F modeling ============== Characteristics of modeling ----------------------------------- 4 POU_D_TGM elements with a hollow circular section: 4 SEG2 meshes .. csv-table:: "elements :math:`\mathrm{AC}` and :math:`\mathrm{BC}` ", "radius: :math:`R=8.305164{10}^{-3}m` Thickness: :math:`e=0.006m` ", "air :math:`A=2.{10}^{-4}{m}^{2}`" "elements :math:`\mathrm{CD}` and :math:`\mathrm{BD}` ", "radius: :math:`R=5.683099{10}^{-3}m` Thickness: :math:`e=0.005m` ", "air :math:`A=1.{10}^{-4}{m}^{2}`" "Poisson's ratio:", ":math:`\nu =0.3` ", "" **Boundary conditions:** DDL_IMPO =( All=' OUI ', DZ= 0., DRX = 0., DRY = 0.) To treat articulated connections, as many knots as bar ends are created. .. image:: images/10000000000000C5000000918FD073A2F9635834.png :width: 1.411in :height: 1.1571in .. _RefImage_10000000000000C5000000918FD073A2F9635834.png: • at nodes :math:`A`, :math:`B`, and :math:`\mathrm{D4}`: DDL_IMPO =_F (All=' OUI ', DX= 0. , D4= 0.,) • at nodes :math:`\mathrm{C1}`, :math:`\mathrm{C2}`, :math:`\mathrm{C3}` and :math:`\mathrm{D3}`, :math:`\mathrm{D4}` continuity of translations, by LIAISON_DDLDX and DY. • no rotation is imposed. Characteristics of the mesh ---------------------------- Number of knots: 8 Number of meshes and types: 4 SEG2 +-------------------------------------------+---------------------------------------------------------------------------------------------+---------------------------+ |Meshing the two hollow sections | +-------------------------------------------+---------------------------------------------------------------------------------------------+---------------------------+ |Elements |Meshing |specifications | +-------------------------------------------+---------------------------------------------------------------------------------------------+---------------------------+ |:math:`\mathrm{AC}` and :math:`\mathrm{BC}`| |240 knots 79 SEG2 415 TRIA3| + + .. image:: images/Object_3.png + + | | :width: 1.652in | | + + :height: 1.6374in + + | | | | + + + + | | | | +-------------------------------------------+---------------------------------------------------------------------------------------------+---------------------------+ |:math:`\mathrm{CD}` and :math:`\mathrm{BD}`| |127 knots 56 SEG2 210 TRIA3| + + .. image:: images/Object_4.png + + | | :width: 1.6508in | | + + :height: 1.5827in + + | | | | + + + + | | | | +-------------------------------------------+---------------------------------------------------------------------------------------------+---------------------------+ notes --------- In this modeling, the complex dynamic response of the system subjected to complex harmonic excitation (:math:`F=-9810.+\mathrm{0.j}`) is calculated in the presence of viscous damping proportional to stiffness and mass. (AMOR_ALPHA = AMOR_BETA =0.1). The results are compared to the results obtained with modeling POU_D_T by taking into account the characteristics :math:`A`, :math:`\mathit{IY}` and :math:`\mathit{IZ}` equal to those calculated by integrations on the fibers. Tested sizes and results ------------------------------ .. csv-table:: "**Point**", "**Displacement (** :math:`m` **)**", "**Reference Type**", "**Reference**", "**% tolerance**" ":math:`C3` "," :math:`\mathit{DX}` ", "'ANALYTIQUE'", "''", "2.6517E-4", "0.50" ":math:`C3` "," :math:`\mathit{DY}` ", "'ANALYTIQUE'", "''", "0.8839E-4", "0.50" ":math:`D3` "," :math:`\mathit{DX}` ", "'ANALYTIQUE'", "''", "3.47902E-3", "0.50" ":math:`D3` "," :math:`\mathit{DY}` ", "'ANALYTIQUE'", "''", "-5.60084E-3", "0.50" .. csv-table:: "**Identification**", "Component", "**Reference Type**", "**Reference**", "**% tolerance**" "Knit :math:`\mathit{AC}` - Knot :math:`A1` - Stitch :math:`1` - SIEQ_ELNO "," :math:`\mathit{TRIAX}` "," ", "'AUTRE_ASTER'", "4.082482905E-01", "0.10" The results (Displacement, Speed and Acceleration) were obtained at a frequency of :math:`\mathrm{100hz}` .. csv-table:: "**Point**", "**Displacement (** :math:`m` **)**", "**Reference Type**", "**Reference**", "**% tolerance**" ":math:`D` "," :math:`\mathit{DX}` "," AUTRE_ASTER ", "-1.64397E-05-9.09482E-06J", "0.10" "", ":math:`\mathit{DY}` "," AUTRE_ASTER ", "2.51858E-05+1.78386E-05J", "0.10" .. csv-table:: "**Point**", "**Speed (** :math:`m/s` **)**", "**Reference Type**", "**Reference**", "**% tolerance**" ":math:`D` "," :math:`\mathrm{DX}` "," AUTRE_ASTER ", "5.71444E-03-0.0103293J", "0.10" "", ":math:`\mathrm{DY}` "," AUTRE_ASTER ", "-0.011208+0.0158247j", "0.10" .. csv-table:: "**Point**", "**Acceleration (** :math:`m/{s}^{2}` **)**", "**Reference Type**", "**Reference**", "**% tolerance**" ":math:`D` "," :math:`\mathrm{DX}` "," AUTRE_ASTER ", "6.490118+3.590490j", "0.10" "", ":math:`\mathrm{DY}` "," AUTRE_ASTER ", "-9.942974-7.0424160j", "0.10"