
  • The first three incidents ik1 until ik8 are always vertices.
  • For quadratic triangle elements, the next 12 incidents are mid-side nodes of possibly curved edges.
  • Linear elements are order 1 elements and quadratic elements are order 2 elements.
  • In HexahedronElement[{e1,,en}], all elements ek need to be of the same order.
  • The hexahedra in HexahedronElement[{e1,,en}] will share common nodes, edges, and faces, but cannot intersect with each other or with themselves.
  • The nodes for a linear and a quadratic hexahedron are shown:
  • For a HexahedronElement, the incidents on the faces must be counterclockwise when viewed from inside the element. An element {i1,,i8} has face incidents {i1,i2,i3,i4}, {i8,i7,i6,i5}, {i1,i5,i6,i2}, {i2,i6,i7,i3}, {i3,i7,i8,i4}, and {i4,i8,i5,i1} for the six faces.
  • The hexahedron element is known in the finite element method as a Lagrange element.
  • Examples

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    Basic Examples  (1)

    Load the package:

    In[1]:=
    Click for copyable input

    Create a mesh with one quad element:

    In[2]:=
    Click for copyable input
    Out[2]=

    Generalizations & Extensions  (4)

    Applications  (1)

    Possible Issues  (6)

    See Also

    ToElementMesh  ToBoundaryMesh  ElementMesh  PointElement  LineElement  TriangleElement  QuadElement  TetrahedronElement

    Tutorials