3. Operands#

3.1. Keyword RESULTAT#

If you want to continue a calculation that has already been executed, RESULTAT indicates which object is enriched (see also ETAT_INIT).

3.2. Operands MODELE/CHAM_MATER/CARA_ELEM#

These operands have the same meaning as in the [U4.51.03] document.

3.3. Operands MODE_STAT/MASS_DIAG#

◊ MODE_STAT = modesty

Name of the static mode required in the case of a calculation with multi-support excitations [R4.05.01]. They are calculated beforehand by the operator MODE_STATIQUE [U4.52.14] with the option “MODE_STAT”.

◊ MASS_DIAG =/'OUI',

/”NON”,

Option to be used with an explicit time scheme [bib2] and which allows solving with a lumped (diagonalized) mass matrix. This option is not available for all types of elements, especially discrete ones (in this case, you have to solve with the consistent mass matrix). By default, it is not possible to use a lumped matrix (emission of a fatal error if the user is in this case).

3.4. Keyword EXCIT#

◊ EXCIT =_F

This keyword factor makes it possible to describe a load (stresses and boundary conditions) at each occurrence, and possibly a multiplying coefficient and/or a type of load.

The operands have the same meaning as in the document [U4.51.03] but there are some specificities related to the dynamics.

Important note for time diagrams:

If one imposes boundary conditions on the move that change over time, one must take into account the primal unknown of the scheme used. These conditions are in fact imposed in acceleration and explicitly (because it is the primal unknown). This means that one must enter in DYNA_NON_LINEla second derivative of the moving signal that one wants to impose. This evolution of the imposed displacement must therefore be differentiable at least twice in time.

3.4.1. Operands CHARGE/FONC_MULT#

♦ CHARGE = \({\mathrm{ch}}_{i}\)

3.4.2. Operand TYPE_CHARGE#

◊ TYPE_CHARGE =/'FIXE_CSTE', [DEFAUT]

/”SUIV”, /”DIDI”,

The operand has the same meaning as in document [U4.51.03], except that a load cannot be driven dynamically, and therefore tchi cannot be FIXE_PILO.

3.4.3. Operands MULT_APPUI/ACCE/VITE/DEPL//DIRECTION/GROUP_NO#

◊ MULT_APPUI = /' NON ', [DEFAUT]

/” OUI “,

♦ ACCE = ac, [function]

♦ VITE = vi, [function]

♦ DEPL = dp, [function]

◊ DIRECTION = (xx, dy, dz, drx, dry, drz), [l_R]

◊ GROUP_NO = lgrno, [l_group_no]

We specify that multi-support calculation is based fundamentally on the additive superposition of movements, cf. [R5.05.05, §2.6], so if static, elastic modes are solutions generating deformations in the structure, then for superposition to be lawful, the behavior of the constituent materials must be linear, and kinematics must also be linear.

Training movements as a function of time therefore produce inertial forces that combine with other loads and the resolution produces a dynamic response in the hypothesis of blocked supports or supports. These inertial drive forces are constructed with the operator CALC_CHAR_SEISME [U4.63.01] based on static modes and the mass matrix. Only the acceleration of the training in each press or support is therefore used for the resolution, and the speeds and displacements in each support or support only serve to reconstruct the complete solution in terms of speeds and movements by additive superposition. It should be noted that the damping forces come only from the speeds resolved under the hypothesis of supports or supports blocked, and not from complete speeds reconstructed by superposition with the speeds at each support or support.

In the case of multi-press excitation (MULT_APPUI = “OUI”), the other operands have exactly the same meaning as in the key word factor EXCIT of the operator DYNA_VIBRA [U4.53.21]. In this case, the fields” DEPL “,” VITE “,” “,” ACCE “correspond respectively to the movements, speeds and accelerations, functions of time, of the driving movement on the supports or supports specified in” GROUP_NO “and for the direction” DIRECTION “. The new fields” DEPL_ABSOLU “,” VITE_ABSOLU “,” ACCE_ABSOLU “are then created in the evol_noli type concept produced by the operator DYNA_NON_LINE and correspond respectively to the movements, speeds and accelerations of the absolute movement, the sum of the driving movement on the supports or supports and the relative movement with respect to this multi-press driving movement.

The linear elastic solutions associated with unit drive movements on supports or supports, cf. [R5.05.05, §2.6], are described by the static MODE_STAT modes specified in the corresponding keyword, see §3.3. If this is not the case, it is then necessary to describe the excitations by movements imposed as a function of time on all supports or supports, and the resolution will be done in absolute reference.

3.5. Keyword CONTACT#

♦ CONTACT = contact

This simple keyword makes it possible to activate the resolution of touch-friction or the consideration of a unilateral link. contact is a concept derived from the operator DEFI_CONTACT [U4.44.11].

The operand has the same meaning as in the document [U4.51.03] .

3.6. Keyword SOUS_STRUC#

◊ SOUS_STRUC =_F

This keyword factor makes it possible to specify which loads to use for the static substructures which are then necessarily part of the model.

The operand has the same meaning as in the document [U4.51.03] .

3.7. Keyword COMPORTEMENT#

The syntax of these keywords common to several commands is described in the document [U4.51.11] .All behavioral relationships supported by STAT_NON_LINEsont are also available in DYNA_NON_LINE, provided that the calculation of the mass matrix of the elements concerned is planned.

3.8. Keyword ETAT_INIT#

◊ ETAT_INIT =_F

Under this keyword the initial conditions of the problem are defined. The operands for the ETAT_INIT keyword have the same meaning as in document [U4.51.03].

Note:

In case the user has specified that the result concept is reentrant, the keyword ETAT_INIT is required. The enriched concept is provided by the keyword RESULTAT.

In dynamics, we can also define the initial speed and acceleration fields.

♦/| FAST = fast

/| ACCE = acce

If the keywords EVOL_NOLI, DEPL, and VITE are absent, we assume that the initial state has zero displacements, speeds and constraints, and we calculate the accelerations corresponding to the loading at the instant instinci defined by the operand INST.

3.9. Keyword INCREMENT#

♦ INCREMENT =_F

Defines the list of calculation times. The operands for the INCREMENT keyword have the same meaning as in document [U4.51.03].

3.10. Keyword NEWTON#

◊ NEWTON =_F

Specify the characteristics of the method for solving the nonlinear incremental problem (Newton-Raphson method). The operands for the NEWTON keyword have the same meaning as in document [U4.51.03].

3.11. Keyword RECH_LINEAIRE#

◊ RECH_LINEAIRE =_F (

◊ METHODE = /” CORDE “[DEFAUT] /” MIXTE “)

Allows you to activate linear search. The operands for the RECH_LINEAIRE keyword have the same meaning as in document [U4.51.03], except that the PILOTAGE method does not exist.

3.12. Keyword SOLVEUR#

◊ SOLVEUR =_F

The syntax of this keyword common to several commands is described in the document [U4.50.01].

3.13. Keyword CONVERGENCE#

◊ CONVERGENCE =_F

This keyword describes the parameters for assessing the convergence of the NEWTON method used to solve the nonlinear mechanical problem. The operands for the CONVERGENCEont keyword have the same meaning as in the document [U4.51.03].

3.14. Keyword ARCHIVAGE#

◊ ARCHIVAGE =_F

Allows you to archive some or all results at all or certain moments of the calculation.

In the absence of this keyword all time steps are archived, including the calculation times newly created by automatically redividing the time step. The operands for the ARCHIVAGE keyword have the same meaning as in the [U4.51.03] document, except for the CHAM_EXCLU keyword.

3.14.1. Operand CHAM_EXCLU#

|”QUICK” |”ACCESS” |”SIEF_ELGA” |”VARI_ELGA”

Allows you to specify the fields that will not be archived, except at the last time step.

3.15. Keyword AMOR_RAYL_RIGI#

* AMOR_RAYL_RIGI = /” ELASTIQUE “, [DEFAUT]

The operator automatically evaluates, assembles and implements in the resolution of the equations of motion all the damping contributions defined in the material field, the characteristics of the elements of the model, and those possibly defined by the keyword AMOR_MODAL, in the resolution of the equations of motion, see § 3.18.

This keyword allows you to specify the stiffness matrix \(\mathrm{K}\) that will be used to build Rayleigh damping \(\mathrm{C}=\alpha \mathrm{.}\mathrm{K}+\beta \mathrm{.}\mathrm{M}\) using the parameters available in the material field.

With the default value (“ELASTIQUE”), we force the calculation of Rayleigh damping with the elastic stiffness matrix.

By choosing the value “TANGENTE”, the \(\mathrm{K}\) matrix will be the same as the one used to calculate the internal forces.

For softening behavior models or GLRC, it is recommended to use the elastic stiffness matrix.

Note: If this keyword is absent, however, the Rayleigh damping calculation is done automatically with the elastic stiffness matrix.

Note:

Option AMOR_MECA, performing the Rayleigh damping calculation, is not available for THM finite elements. To perform a calculation with these elements, it is necessary to leave the material parameters affected on the cells carrying finite elements from THM AMOR_ALPHA and AMOR_BETAégaux to 0.

3.16. Keyword VNOR#

◊ VNOR =

This option allows us to take into account the case of an emissive border. The most common case is the radiative one (or partially radiative if we define a reflection coefficient \(\alpha \ne 0\)). In the case of a radiative border VNOR = 1 (option activated by default). In the case of an emissive border VNOR = -1. This coefficient is multiplied by the value of the impedance of the absorbing fluid boundaries (”3D_ FLUI_ABSO “, “2D_ FLUI_ABSO” and “AXIS_FLUI_ABSO”). If none of these elements are present in the model, this option will not be taken into account.

3.17. Keyword MATR_ELEM_AMOR#

◊ MATR_ELEM_AMOR = MatrAmor [matr_elem]

This keyword allows you to add elementary matrices for amortization. This damping will occur in the matrix operator in addition to the other damping options, for example, if Rayleigh damping is defined via the material characteristics AMOR_ALPHA and AMOR_BETA.

3.19. Description of the integration diagram in time [R5.05.05]#

♦ SCHEMA_TEMPS =_F ()
◊ STOP_CFL = /' OUI ', [DEFAUT]
                      /' NON ',
◊ FORMULATION = /' DEPLACEMENT ',
                     /' VITESSE ',
                     /' ACCELERATION ',

We can use the implicit Newmark methods (keyword SCHEMA =” NEWMARK “or modified mean acceleration: SCHEMA =” HHT” with MODI_EQUI = “NON”), or Hilber-Hughes-Taylor (HHT) () (SCHEMA =” “or modified mean acceleration: =”” with MODI_EQUI = “HHT OUI “). It is also possible to use the non-overshooting version of the full HHT diagram (see [R5.05.05] for more details), using the SCHEMA =” NOHHT “keyword (see [R5.05.05]). Alternatively, it is possible to choose an explicit method such as centered differences (keyword SCHEMA =” DIFF_CENT “) or a dispersive schema of type TCHAMWA (keyword SCHEMA =” TCHAMWA”).

With an implicit schema, resolutions for displacement, speed, or acceleration are currently available (keyword FORMULATION = “DEPLACEMENT”, “VITESSE”, or “ACCELERATION”). Note that speed resolution is not available for HHT schemes (keyword SCHEMA = “HHT” or “NOHHT”). Moreover, with an explicit schema, we can only solve by acceleration (keyword FORMULATION = “ACCELERATION”).

Since explicit patterns are conditionally stable, it may be useful to check whether the step The time given at the input of the calculation complies with the stability condition (condition CFL). If STOP_CFL = “OUI” (default), then if the list of moments provided by the user includes one or more time steps greater than the stability condition, the calculation stops with a fatal error. If STOP_CFL = “NON”, an alarm is set off and the calculation continues.

In all cases, the critical time step is given in the message file for information.

The calculation of the CFL is not programmed for all the elements (in particular the discrete elements are ignored.); the CFL estimated by Code_Aster may therefore be larger (less penalizing) than the real CFL, with the risks of sudden discrepancies that result.

Explicitly, it is also recommended to use a lumped (diagonalized) mass matrix: what can be obtained with the keyword MASS_DIAG = “OUI” [§ 7].

Notes:

The choice MASS_DIAG =” NON “is not recommended with cases* DKT.

With the elements DKT/DKTGil is necessary to specify in AFFE_CARA_ELEM, under the factor key COQUE, the simple keyword INER_ROTA = “OUI”. Otherwise the mass matrix is singular and the explicit schema * is unusable.
Explicitly, we do not recommend the use of quadratic finite elements (which can generate parasitic oscillations on solution fields) .
For multi-step schemes (Newmark with MODI_EQUI =” OUI “), it is necessary to recalculate the internal forces at the previous moment. This mode of operation is problematic at the first moment when the calculation is resumed. In fact, if we have command variables (which therefore depend on the moment of calculation), it is necessary to recover the value of the previous moment. This is not always possible, especially if you are not in reuse and if ETAT_INIT is done from individual fields (no use of the keyword ETAT_INIT/EVOL_NOLI *). In this case, this contribution is not calculated at the previous step, which may possibly slightly modify the convergence of the algorithm.
It is therefore strongly recommended to specify the initial state using the ETAT_INIT/EVOL_NOLI keyword, in order to allow the calculation of the internal forces at the previous moment. *

3.19.1. Case SCHEMA = “NEWMARK”#

◊ BETA = /0.25, [DEFAUT]

/beta, [R]

◊ GAMMA = /0.5, [DEFAUT]

/range, [R]

The time integration method is that of NEWMARK, with the given values of the beta and gamm parameters.

When neither beta nor gamm is specified, we have the method called « trapezium rule » (\(\mathrm{beta}=0.25\); \(\mathrm{gamm}=0.5\)) which, on a linear basis, is unconditionally stable and does not provide any parasitic dissipation (i.e. numerical damping), but which, in non-linear mode, can be unstable [bib1] [bib2].

3.19.2. Case SCHEMA = “HHT”#

◊ ALPHA = /-0.1, [DEFAUT]

/alpha, [R]

◊ MODI_EQUI = /” OUI “, [DEFAUT]

/” NON “,

For MODI_EQUI = “NO”, the time integration method (implicit integration diagram) is that of the modified mean acceleration (from the Newmark family) ([bib1], [bib2]), with the negative value of alph given. The greater | alph|, the greater the numerical damping provided by the calculation. But this dissipation is sometimes necessary, in a non-linear way, to ensure stability (unless damping by material is assigned to the structure).

For MODI_EQUI = “YES” (value by default), the time integration method (implicit integration scheme) is that of Hilber‑Hughes‑Taylor (HHT or:math: alphamathrm {-}text {method}) [bib2], with the negative value of alph given. The greater | alph|, the greater the numerical damping provided by the calculation. Compared to the previous diagram (MODI_EQUI = “NO”) of modified mean acceleration, the induced numerical damping is more « selective »: it is weaker at low and medium frequencies (asymptotically zero at zero frequency) and it will increase more quickly when the frequency becomes high.

This second diagram is based on the first with, in addition, a modification of the equilibrium equation (internal and external efforts are delayed in time) [bib2].

3.19.3. Case SCHEMA = “DIFF_CENT”#

The centered differences schema is an explicit second-order diagram from the Newmark family, with parameters BETA = 0 and GAMMA = 0.5. It is a single-step diagram that does not have digital dissipation.

3.19.4. Case SCHEMA = “TCHAMWA”#

◊ PHI = /1.05, [DEFAUT]

/phi, [R]

An alternative to the patterns of centered differences is the schema developed by Bertrand Tchamwa and Christian Wielgosz.

This explicit schema has several interesting features. It is not a Newmark derivative, and the variation of its parameter PHI allows controllable digital dissipation of high frequencies. When it is 1, the dissipation is zero. To avoid degrading the Current condition too much and to maintain stability properties comparable to the centered differences scheme, it is recommended not to choose a PHI greater than 1.10. 1.05 is the value chosen by default.

3.19.5. Operand COEF_MASS_SHIFT#

◊ COEF_MASS_SHIFT =/0. [DEFAUT]

                 /key

The coef coefficient data makes it possible to perform a shift of the mass matrix \(M\) which becomes:

\(M\text{'}\mathrm{=}M+\mathit{coef}K\)

The value of this coefficient, by default zero, must be non-zero to be able to dynamically invert the mass matrix with an explicit diagram when it has zero terms for certain specific degrees of freedom, for example the pressure for the HM modeling elements.

The entry of this coefficient also makes it possible to greatly improve the convergence in dynamics with an implicit diagram in this same type of modeling by imposing a cutoff frequency that is inversely proportional to the coef value (at the cost of a slight distortion of all the natural frequencies of the system).

3.20. Keyword CRIT_STAB#

◊ CRIT_STAB =_F

This keyword makes it possible to trigger the calculation, at the end of each time increment, of a stability criterion, identical to what is proposed in STAT_NON_LINE. This criterion is useful for detecting, during loading, the point at which stability is lost (for example by buckling). This is not a stability criterion in the dynamic sense (negative damping). The operands of the CRIT_STAB keyword have the same meaning as in the document [U4.51.03].

However, it should be noted that the use of CRIT_STAB on coupled fluid-structure models (formulation \((u,p,\phi )\), cf. documentation [R4.02.02], which are available with DYNA_NON_LINEmais not STAT_NON_LINE) requires the exclusion of fluid degrees of freedom since the overall assembled stiffness matrix is singular for these degrees of freedom. To do this, you must combine the keywords DDL_EXCLUS (excluding all degrees of freedom specific to fluid elements, such as” PRES “,” PHI “and, in cases with free surface,” DH “) and MODI_RIGI =” OUI “. More details are given in the [U4.51.03], [U2.06.11], and [U2.08.04] documentation.

All results are stored in a table_container data structure with the name “ANALYSE_MODALE” attached to the evol_noli data structure. The buckling modes (TYPE =” FLAMBEMENT “) are stored as TYPE_MODE =” MODE_FLAMB” in the table while the stability modes (TYPE =” STABILITE “) are stored there as TYPE_MODE =” MODE_STAB” (see § 4).

3.21. Keyword MODE_VIBR#

◊ MODE_VIBR =_F (

◊ OPTION = /” PLUS_PETITE “, [DEFAUT] /” BANDE “, /” CALIBRATION “, If OPTION =” PLUS_PETITE “ { ◊ NMAX_FREQ = /3, [DEFAUT] /nbfreq, [I] } If OPTION =” BANDE “ { ◊ FREQ = intba, listr8 } If OPTION =” CALIBRATION “ { ◊ FREQ = intba, listr8 } ◊ MATR_RIGI = /” ELASTIQUE “, [DEFAUT] /” TANGENTE “, /” SECANTE “, ◊/LIST_INST = list_r8, listr8 /INST = l_r8, [R] /PAS_CALC = not, [I] ◊ PRECISION = /1.e-6 [DEFAUT] /prec

* CRITERE = /” RELATIF “, [DEFAUT]

This keyword makes it possible to trigger the calculation, at the end of each time increment, of a search for specific vibratory modes.

This criterion is useful for monitoring, during the transitory calculation, the evolution of the vibratory response of the nonlinear structure.

This criterion is calculated as follows: at the end of a time step, we solve \(\mathit{det}(K\mathrm{-}{\omega }^{2}\mathrm{.}M)\mathrm{=}0\). \(K\) can either be the elastic stiffness matrix, or the tangent matrix coherent at the current moment, or the secant matrix. \(M\) is the mass matrix. This modal analysis is only allowed for symmetric matrices (mass and stiffness).

The keyword OPTION allows you to choose the type of search:

OPTION =” PLUS_PETITE “: the NMAX_FREQ eigenvectors and eigenvalues corresponding to the smallest eigenvalues;
OPTION =” BANDE “: the eigenvectors and eigenvalues for the frequencies included in the FREQ band;
OPTION =” CALIBRATION “including just the number of eigenvalues for the frequencies in the FREQ band.

All results are stored in a table_container data structure with the name “ANALYSE_MODALE” attached to the evol_noli data structure. Vibratory modes are stored as TYPE_MODE =” DEPL_VIBR “in the table (see § 4).

The times for which we want to perform a vibratory mode calculation are given by a list of moments LIST_INST or INST (list_r8 or l_r8) or by a frequency PAS_CALC (every \(\mathit{npas}\) of time).

In the absence of these keywords, vibratory modal analysis is carried out at every time step.

The keywords PRECISION and CRITERE allow you to select the moments, cf. [U4.71.00].

Note on the moment:

If LIST_INST or INSTde MODE_VIBR contains times equal to or earlier than the initial instant of DYNA_NON_LINE, Code_Aster will ignore calculating vibration modes for these times.

3.22. Operand ENERGIE#

◊ ENERGIE = _F ()

This keyword allows you to activate the calculation of the energy balance, its display during calculation and its storage in the name table PARA_CALC. The energy balance can be retrieved from this table using the RECU_TABLE [U4.71.02] command.

3.23. Operand PROJ_MODAL#

This keyword makes it possible to do the calculation on a modal (or Ritz) basis previously calculated. It is to be used with an explicit time integration diagram.

3.23.1. Operands MODE_MECA, NB_MODE#

♦ MODE_MECA = fashion, [mode_meca]

◊ NB_MODE = nbmode, [I]

We specify the base to use (MODE_MECA) and the number of modes (NB_MODE).

Important note:

The modal base must be based on a numbering consistent with that of the calculated evolution (cf. [§ 11]): same numbering profile.

3.23.2. Operands MASS_GENE, RIGI_GENE, AMOR_GENE#

◊/MASS_GENE = massgen, [Matr_asse_gene_r]

RIGI_GENE = rigigen, [matr_asse_gene_r] AMOR_GENE = amorgen, [matr_asse_gene_r]

These operands are used together in the case where one wants to dynamically condense a part of the model to linear behavior, by strictly calculating by DYNA_NON_LINE only domains with non-linear behavior. This is in order to reduce the size of the calculation model. In this case, it is necessary to calculate a Ritz modal base on all the domains: the nonlinear domain modeled for the calculation using DYNA_NON_LINE and the other linear domains condensed dynamically. This base must be orthogonalized with respect to the mass and to the linear stiffness of all the domains. It must simply be representative of movements active in all fields. On the other hand, only the modes obtained by reducing the Ritz base to the calculation model treated by DYNA_NON_LINE will be entered behind MODE_MECA. An example of calculation is provided by test case SDNV107A [V5.03.107].

The MASS_GENE operand allows you to enter the projection of the mass matrix of all the domains based on Ritz with diagonal storage. The operand RIGI_GENE allows you to enter the projection of the stiffness matrix of the condensed linear domains alone on the Ritz basis with full storage. The operand AMOR_GENE allows you to optionally enter the projection of a damping matrix (if it exists) of condensed linear domains alone on a Ritz basis with full storage.

3.23.3. Operands DEPL_INIT_GENE, VITE_INIT_GENE, ACCE_INIT_GENE#

◊ DEPL_INIT_GENE = deplgen, [vect_asse_gene]

◊ VITE_INIT_GENE = speed, [vect_asse_gene]

◊ ACCE_INIT_GENE = accegen, [vect_asse_gene]

These operands are associated with the use of operands MASS_GENE, RIGI_GENE and possibly AMOR_GENE in the key word PROJ_MODAL. They serve to introduce a generalized vector resulting from the projection by PROJ_VECT_BASE (TYPE =” DEPL “) of a field displacement or speed or acceleration of the complete model (including the linear behavior domain) on the modal basis of this complete model. This generalized vector will serve as the initial condition for the evolution of the generalized coordinates of the calculation on the model reduced to the non-linear domain. It will then also be necessary to fill in the operands of the ETAT_INIT keyword with corresponding fields displacement, speed, acceleration, constraint, internal variable of the reduced model. An example of calculation is provided by test case SDNV107C [V5.03.107].

3.24. Keyword EXCIT_GENE#

◊ EXCIT_GENE =_F (

♦ VECT_GENE = vectgen, [vect_asse_gene]

)

This repeatable keyword is associated with the use of the operands MASS_GENE, RIGI_GENE and possibly AMOR_GENE in the key word PROJ_MODAL. It is used to introduce the forces applied to dynamically condensed and non-modelled domains of linear behavior in the calculation using an explicit time integration scheme. These forces are projected on the basis of Ritz calculated over all domains.

VECT_GENE is used to fill in the force vectors projected on the Ritz base. FONC_MULT is used to fill in the time-dependent multiplier function associated with each vector within an occurrence of the EXCIT_GENE keyword.

3.25. Operand INFO#

◊ INFO = under

Allows various intermediate printings to be made in the message file.

Other impressions are made systematically during the nonlinear calculation, regardless of the value assigned to the INFO keyword: these are the impressions of the residuals and the relative displacement increments during Newton iterations.

Be careful, .mess files can become very important with INFO = 2.

3.26. Operand TITRE#

◊ TITRE = tx

tx is the title of the calculation. It will be printed at the top of the results. See [U4.03.01].