Modeling A ============== In this modeling, for pressure loading, loading is applied using a constant distributed pressure or constant surface forces for load 1, and a distributed pressure or distributed forces functions of :math:`z` for load 2. In this modeling, for surface force loading, loading is applied using constant surface forces for load No. 1, and surface forces based on :math:`z` for load No. 2. Characteristics of the mesh ---------------------------- The structure is meshed with hexahedra with 8 knots. The number of elements is as small as possible, i.e. one element along the :math:`\mathrm{Ox}` axis, 2 elements along the :math:`\mathrm{Oy}` axis (in order to be able to define the nodes in the middle plane at :math:`y=\mathrm{LY}/2`), and 5 elements along the :math:`\mathrm{Oz}` axis. Along the :math:`\mathrm{Oz}` axis, the number of elements is odd so that the interface does not coincide with the faces of the elements; the 3 layers of central elements use X- FEM elements, and the 2 layers of elements at the top and bottom use conventional elements. .. image:: images/100000000000027F000002D9CB9138DC7306F743.png :width: 2.0665in :height: 2.3626in .. _RefImage_100000000000027F000002D9CB9138DC7306F743.png: **Figure** 2.1-1 **: 3D mesh** Features tested ----------------------- The PRES_REP keyword of the AFFE_CHAR_MECA [:ref:`U4.44.01 `] operator makes it possible to apply a constant distributed pressure to skin elements. When pressure is a function or a formula, we use the PRES_REP keyword from AFFE_CHAR_MECA_F [:ref:`U4.44.01 `]). This feature is tested with load #2. In fact, with X- FEM, you cannot define an upper and lower lateral surface as a group of elements. In the present case, a single group of elements comprising all the lateral surface cells is defined, and a pressure that is a function of :math:`z` is applied to this group of elements. The FORCE_FACE keyword of the AFFE_CHAR_MECA [:ref:`U4.44.01 `] operator makes it possible to apply a constant surface force to skin elements. When surface strength is a function or a formula, we use the FORCE_FACE keyword from AFFE_CHAR_MECA_F [:ref:`U4.44.01 `]). Tested sizes and results ------------------------------ The POST_MAIL_XFEM operator makes it possible to mesh the cracks represented by the X- FEM method. The operator POST_CHAM_XFEM then makes it possible to export the results X- FEM to this new mesh. These two operators should only be used after the calculation in post-processing views. They allow nodes to be generated just below and above the interface and to show their movements. For each lateral face of the structure (:math:`y=0` and :math:`y=\mathrm{LY}`), we test the movements of the nodes located just above and just below the level set. Compression loading (pressure loading) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. csv-table:: "**Identification**", "**Reference**" ":math:`\mathrm{DY}` for all nodes on the left surface located just below the interface", "10-6" ":math:`\mathrm{DY}` for all nodes on the left surface located just above the interface", "10-6" ":math:`\mathrm{DY}` for all nodes on the right surface located just below the interface", "-10-6" ":math:`\mathrm{DY}` for all nodes on the right surface located just above the interface", "-10-6" Compression loading/traction (pressure loading) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. csv-table:: "**Identification**", "**Reference**" ":math:`\mathrm{DY}` for all nodes on the left surface located just below the interface", "-10-6" ":math:`\mathrm{DY}` for all nodes on the left surface located just above the interface", "10-6" ":math:`\mathrm{DY}` for all nodes on the right surface located just below the interface", "10-6" ":math:`\mathrm{DY}` for all nodes on the right surface located just above the interface", "-10-6" Compression loading (surface force loading) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. csv-table:: "**Identification**", "**Reference**" ":math:`\mathrm{DY}` for all nodes on the left surface located just below the interface", "10-6" ":math:`\mathrm{DY}` for all nodes on the left surface located just above the interface", "10-6" ":math:`\mathrm{DY}` for all nodes on the right surface located just below the interface", "-10-6" ":math:`\mathrm{DY}` for all nodes on the right surface located just above the interface", "-10-6" Compression/tensile loading (surface force loading) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. csv-table:: "**Identification**", "**Reference**" ":math:`\mathrm{DY}` for all nodes on the left surface located just below the interface", "-10-6" ":math:`\mathrm{DY}` for all nodes on the left surface located just above the interface", "10-6" ":math:`\mathrm{DY}` for all nodes on the right surface located just below the interface", "10-6" ":math:`\mathrm{DY}` for all nodes on the right surface located just above the interface", "-10-6" To test all the nodes at once, we test the minimum and the maximum of the column.