Description =========== Geometry --------- The study model is a cylindrical envelope with an average radius :math:`R=21.9m`, a height :math:`H=49.6m` and a thickness :math:`t=0.6m`. The cable anchors on the sides of the cylinder have a length of :math:`L=1.5m` and a width of :math:`l=0.5m`. As for the cables, they are positioned on the outer skin of the cylinder. They are then offset by a distance :math:`e=0.25m`. The model is composed of :math:`20` horizontal cables and :math:`20` vertical cables. The figures below show the various components of the study model. +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ | | | + .. image:: images/10000000000002B8000002B405497A0FF58AA6CA.jpg + .. image:: images/10000000000002B6000002A6A046E942DD436B6E.jpg + | :width: 2.3307in | :width: 2.5634in | + :height: 2.7563in + :height: 2.7563in + | | | + + + | | | +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ |Cylinder |Vertical cables | +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ | | | + .. image:: images/10000000000002B6000002873EC0843B29111CA1.jpg + .. image:: images/10000000000002B6000002ABCADF52BD128841E4.jpg + | :width: 2.6417in | :width: 2.4055in | + :height: 2.7563in + :height: 2.7563in + | | | + + + | | | +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ |Horizontal cables |Study model | +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ Meshing -------- The cables are meshed with SEG2 meshes. The cylinder and the cable anchors are meshed with QUAD4 meshes. The discretization in space for the various components is at most :math:`f=1.0m`. The following figures represent the meshes for the various parts of the model. +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ | | | + .. image:: images/10000000000002B60000028C429B7F395D65E08F.jpg + .. image:: images/10000000000002B6000002AACF0CE903756D9D78.jpg + | :width: 2.7008in | :width: 2.5472in | + :height: 2.7563in + :height: 2.7563in + | | | + + + | | | +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ |Horizontal cable meshing |Vertical cable meshing | +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ | | + .. image:: images/10000000000002B8000002B4EFDD981B781C0C57.jpg + | :width: 2.3508in | + :height: 2.7563in + | | + + | | +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ |Cylinder mesh and anchors | +-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+ Material properties ------------------------ The properties of concrete for the cylinder and the anchors and of steel for the pretension cables are listed in the following table. .. csv-table:: "**Material**", "**Concrete**", "**Steel**" "**Young Module**", ":math:`4\times {10}^{10}\mathit{Pa}` "," :math:`1.93\times {10}^{11}\mathit{Pa}`" "**Fish Coefficient**", ":math:`0.2` "," :math:`0.0`" "**Density**", ":math:`2500\mathit{kg}/{m}^{3}` "," :math:`7850\mathit{kg}/{m}^{3}`" "**Elastic limit stress**", ":math:`n/a` "," :math:`1.94\times {10}^{11}\mathit{Pa}`" Boundary conditions and loads ------------------------------------- The cylinder and the anchors are embedded at the top and bottom. Initially, a voltage equal to :math:`3.75\times {10}^{6}N` is imposed in the cables. The nodes at the ends of vertical and horizontal cables are considered "active." In a second step, the cylinder is subjected to an internal pressure that increases over time (from :math:`{P}_{i}=0\mathit{Pa}` to :math:`{P}_{f}=1\mathit{kbar}` in :math:`\Delta t\mathrm{=}1\mathit{ms}`). This load is shown in the following graph. .. image:: images/Object_99.png :width: 4.7244in :height: 2.9634in .. _RefSchema_Object_99.png: Main stages of testing ---------------------------- Macro-control DEFI_CABLE_BP is used to obtain the kinematic relationships between the cylinder and the cables as well as the load related to the tension in the cables. The macro-command CALC_PRECONT is then launched to prestress the structure using the tensions of the given cables. The result of this prestress is given in initial state to the macro-command CALC_EUROPLEXUS in order to calculate the mechanical response of the prestressed cylinder to the internal pressure load. To validate the results from CALC_EUROPLEXUS, we do the same calculation with the DYNA_NON_LINE operator. From the two concept results obtained, the following are extracted: * the evolution as a function of the time of movement on the reference point located halfway up the cylinder, i.e. in :math:`(\mathrm{0,}R,H/2)`, noted :math:`{N}_{\mathit{ref}}^{\mathit{cyl}}`. * the resulting forces of membrane :math:`\mathit{Nxx}` and :math:`\mathit{Nyy}`, at three different times in a cylinder cell having a node in common with the reference node of the cylinder, noted :math:`{M}_{\mathit{ref}}^{\mathit{cyl}}`. * the normal force in an element of the horizontal cable located closest to halfway up the cylinder and farthest from the anchors, noted :math:`{\mathit{EL}}_{\mathit{ref}}^{\mathit{câb}}`.