/IMPL/DT/3

Engine Keyword Implicit automatic time step control with Riks method.

Format

/IMPL/DT/3

It_w L_arc L_dtn Δ T s c a _ d MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaads fadaWgaaWcbaGaam4CaiaadogacaWGHbGaai4xaiaadsgaaeqaaaaa @3CA7@ Δ T s c a _ max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaads fadaWgaaWcbaGaam4CaiaadogacaWGHbGaai4xaiaadsgaaeqaaaaa @3CA7@ C_type W_scal

Definitions

Data Description SI Unit Example
lt_w If the solution of a time step converges within It_w iterations, the next time step will be increased by a factor controlled by Δ T s c a _ max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaads fadaWgaaWcbaGaam4CaiaadogacaWGHbGaai4xaiaadsgaaeqaaaaa @3CA7@ .
= 0
Set to 12
  
L_arc Input arc-length.
= 0
Will be calculated automatically.
  
L_dtn Maximum number of iterations before resetting and decreasing the time step by a factor of Δ T s c a _ d MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaads fadaWgaaWcbaGaam4CaiaadogacaWGHbGaai4xaiaadsgaaeqaaaaa @3CA7@ .
= 0
Set to 25
  
Δ T s c a _ d MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaads fadaWgaaWcbaGaam4CaiaadogacaWGHbGaai4xaiaadsgaaeqaaaaa @3CA7@ Scale factor for decreasing the time step when L_dtn is reached.
= 0
Set to 0.67
  
Δ T s c a _ max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaads fadaWgaaWcbaGaam4CaiaadogacaWGHbGaai4xaiaadsgaaeqaaaaa @3CA7@ Maximum scale factor for increasing the time step.
= 0
Set to 1.2
  
C_type
= 0
Set to 2
= 1
Crisfield constraint equation.
= 2
Modified Forde & Steimer equation.
  
W_scal Scale factor for controlling the loading contribution in the constraint equation.

Default = 0.0

  

Comments

  1. The Riks type arc-length method is suitable for nonlinear static analysis of unstable problems like buckling, snap-through. It solves at the same time for the displacement vector and for a loading scale factor by adding a constraint equation.

    This method can only be used for static analysis and the loading should be proportional in each restart run.

  2. A constant arc length can be defined by giving Δ T s c a _ d = Δ T s c a _ max = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeuiLdqKaamivamaaBaaaleaacaWGZbGaam4yaiaadggacaGGFbGa amizaaqabaGccqGH9aqpcqqHuoarcaWGubWaaSbaaSqaaiaadohaca WGJbGaamyyaiaac+faciGGTbGaaiyyaiaacIhaaeqaaOGaeyypa0Ja aGymaaaa@4C96@ or directly defining L_arc. Otherwise, an adaptive arc length based on the convergence rate will be used. The adjustment is:(1)
    L _ n e w = L _ o l d ⋅ ( I t _ w I t _ o l d ) 0.5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaamitaiaac+facaWGUbGaamyzaiaadEhacqGH9aqpcaWGmbGaai4x aiaad+gacaWGSbGaamizaiabgwSixpaabmGabaWaaSaaaeaacaWGjb GaamiDaiaac+facaWG3baabaGaamysaiaadshacaGGFbGaam4Baiaa dYgacaWGKbaaaaGaayjkaiaawMcaamaaCaaaleqabaGaaGimaiaac6 cacaaI1aaaaaaa@5346@

    Where, It_old is the number of convergence iterations of previous load increment.

  3. The time step adjustment uses the same factor than arc length but bound by Δ T s c a _ d MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaads fadaWgaaWcbaGaam4CaiaadogacaWGHbGaai4xaiaadsgaaeqaaaaa @3CA7@ and Δ T s c a _ max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaads fadaWgaaWcbaGaam4CaiaadogacaWGHbGaai4xaiaadsgaaeqaaaaa @3CA7@ . Each new time step is only the predictor value as Riks method will give the final time step at the end of each load increment. Therefore, a negative time step can be obtained for some loading increments.
  4. Riks method can only be used with Modified Newton (only in the sense of reforming the stiffness matrix) and line search methods, but a small number (L_A ≤ 3) is recommended for the reforming frequency of the stiffness matrix.
  5. A maximum cycle number (see /IMPL/NCYCLE/STOP) can be used to stop the run in case the solution never reaches the specified load.
  6. If /IMPL/DT/1, /IMPL/DT/2, or /IMPL/DT/3 are not present, the only time step controls are /IMPL/NCYCLE/STOP and /IMPL/DT/STOP. In the case of divergence, the time step will be reduced by half and repeated.
  7. For the post-buckling simulations involving contact, the Riks method may not work, especially if contact has not occurred at beginning or contact is lost during the simulation. In this case, it is better to use implicit dynamic analysis.
  8. If the Riks analysis includes irreversible deformation such as plasticity and a restart, using another Riks step is attempted while the magnitude of load on the structure is decreasing, the solver will find the elastic unloading solution. Therefore, restart should occur at a point in the analysis where the load magnitude is increasing, if plasticity is present.