Modellations ============= Depending on the models, the objects are meshed with different elements: **Modeling A:** cube: 1 HEXA8 element with 8 nodes faces: 1 QUAD4 element with 4 knots **Modeling B:** cube: 6 elements TETRA4 with 4 nodes faces: 2 TRIA3 elements with 3 knots **C modeling:** same modeling as in A with quadratic elements **D modeling:** same modeling as in B with quadratic elements **3.1** **Tested quantities and results of modeling A** Modeling A consists of a CUB8 element for the cube and a QUA4 element for each face. The behavior is elastic (commands MECA_STATIQUE then STAT_NON_LINE (check)). The values given by EPSI_ELGA; EPSI_ELNO, SIEF_ELGA, SIEF_ELNO,,,, SIEF_ELGA, SIGM_ELNO are tested at various points in the main directions of the reinforcement plies, obtained respectively with the commands MECA_STATIQUE and STAT_NON_LINE. For **MECA_STATIQUE**: +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |Integration points |EPSI_ELGA (in the main direction of the reinforcing sheet) |SIEF_ELGA (in the main direction of the reinforcing sheet) | + +----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ | |*Aster_code* |Reference|Gap (:math:`\text{\%}`)|*Aster_code* |Reference |Ecart| +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA1 — Point 1 (tablecloth GEOZ)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA2 — Point 1 (tablecloth GEOZ)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA3 — Point 1 (tablecloth GEOY)|1.8264 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA4 — Point 1 (tablecloth GEOY)|1.8264 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA5 — Point 1 (tablecloth GEOX)|2 |2 |0 |4E11 |4E11 |0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA6 — Point 1 (tablecloth GEOX)|2 |2 |0 |4E11 |4E11 |0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ +---------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |Bow |EPSI_ELNO (in the main direction of the reinforcing sheet) |SIGM_ELNO (in the main direction of the reinforcing sheet) | + +----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ | |*Aster_code* |Reference|Gap (:math:`\text{\%}`)|*Aster_code* |Reference |Ecart| +---------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |NO1 (tablecloth GEOZ)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +---------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |NO1 (tablecloth GEOY)|1.8264 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +---------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |NO1 (tablecloth GEOX)|2 |2 |0 |4E11 |4E11 |0 | +---------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ For **STAT_NON_LINE** +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |Integration points |EPSI_ELGA (in the main direction of the reinforcing sheet) |SIEF_ELGA (in the main direction of the reinforcing sheet) | + +----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ | |*Aster_code* |Reference|Gap (:math:`\text{\%}`)|*Aster_code* |Reference |Ecart| +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA1 — Point 1 (tablecloth GEOZ)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA2 — Point 1 (tablecloth GEOZ)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA3 — Point 1 (tablecloth GEOY)|1.8264 |1.8263 |0.003 |3.6527E11 |3.6527E11 |0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA4 — Point 1 (tablecloth GEOY)|1.8264 |1.8263 |0.003 |3.6527E11 |3.6527E11 |0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA5 — Point 1 (tablecloth GEOX)|2 |2 |0 |4E11 |4E11 |0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA6 — Point 1 (tablecloth GEOX)|2 |2 |0 |4E11 |4E11 |0 | +-------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ +---------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |Bow |EPSI_ELNO (in the main direction of the reinforcing sheet) |SIEF_ELNO (in the main direction of the reinforcing sheet) | + +----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ | |*Aster_code* |Reference|Gap (:math:`\text{\%}`)|*Aster_code* |Reference |Ecart| +---------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA1 - NO1 (GEOZ tablecloth)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +---------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA2 - NO1 (GEOY tablecloth)|1.8264 |1.8263 |0.003 |3.6527E11 |3.6527E11 |0 | +---------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA3 - NO1 (GEOX tablecloth)|2 |2 |0 |4E11 |4E11 |0 | +---------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ The total potential energy value is also tested using calculation STAT_NON_LINE. The analytical solution is calculated from all the uniaxial deformations in the grids, from the equation: .. image:: images/Object_11.svg :width: 139 :height: 46 .. _RefImage_Object_11.svg: where :math:`A` refers to the elasticity tensor. The results obtained are as follows: .. csv-table:: "", "*Code_Aster*", "Analytical reference", "Variance" "Total potential energy (:math:`J`)", "2.8173E10", "2.8173E10", "0" **3.2** **Tested quantities and B modeling results** Model B consists of six TETRA4 elements for the cube and two TRIA3 elements for each face. The behavior is elastic using the MECA_STATIQUE command and then the STAT_NON_LINE command (check). The values given by EPSI_ELGA; EPSI_ELNO, SIEF_ELGA, SIEF_ELNO;;;; SIEF_ELGA; SIGM_ELNO are tested at various points in the main directions of the reinforcement plies, obtained respectively with the commands MECA_STATIQUE and STAT_NON_LINE. For **MECA_STATIQUE**: +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |Integration points |EPSI_ELGA (in the main direction of the reinforcing sheet) |SIEF_ELGA (in the main direction of the reinforcing sheet) | + +----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ | |*Aster_code* |Reference|Gap (:math:`\text{\%}`)|*Aster_code* |Reference |Ecart| +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA1 — Point 1 (tablecloth GEOZ) |1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA2 — Point 1 (tablecloth GEOZ) |1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA3 — Point 1 (tablecloth GEOZ) |1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA4 — Point 1 (tablecloth GEOZ) |1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA5 — Point 1 (tablecloth GEOX) |2 |2 |0 |4E11 |4E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA6 — Point 1 (tablecloth GEOX) |2 |2 |0 |4E11 |4E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA11 — Point 1 (tablecloth GEOZ)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA21 — Point 1 (tablecloth GEOZ)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA31 — Point 1 (tablecloth GEOY)|1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA41 — Point 1 (tablecloth GEOY)|1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA51 — Point 1 (tablecloth GEOX)|2 |2 |0 |4E11 |4E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA61 — Point 1 (tablecloth GEOX)|2 |2 |0 |4E11 |4E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |Bow |EPSI_ELNO (in the main direction of the reinforcing sheet) |SIGM_ELNO (in the main direction of the reinforcing sheet) | + +----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ | |*Aster_code* |Reference|Gap (:math:`\text{\%}`)|*Aster_code* |Reference |Ecart| +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA1 - NO1 (GEOZ tablecloth) |1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA2 - NO1 (GEOY tablecloth) |1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA3 - NO1 (GEOX tablecloth) |2 |2 |0 |4E11 |4E11 |0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA11 - NO1 (GEOZ tablecloth)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA21 - NO1 (GEOY tablecloth)|1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA31 - NO1 (GEOX tablecloth)|2 |2 |0 |4E11 |4E11 |0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ For **STAT_NON_LINE** +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |Integration points |EPSI_ELGA (in the main direction of the reinforcing sheet) |SIEF_ELGA (in the main direction of the reinforcing sheet) | + +----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ | |*Aster_code* |Reference|Gap (:math:`\text{\%}`)|*Aster_code* |Reference |Ecart| +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA1 — Point 1 (tablecloth GEOZ) |1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA2 — Point 1 (tablecloth GEOZ) |1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA3 — Point 1 (tablecloth GEOY) |1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA4 — Point 1 (tablecloth GEOY) |1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA5 — Point 1 (tablecloth GEOX) |2 |2 |0 |4E11 |4E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA6 — Point 1 (tablecloth GEOX) |2 |2 |0 |4E11 |4E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA11 — Point 1 (tablecloth GEOZ)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA21 — Point 1 (tablecloth GEOZ)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA31 — Point 1 (tablecloth GEOY)|1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA41 — Point 1 (tablecloth GEOY)|1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA51 — Point 1 (tablecloth GEOX)|2 |2 |0 |4E11 |4E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA61 — Point 1 (tablecloth GEOX)|2 |2 |0 |4E11 |4E11 |0 | +--------------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |Bow |EPSI_ELNO (in the main direction of the reinforcing sheet) |SIEF_ELNO (in the main direction of the reinforcing sheet) | + +----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ | |*Aster_code* |Reference|Gap (:math:`\text{\%}`)|*Aster_code* |Reference |Ecart| +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA1 - NO1 (GEOZ tablecloth) |1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA2 - NO1 (GEOY tablecloth) |1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA3 - NO1 (GEOX tablecloth) |2 |2 |0 |4E11 |4E11 |0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA11 - NO1 (GEOZ tablecloth)|1.067 |1.067 |0.001 |2.13397E11 |2.13397E11|0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA21 - NO1 (GEOY tablecloth)|1.8263 |1.8263 |0 |3.6527E11 |3.6527E11 |0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+ |MA31 - NO1 (GEOX tablecloth)|2 |2 |0 |4E11 |4E11 |0 | +----------------------------+----------------------------------------------------------+---------+-----------------------+----------------------------------------------------------+----------+-----+