3. Modeling A#

3.1. 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 \(2.5\) .The sphere of radius 2. and centered at node 1 has a non-empty intersection with the elements shaded in the figure, i.e. \(\mathit{Tr6a}\), \(\mathit{Tr6b}\), \(\mathit{Tr7a}\), \(\mathit{Tr10b}\), \(\mathit{Tr11a}\) and \(\mathit{Tr11b}\). We apply a pressure equal to \(–1.\) on this list of name \(\mathit{GM1}\) constructed using the « SPHERE » option from CREA_GROUP_MAde the DEFI_GROUP command and a pressure equal to \(1.\) on this list defined in extension.

Load case no. 2: CYLINDRE

	The cylinder with radius \(2\) with an axis \(z\) and passing through the node \(1\) has a non-empty intersection with the elements shaded in the figure, that is, \(\mathit{Tr6a}\), \(\mathit{Tr6b}\), \(\mathit{Tr7a}\), \(\mathit{Tr10b}\), \(\mathit{Tr11a}\) and \(\mathit{Tr11b}\). We apply a pressure equal to \(–1.\). name \(\mathit{GM2}\) 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.

Load case #3: **** BANDE **

	The elements of the hatched area i.e. \(\mathit{Tr5A}\), \(\mathit{Tr5B}\), \(\mathit{Tr6A}\), \(\mathit{Tr6B}\),, \(\mathit{Tr7A}\),, \(\mathit{Tr7B}\), \(\mathit{Tr8A}\), \(\mathit{Tr8B}\), \(\mathit{Tr9A}\), \(\mathit{Tr9B}\), BELGRADE, \(\mathit{Tr10A}\) \(\mathit{Tr10B}\) \(\mathit{Tr11A}\) \(\mathit{Tr11B}\), \(\mathit{Tr12A}\), \(\mathit{Tr12B}\) define the intersection of the plate with the band whose sides are parallel to the axis \(x\), whose middle passes through the node \(\mathit{N1}\), and whose half-width is equal to \(2\) .A pressure equal to \(–1.\) is applied to this zone, which is defined geometrically, and whose middle passes through the node, and whose half-width is equal to. \(\mathit{GM3}\) using the option « BANDE » of CREA_GROUP_MAde the command DEFI_GROUP and a pressure equal to \(1.\) on this zone defined in extension.

Load case #4: FACE_NORMALE

	We define the elements of the plate as being perpendicular to the \(z\) axis using the « FACE_NORMALE » option of CREA_GROUP_MAde the command DEFI_GROUP .We apply a pressure equal to \(–1.\) to this list with the name \(\mathit{GM4}\) and a pressure equal to \(1.\) to the same list defined in extension (here all the cells).

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 \(\mathit{N1}\) and radius \(2.5\) (this is the length of the side of an element) .This list of nodes with the name \(\mathit{GN1}\) is defined using the « ENV_SPHERE » option of CREA_GROUP_NOde the DEFI_GROUP command. We apply a nodal force \({F}_{z}\mathrm{=}–1\) in each of the nodes in this list and a \({F}_{z}\mathrm{=}1\) node strength in each of the nodes in the same list defined in extension \((\mathit{N3},\mathit{N5},\mathit{N7},\mathit{N9})\).

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 \(z\) passing through node 1 and radius 2.5.This list of nodes with the name \(\mathit{GN2}\) is defined using the option « ENV_CYLINDRE « from CREA_GROUP_NOde the command DEFI_GROUP .A nodal force \({F}_{z}\mathrm{=}–1\) 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 \({F}_{z}\mathrm{=}1\) in each of the nodes in the same list defined in extension \((\mathit{N3},\mathit{N5},\mathit{N7},\mathit{N9})\).

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 \(x\) .This list of nodes with the name \(\mathit{GN3}\) is defined using the « PLAN » option of CREA_GROUP_NOde the command GROUP_NO .We apply a nodal force \({F}_{z}\mathrm{=}–1\) to each of the nodes in this list and a nodal force \({F}_{z}\mathrm{=}1\) to each of the nodes in this list. nodes from the same list defined in extension.

The mesh consists of 32 DKT meshes.

We are testing the following options for creating a group of elements from the DEFI_GROUP command for 3D:

and the following options for creating a group of nodes from the DEFI_GROUP command: