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GooseFEM::Mesh::Hex8
********************
[:download:`source: MeshHex8.h <../src/GooseFEM/MeshHex8.h>`]
[:download:`source: MeshHex8.cpp <../src/GooseFEM/MeshHex8.cpp>`]
Naming convention
=================
The following naming convention is used:
* **Front**: all nodes whose coordinates :math:`0 \leq x \leq L_x`, :math:`0 \leq y \leq L_y`, :math:`z = 0`.
* **Back**: all nodes whose coordinates :math:`0 \leq x \leq L_x`, :math:`0 \leq y \leq L_y`, :math:`z = L_z`.
* **Bottom**: all nodes whose coordinates :math:`0 \leq x \leq L_x`, :math:`0 \leq z \leq L_z`, :math:`y = 0`.
* **Top**: all nodes whose coordinates :math:`0 \leq x \leq L_x`, :math:`0 \leq z \leq L_z`, :math:`y = L_y`.
* **Left**: all nodes whose coordinates :math:`0 \leq y \leq L_y`, :math:`0 \leq z \leq L_z`, :math:`x = 0`.
* **Right**: all nodes whose coordinates :math:`0 \leq y \leq L_y`, :math:`0 \leq z \leq L_z`, :math:`x = L_x`.
The edges and corners follow from the intersections, i.e.
* **FrontBottomEdge**: all nodes whose coordinates :math:`0 \leq x \leq L_x`, :math:`y = 0`, :math:`z = 0`.
* ...
* **FrontBottomLeftCorner**: the node whose coordinate :math:`x = 0`, :math:`y = 0`, :math:`z = 0`.
* ...
.. image:: figures/MeshHex8/naming_convention.svg
:width: 350px
:align: center
``GooseFEM::Mesh::Hex8::Regular``
=================================
.. .. code-block:: cpp
.. GooseFEM::Mesh::Quad4::Regular(size_t nelx, size_t nely, double h=1.);
.. Regular mesh of linear quadrilaterals in two-dimensions. The element edges are all of the same size :math:`h` (by default equal to one), optional scaling can be applied afterwards. For example the mesh shown below that consists of 21 x 11 elements. In that image the element numbers are indicated with a color, and likewise for the boundary nodes.
.. Methods:
.. .. code-block:: cpp
.. // A matrix with on each row a nodal coordinate:
.. // [ x , y ]
.. MatD = GooseFEM::Mesh::Quad4::Regular.coor();
.. // A matrix with the connectivity, with on each row to the nodes of each element
.. MatS = GooseFEM::Mesh::Quad4::Regular.conn();
.. // A list of boundary nodes
.. ColS = GooseFEM::Mesh::Quad4::Regular.nodesBottom();
.. ColS = GooseFEM::Mesh::Quad4::Regular.nodesTop();
.. ColS = GooseFEM::Mesh::Quad4::Regular.nodesLeft();
.. ColS = GooseFEM::Mesh::Quad4::Regular.nodesRight();
.. // A matrix with periodic node pairs on each row:
.. // [ independent nodes, dependent nodes ]
.. MatS = GooseFEM::Mesh::Quad4::Regular.nodesPeriodic();
.. // The node at the origin
.. size_t = GooseFEM::Mesh::Quad4::Regular.nodeOrigin();
.. // A matrix with DOF-numbers: two per node in sequential order
.. MatS = GooseFEM::Mesh::Quad4::Regular.dofs();
.. // A matrix with DOF-numbers: two per node in sequential order
.. // All the periodic repetitions are eliminated from the system
.. MatS = GooseFEM::Mesh::Quad4::Regular.dofsPeriodic();
.. ``GooseFEM::Mesh::Quad4::FineLayer``
.. ====================================
.. Regular mesh with a fine layer of quadrilateral elements, and coarser elements above and below.
.. .. image:: figures/MeshQuad4/FineLayer/example.svg
.. :width: 500px
.. :align: center
.. .. note::
.. The coarsening depends strongly on the desired number of elements in horizontal elements. The becomes clear from the following example:
.. .. code-block:: cpp
.. mesh = GooseFEM::Mesh::Quad4::FineLayer(6*9 ,51); // left image : 546 elements
.. mesh = GooseFEM::Mesh::Quad4::FineLayer(6*9+3,51); // middle image : 703 elements
.. mesh = GooseFEM::Mesh::Quad4::FineLayer(6*9+1,51); // right image : 2915 elements
.. .. image:: figures/MeshQuad4/FineLayer/behavior.svg
.. :width: 1000px
.. :align: center
.. Methods:
.. .. code-block:: cpp
.. // A matrix with on each row a nodal coordinate:
.. // [ x , y ]
.. MatD = GooseFEM::Mesh::Quad4::Regular.coor();
.. // A matrix with the connectivity, with on each row to the nodes of each element
.. MatS = GooseFEM::Mesh::Quad4::Regular.conn();
.. // A list of boundary nodes
.. ColS = GooseFEM::Mesh::Quad4::Regular.nodesBottom();
.. ColS = GooseFEM::Mesh::Quad4::Regular.nodesTop();
.. ColS = GooseFEM::Mesh::Quad4::Regular.nodesLeft();
.. ColS = GooseFEM::Mesh::Quad4::Regular.nodesRight();
.. // A matrix with periodic node pairs on each row:
.. // [ independent nodes, dependent nodes ]
.. MatS = GooseFEM::Mesh::Quad4::Regular.nodesPeriodic();
.. // The node at the origin
.. size_t = GooseFEM::Mesh::Quad4::Regular.nodeOrigin();
.. // A matrix with DOF-numbers: two per node in sequential order
.. MatS = GooseFEM::Mesh::Quad4::Regular.dofs();
.. // A matrix with DOF-numbers: two per node in sequential order
.. // All the periodic repetitions are eliminated from the system
.. MatS = GooseFEM::Mesh::Quad4::Regular.dofsPeriodic();
.. // A list with the element numbers of the fine elements in the center of the mesh
.. // (highlighted in the plot below)
.. ColS = GooseFEM::Mesh::Quad4::FineLayer.elementsFine();
.. .. image:: figures/MeshQuad4/FineLayer/example_elementsFine.svg
.. :width: 500px
.. :align: center
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