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MeshQuad4.rst
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GooseFEM::Mesh::Quad4
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[:download:`GooseFEM/MeshQuad4.h <../src/GooseFEM/MeshQuad4.h>`, :download:`GooseFEM/MeshQuad4.cpp <../src/GooseFEM/MeshQuad4.cpp>`]
``GooseFEM::Mesh::Quad4::Regular``
==================================
.. todo::
Update
.. 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.
.. image:: figures/MeshQuad4/Regular/example.svg
:width: 500px
: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();
``GooseFEM::Mesh::Quad4::FineLayer``
====================================
.. todo::
Update
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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