Modeling A ============== Characteristics of modeling ----------------------------------- The elements are DKT. 7 load cases are defined in the following way: **Load case 1:** **** SPHERE ** +-------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |The side of an element is equal to :math:`2.5` .The sphere of radius 2. and centered at node 1 has a non-empty intersection with the elements shaded in the figure, i.e. :math:`\mathit{Tr6a}`, :math:`\mathit{Tr6b}`, :math:`\mathit{Tr7a}`, :math:`\mathit{Tr10b}`, :math:`\mathit{Tr11a}` and :math:`\mathit{Tr11b}`. We apply a pressure equal to :math:`–1.` on this list of name :math:`\mathit{GM1}` constructed using the "SPHERE" option from CREA_GROUP_MAde the DEFI_GROUP command and a pressure equal to :math:`1.` on this list defined in extension.| + .. image:: images/1000172A0000184A0000140DBCAE6B405701F787.svg + + | :width: 313 | | + :height: 258 + + | | | + + + | | | +-------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ **Load case no. 2:** **CYLINDRE** +-------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |The cylinder with radius :math:`2` with an axis :math:`z` and passing through the node :math:`1` has a non-empty intersection with the elements shaded in the figure, that is, :math:`\mathit{Tr6a}`, :math:`\mathit{Tr6b}`, :math:`\mathit{Tr7a}`, :math:`\mathit{Tr10b}`, :math:`\mathit{Tr11a}` and :math:`\mathit{Tr11b}`. We apply a pressure equal to :math:`–1.`. name :math:`\mathit{GM2}` constructed using the "CYLINDRE" option of CREA_GROUP_MAde the DEFI_GROUP command and a pressure equal to 1. on this list defined in extension.| + .. image:: images/1000172A0000184A0000140DBCAE6B405701F787.svg + + | :width: 313 | | + :height: 258 + + | | | + + + | | | +-------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ **Load case #3:** **** BANDE ** +-------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |The elements of the hatched area i.e. :math:`\mathit{Tr5A}`, :math:`\mathit{Tr5B}`, :math:`\mathit{Tr6A}`, :math:`\mathit{Tr6B}`,, :math:`\mathit{Tr7A}`,, :math:`\mathit{Tr7B}`, :math:`\mathit{Tr8A}`, :math:`\mathit{Tr8B}`, :math:`\mathit{Tr9A}`, :math:`\mathit{Tr9B}`, BELGRADE, :math:`\mathit{Tr10A}` :math:`\mathit{Tr10B}` :math:`\mathit{Tr11A}` :math:`\mathit{Tr11B}`, :math:`\mathit{Tr12A}`, :math:`\mathit{Tr12B}` define the intersection of the plate with the band whose sides are parallel to the axis :math:`x`, whose middle passes through the node :math:`\mathit{N1}`, and whose half-width is equal to :math:`2` .A pressure equal to :math:`–1.` is applied to this zone, which is defined geometrically, and whose middle passes through the node, and whose half-width is equal to. :math:`\mathit{GM3}` using the option "BANDE" of CREA_GROUP_MAde the command DEFI_GROUP and a pressure equal to :math:`1.` on this zone defined in extension.| + .. image:: images/100013760000136E000012667381099F13AA8AE9.svg + + | :width: 313 | | + :height: 258 + + | | | + + + | | | +-------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ **Load case #4:** **FACE_NORMALE** +-------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |We define the elements of the plate as being perpendicular to the :math:`z` axis using the "FACE_NORMALE" option of CREA_GROUP_MAde the command DEFI_GROUP .We apply a pressure equal to :math:`–1.` to this list with the name :math:`\mathit{GM4}` and a pressure equal to :math:`1.` to the same list defined in extension (here all the cells).| + .. image:: images/100010160000136E00001266273E365C9FB2ED4D.svg + + | :width: 313 | | + :height: 258 + + | | | + + + | | | +-------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ **Load case no. 5:** **ENV_SPHERE** +-------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |Nodes 3, 5, 7, and 9 are defined as being the nodes of the mesh belonging to the intersection of the plate with the intersection of the plate with the sphere of center :math:`\mathit{N1}` and radius :math:`2.5` (this is the length of the side of an element) .This list of nodes with the name :math:`\mathit{GN1}` is defined using the "ENV_SPHERE" option of CREA_GROUP_NOde the DEFI_GROUP command. We apply a nodal force :math:`{F}_{z}\mathrm{=}–1` in each of the nodes in this list and a :math:`{F}_{z}\mathrm{=}1` node strength in each of the nodes in the same list defined in extension :math:`(\mathit{N3},\mathit{N5},\mathit{N7},\mathit{N9})`.| + .. image:: images/100010240000136E00001266A8A836BBD4F3AD0C.svg + + | :width: 313 | | + :height: 258 + + | | | + + + | | | +-------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ **Load case #6:** **ENV_CYLINDRE** +-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |Nodes 3, 5, 7 and 9 are defined as being the nodes of the mesh belonging to the intersection of the plate with the cylinder with axis :math:`z` passing through node 1 and radius 2.5.This list of nodes with the name :math:`\mathit{GN2}` is defined using the option "ENV_CYLINDRE "from CREA_GROUP_NOde the command DEFI_GROUP .A nodal force :math:`{F}_{z}\mathrm{=}–1` is applied to each of the nodes in this list and a nodal force is applied to each of the nodes in this list and a nodal force :math:`{F}_{z}\mathrm{=}1` in each of the nodes in the same list defined in extension :math:`(\mathit{N3},\mathit{N5},\mathit{N7},\mathit{N9})`.| + .. image:: images/100010240000136E00001266A8A836BBD4F3AD0C.svg + + | :width: 313 | | + :height: 258 + + | | | + + + | | | +-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ **Load case #7: "PLAN "** +-------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |Nodes 14, 15, 16, 17, and 18 are defined as belonging to the plane passing through node 14 and whose normal is parallel to :math:`x` .This list of nodes with the name :math:`\mathit{GN3}` is defined using the "PLAN" option of CREA_GROUP_NOde the command GROUP_NO .We apply a nodal force :math:`{F}_{z}\mathrm{=}–1` to each of the nodes in this list and a nodal force :math:`{F}_{z}\mathrm{=}1` to each of the nodes in this list. nodes from the same list defined in extension.| + .. image:: images/100010160000136E00001266273E365C9FB2ED4D.svg + + | :width: 313 | | + :height: 258 + + | | | + + + | | | +-------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Characteristics of the mesh ---------------------------- The mesh consists of 32 DKT meshes. Tested features ----------------------- We are testing the following options for creating a group of elements from the DEFI_GROUP command for 3D: * 'SPHERE' * 'CYLINDRE' * 'BANDE' * 'FACE_NORMALE' and the following options for creating a group of nodes from the DEFI_GROUP command: * 'ENV_SPHERE' * 'ENV_CYLINDRE' * 'PLAN'