17. Keyword RIGI_PARASOL#

17.1. Syntax#

RIGI_PARASOL = _F (

# Meshes used to distribute the characteristics of discretes

♦ GROUP_MA = l_gma, [l_group_ma]

# POI1 meshes corresponding to discrete

◊/GROUP_MA_POI1 = gmapoi1, [group_ma]

# SEG2 meshes corresponding to discrete

/GROUP_MA_SEG2 = l_gma, [l_group_ma]

# Distribution functions

♦/FONC_GROUP = l_fg, [l_function]

/COEF_GROUP = l_cg, [l_real]

# Overall stiffness to be distributed

♦ CARA = /. | 'k_tr_d_n'|'k_t_d_n'|

|'k_tr_d_l'|'k_t_d_l'|

/| 'A_tr_d_n'|'a_t_d_n'|

|'a_tr_d_l'|'a_t_d_l' [l_txm]

♦ VALE = l_val, [l_real]

◊ REFERENCE = ['LOCAL'|'GLOBAL'], [default]

# Center of gravity

♦ GROUP_NO_CENTRE = no, [group_no]

/COOR_CENTRE = l_xyz, [l_real]

# Output unit

◊ UNITE = unit, [integer]

),

17.2. Affordable characteristics#

This functionality corresponds to a methodology used to determine the characteristics of discrete elements (translation and/or rotation springs) to be applied to the nodes of a raft based on results obtained by the code PARASOL.

This option is available in 3D and 2D. In the 3D case the floor will be modeled by a surface, in the 2D case it will be modeled by a line (ssnl130 test [V6.02.130]). In the 2D case the discretes are “2D_DIS_TR” or “2D_DIS_T”.

The modeling “DIS_TR| DIS_T” in 3D or “2D_DIS_TR|2D_DIS_T” in 2D must be assigned to the group of nodes that make up the raft. The cells that make up the frame (belonging to the l_gma groups) carry plate modeling (DKT, DST) or 3D face modeling (sdls108 test [V2.03.108]).

It is necessary to distinguish a group of elements to write it off, to be declared behind the keyword GROUP_MA of the keyword factor RIGI_PARASOL, and a group of elements with 1 node based on the nodes of this grid that must be modeled and declared in AFFE_MODELE in the form of point cells of type POI1. If the meshes are of type POI1, it must be indicated using the keyword GROUP_MA_POI1 of the keyword factor RIGI_PARASOL.

The use of POI1 point cells is necessary for the assignment of laws of behavior in nonlinear calculation operators.

17.3. Description of operands#

♦ GROUP_MA

List of the mesh groups that make up the base plate.

◊ GROUP_MA_POI1

List of point groups including the nodes of the mesh groups defined by GROUP_MA. This makes it possible to declare the nodes of a foundation defined by meshes as POI1 point cells in order to assign the RIGI_PARASOL characteristics to them. This makes it possible to assign materials or behaviors to them in order to use a nonlinear operator. If it is not present, the nodes are considered to be late meshes for a strictly linear study.

♦ FONC_GROUP/COEF_GROUP

List of real functions or coefficients. There are as many arguments in this list as there are cell groups that make up the grid (defined under the GROUP_MA keyword). The functions must have the distance to the center of gravity as their abscissa (keyword defined by GROUP_NO_CENTRE/COOR_CENTRE).

♦ CARA/VALE

The overall ground stiffness, from code PARASOL, is provided by the user using the keywords CARA and VALE as for the discrete elements. You can also select the nature of the frame of reference (global or local) in which the characteristics of the springs are defined (keyword REPERE). Stiffnesses or dampenings defined only in translation can also be distributed (K_T_D_N or A_T_D_N, no stiffness in rotation), in this case it is only necessary:

◦ in 3D to give 3 values behind \(\mathit{VALE}=({k}_{x},{k}_{y},{k}_{z})\).

◦ in 2D to give 2 values behind \(\mathit{VALE}=({k}_{x},{k}_{y})\).

♦/GROUP_NO_CENTRE = gno

/COOR_CENTRE = l_xyz

To define the center of the grid (calculated by the code PARASOL), you can either give the coordinates (three real numbers given behind the COOR_CENTRE keyword), or give the name of a group containing a single node of the mesh (keyword GROUP_NO_CENTRE).

◊ UNITE

If this keyword is present, Code_Aster creates a file, corresponding to the unit number, which contains the stiffness of the discretes assigned to the various nodes.

17.4. Principle for determining the characteristics of discrete elements#

The document [R4.05.01] « Seismic response by transient analysis » gives theoretical information on the method used.

17.4.1. Discreet in translation#

In 3D, the base is represented by a set of surface elements with a center of gravity \(O\). We therefore have 3 global quantities that characterize the coupling between the ground and the frame: 3 translation stiffness \({K}_{x},{K}_{y},{K}_{z}\).

In 2D, the slab is represented by a set of linear elements with a center of gravity \(O\). We therefore have 2 global quantities that characterize the coupling between the ground and the frame: 2 translation stiffness \({K}_{x},{K}_{y}\).

Note: It is the same reasoning for discretes such as « amortization » .

17.4.2. Discretes in translation and rotation#

In 3D, the base is represented by a set of surface elements with a center of gravity \(O\). We therefore have 6 global quantities that characterize the coupling between the ground and the frame: 3 translational stiffness \({K}_{x},{K}_{y},{K}_{z}\), 3 rotational stiffness \({\mathit{Kr}}_{x},{\mathit{Kr}}_{y},{\mathit{Kr}}_{z}\).

In 2D, the slab is represented by a set of linear elements with a center of gravity \(O\). We therefore have 3 global quantities that characterize the coupling between the ground and the frame: 2 translational stiffness \({K}_{x},{K}_{y}\), 1 rotational stiffness \({\mathit{Kr}}_{z}\).

Note: It is the same reasoning for discretes such as « amortization » .

17.4.3. Discreet stiffness and damping distribution#

If you want to distribute both stiffness and damping, you must specify it under the keyword CARA, for example: CARA = (“K_T_D_N”, “A_T_D_N”), both in 2D and in 3D.

The values to be distributed will be given under VALE. For example:

in 3D with CARA = (“K_T_D_N”, “A_T_D_N”),

VALE = (\({K}_{x}\), \({K}_{Y}\), \({K}_{Z}\), \({A}_{X}\), \({A}_{Y}\), \({A}_{Z}\)).
in 2D with CARA = (“K_T_D_N”, “A_T_D_N”),

VALE = (\({K}_{x}\), \({K}_{Y}\), \({A}_{X}\), \({A}_{Y}\)).
in 3D with CARA = (“K_TR_D_N”, “A_TR_D_N”),

VALE = (\({K}_{x}\), \({K}_{Y}\), \({K}_{Z}\), \({\mathit{Kr}}_{x}\),, \({\mathit{Kr}}_{y}\), \({\mathit{Kr}}_{z}\),

\({A}_{X}\), \({A}_{Y}\), \({A}_{Z}\), \({\mathit{Ar}}_{x}\),, \({\mathit{Ar}}_{y}\), \({\mathit{Ar}}_{z}\)).
in 2D with CARA = (“K_TR_D_N”, “A_TR_D_N”),

VALE = (\({K}_{x}\), \({K}_{Y}\), \({\mathit{Kr}}_{z}\), \({A}_{X}\), \({A}_{Y}\), \({\mathit{Ar}}_{z}\)).

Note: If in CARA we give the discrete d*dampening* then that of the stiffness, it must give the damping characteristics then the stiffness one s , for example in 2D:

CARA = (“A_T_D_N”, “K_T_D_N”)

VALE = (\({A}_{X}\), \({A}_{Y}\), \({K}_{x}\), \({K}_{Y}\))

17.4.4. Distribution method#

At each node of the radiator mesh, Code_Aster searches for the stiffness characteristics of a discrete element of type K_TR_D_N \(({k}_{x},{k}_{y},{k}_{z},{\mathit{kr}}_{x},{\mathit{kr}}_{y},{\mathit{kr}}_{z})\) cf. [R4.05.01].

To determine the translational stiffness, it is necessary that they be proportional to the area represented by the node and to a distribution function depending on the distance from the center of gravity of the raft. Let \(S(P)\) be the area attached to node \(P\) and \(f(r)\) the distribution function where \(r\) is the distance from node \(P\) to node \(O\).

For the stiffness of rotation, the remainder (what is left after removing the contributions due to translations) is distributed in the same way as the translations.

If we calculate the forces and the moments resulting from the point \(O\) due to the distribution of the springs in each node of the frame mesh and if we identify them with the values obtained by PARASOL, we obtain the following formulas:

\(\begin{array}{ccc}{k}_{x}={K}_{x}/\left(\sum _{p}S(p)f(\mathit{op})\right)& ;& {k}_{x}(p)={k}_{x}S(p)f(\mathit{op})\\ {k}_{y}={K}_{y}/\left(\sum _{p}S(p)f(\mathit{op})\right)& ;& {k}_{y}(p)={k}_{y}S(p)f(\mathit{op})\\ {k}_{z}={K}_{z}/\left(\sum _{p}S(p)f(\mathit{op})\right)& ;& {k}_{z}(p)={k}_{z}S(p)f(\mathit{op})\end{array}\)

\(\begin{array}{ccc}{k}_{\mathit{rx}}=\left({K}_{\mathit{rx}}-\sum _{p}\left({k}_{z}(p){y}_{\mathit{op}}^{2}+{k}_{y}(p){z}_{\mathit{op}}^{2}\right)\right)/\left(\sum _{p}S(p)f(\mathit{op})\right)& ;& {k}_{\mathit{rx}}(p)={k}_{\mathit{rx}}S(p)f(\mathit{op})\\ {k}_{\mathit{ry}}=\left({K}_{\mathit{ry}}-\sum _{p}\left({k}_{x}(p){z}_{\mathit{op}}^{2}+{k}_{z}(p){x}_{\mathit{op}}^{2}\right)\right)/\left(\sum _{p}S(p)f(\mathit{op})\right)& ;& {k}_{\mathit{ry}}(p)={k}_{\mathit{ry}}S(p)f(\mathit{op})\\ {k}_{\mathit{rz}}=\left({K}_{\mathit{rz}}-\sum _{p}\left({k}_{x}(p){y}_{\mathit{op}}^{2}+{k}_{y}(p){x}_{\mathit{op}}^{2}\right)\right)/\left(\sum _{p}S(p)f(\mathit{op})\right)& ;& {k}_{\mathit{rz}}(p)={k}_{\mathit{rz}}S(p)f(\mathit{op})\end{array}\)

Note 1:

Calculation of the area attached to the point \(P\) .

For each surface mesh of the raft, we calculate the area in 3D, the length of the line in 2D, we divide it by the number of vertices of the mesh and we assign this contribution to each node of the mesh. We then ensure: \({S}_{\mathit{radier}}=\sum _{p}S(p)\).

Note 2:

It is considered that the same formulas can be applied to distribute discrete damping elements.

17.5. Example of use#

Example #1:

RIGI_PARASOL = _F (GROUP_MA = write off, COEF_GROUP = 2., NOEUD_CENTRE = “P1”,

CARA = (“K_TR_D_N”, “A_TR_D_N”), VALE = (6 real, 6 real),)

Example #2:

RIGI_PARASOL =_F (GROUP_MA =” DALLE “, COEF_GROUP =1.0, GROUP_NO_CENTRE =” PCDG”,

GROUP_MA_POI1 =” RESSORT “, REPERE =” GLOBAL”,

CARA =” K_T_D_N “, VALE =( 3 real ones),),