Reference solution ===================== Calculation method used for the reference solution -------------------------------------------------------- The reference arrow is calculated on a very fine mesh with HEXA20 elements. It is considered to be the reference solution. It corresponds to the C model. Benchmark results ---------------------- **Elasticity**: +---------+-------------------------------------------------------------------------------------------------------------------------------------------+---------+ |**Point**|**Size and unit** |**Value**| +---------+-------------------------------------------------------------------------------------------------------------------------------------------+---------+ |:math:`P`|Arrow |3.72 | + + + + | | | | + + .. image:: images/Object_5.svg + + | | :width: 18 | | + + :height: 25 + + | | | | + + + + | | | | + + + + | | | | + + (:math:`\mathrm{mm}`) + + | | | | +---------+-------------------------------------------------------------------------------------------------------------------------------------------+---------+ |:math:`P`|Arrow |-0.439 | + + + + | | | | + + .. image:: images/Object_6.svg + + | | :width: 18 | | + + :height: 25 + + | | | | + + + + | | | | + + + + | | | | + + (:math:`\mathrm{mm}`) + + | | | | +---------+-------------------------------------------------------------------------------------------------------------------------------------------+---------+ **Plasticity**: (Von Mises law with isotropic work hardening) +---------+-------------------------------------------------------------------------------------------------------------------------------------------+---------+ |**Point**|**Size and unit** |**Value**| +---------+-------------------------------------------------------------------------------------------------------------------------------------------+---------+ |:math:`P`|Arrow |4.548 | + + + + | | | | + + .. image:: images/Object_7.svg + + | | :width: 18 | | + + :height: 25 + + | | | | + + + + | | | | + + + + | | | | + + (:math:`\mathrm{mm}`) + + | | | | +---------+-------------------------------------------------------------------------------------------------------------------------------------------+---------+ |:math:`P`|Arrow |-0.5127 | + + + + | | | | + + .. image:: images/Object_8.svg + + | | :width: 18 | | + + :height: 25 + + | | | | + + + + | | | | + + + + | | | | + + (:math:`\mathrm{mm}`) + + | | | | +---------+-------------------------------------------------------------------------------------------------------------------------------------------+---------+ Bibliographical references --------------------------- [:ref:`1 <1>`] [:ref:`R3.06.11 `] Aster reference document: Sub-integrated HEXA8 finite elements stabilized by the ASM method. X.Desroches [:ref:`2 <2>`] T.Belytschko and L.P.Bindeman. Assumed strain stabilization of the eight node hexahedral element. *Computer Methods in Applied Mechanics and Engineering, 105 (1993), pp 225-260* [:ref:`3 <3>`] F.Abed-Meraïm and A.Combescure. Stabilization of under-integrated finite elements. *Internal Report No. 247 LMT -Cachan, January 2001*