12.3.2 Load Steps

The LOAD commands specify the execution of load steps.

    (syntax)

LOADNR

loset refers to a load set from table 'LOADS' [§2.3.7]. Default is the lowest available load set number.

STEPS

specifies how to apply step sizes. Via method you may specify the step sizes explicitly, or you may let DIANA determine them automatically. [STEPS]

RESTOR

restores data for step step which must have been saved previously [§12.3.9].

method

indicates how the step sizes are to be chosen. [EXPLIC]

EXPLIC

explicitly specified step sizes [§12.3.2.1].

ITERAT

iteration based automatic step size control [§12.3.2.2].

ENERGY

energy based automatic step size control [§12.3.2.3].

AUTOMA

automatic step size control [§12.3.2.5].

SAVE

saves data of specified steps for future restart [§12.3.9].

In case time dependent material or geometrical properties are used, the current time is taken into account. The current time is zero by default [§12.3.1].

Default    (file.dcf)

*NONLIN
[ commands ]
EXECUT LOAD
*END

Due to these commands DIANA will execute a load step with load set 1 and a factor of 1, applying the default integration scheme and solution procedure, but no stop criteria. The same would occur if you had given the following commands:

    (file.dcf)

*NONLIN
[ commands ]
BEGIN EXECUT
 BEGIN LOAD
  LOADNR=lowest
  BEGIN STEPS
   EXPLIC SIZES 1.0
  END STEPS
 END LOAD
END EXECUT
*END

12.3.2.1 Explicitly Specified Load Step Sizes

Via the EXPLIC commands you may specify load step sizes explicitly.

    (syntax)

SIZES

sizes are explicitly specified load step sizes. The number of values specifies the number of steps to be executed.

ARCLEN

applies Arc-length control [§12.3.2.4].

12.3.2.2 Iteration Based Adaptive Loading

The ITERAT commands cause automatic adaptive load increments, based on the number of iterations.

    (syntax)

INISIZ=is

is the initial size for the first step. [is=1.]

CONTIN

asks DIANA to ignore the initial step size is and to continue with the step size of the previous EXECUTE block.

NITERA=ni

is the number of iterations (should be considered as optimal). [ni=6]

MAXSIZ=maxs

is the upper limit of the step size. [maxs=10⁶ ]

MINSIZ=mins

is the lower limit of the step size. [mins=10^-3 ]

DIANA applies the specified limits in the zero-iteration of each step to determine a first estimation of the step size.

NSTEPS=ns

is the number of steps [§30.1.5.3]. [ns=1]

GAMMA=gam

specifies the exponent $\gamma$ from Equation (30.33) [ $\gamma$ = 0.5 ] which we can now write as

$$\Delta \Delta \lambda_{{0}}^{} {\frac{{ ^{t}\Delta l }}{{ \sqrt{ \delta \mathbf{u}_{0}^{\mathrm{\scriptscriptstyle{T}}}\: \delta \mathbf{u}_{0} } }}} \left(\vphantom{ \frac{ \texttt{\textit{ni}} } { ^{t}{N} } }\right. {\frac{{ \texttt{\textit{ni}} }}{{ ^{t}{N} }}} \left.\vphantom{ \frac{ \texttt{\textit{ni}} } { ^{t}{N} } }\right)^{{\! \gamma}}_{}$$ (12.2)

with ^tN the number of iterations from the previous step, this results in ^t+$\Delta$t$\Delta$$\lambda_{{0}}^{}$ the size increment for the current step.

lodunl

specifies a loading-unloading method. In the Adaptive Arc-length methods, loading-unloading can be determined with various methods. See §30.1.5.3 for background theory. [SIGN]

SIGN

for automatic loading-unloading for the incremental step sizes similar to Spherical Path Arc-length control. This method may only be used in combination with Arc-length control. The Updated Normal Plane method is recommended in this case [§12.3.2.4].

PIVOTS

for loading-unloading depending on existence of negative pivots in the triangulated stiffness matrix. This method may only be used in combination with a Newton-Raphson iteration process [§12.3.5.1]. This method cannot be used in combination with an iterative solution procedure [§26.4].

ARCLEN

applies Arc-length control [§12.3.2.4].

12.3.2.3 Energy Based Adaptive Loading

Due to the ENERGY commands DIANA will apply automatic adaptive load increments, based on energy.

    (syntax)

INISIZ=is

is the initial size for the first step. [is=1.]

CONTIN

asks DIANA to ignore the initial step size is and to continue with the step size of the previous EXECUTE block.

MAXSIZ=maxs

is the upper limit of the step size. [maxs=10⁶ ]

MINSIZ=mins

is the lower limit of the step size. [mins=10^-3 ]

DIANA applies the specified limits in the zero-iteration of each step to determine a first estimation of the step size.

NSTEPS=ns

is the number of steps [§30.1.5.3]. [ns=1]

lodunl

specifies a loading-unloading method. In the Adaptive Arc-length methods, loading-unloading can be determined with various methods, see §30.1.5.3 for background theory. [SIGN]

SIGN

for automatic loading-unloading for the incremental step sizes similar to Spherical Path Arc-length control. This method may only be used in combination with Arc-length control. The Updated Normal Plane method is recommended in this case [§12.3.2.4].

PIVOTS

for loading-unloading depending on existence of negative pivots in the triangulated stiffness matrix. This method may only be used in combination with a Newton-Raphson iteration process [§12.3.5.1]. This method cannot be used in combination with an iterative solution procedure [§26.4].

ARCLEN

applies Arc-length control [§12.3.2.4].

12.3.2.4 Arc-length Control

The optional ARCLEN commands specify a selection of displacements to be accounted for in Arc-length iteration methods. This option is called `Indirect Displacement control' and may be useful in case of local snap-through or snap-back behavior.

Arc-length methods may only be used in combination with nodal or element loads, not with prescribed non-zero displacements or with time steps. Arc-length methods fail if the loading is dominantly nonconservative. Arc-length methods adapt the loading during iterations in one load step. For adaptive loading in consecutive load steps use the adaptive loading options of the STEPS command [§12.3.2]. See §30.1.5.2 for background theory.

    (syntax)

method

indicates the Arc-length method to be applied: [UPDATE] SPHERI for the Spherical Path Arc-length method [§30.1.5.2], UPDATE for the Updated Normal Plane Arc-length method [§30.1.5.2].

control

selects a set of degrees of freedom to be applied in Arc-length control: [REGULA] REGULA for regular indirect displacement control, CMOD for CMOD control.

Indirect Displacement Control    (syntax)

In regular indirect displacement Arc-length control the SET block defines a set of degrees of freedom (30.31). You may specify multiple SET blocks.

NODES

nodes is a series of nodes, specified by numbers and/or groups.

TYPE

type specifies a degree of freedom type: TRANSL for translation or ROTATI for rotation.

DIRECT

dirnr is a direction number referring to table 'DIRECT'.

ALPHA

alpha and the direction determine the weight factors $\alpha$ .

    (file.dcf)

*NONLIN
[ commands ]
BEGIN EXECUTE
 BEGIN LOAD
  LOADNR=2
  BEGIN STEPS
   BEGIN EXPLIC
    SIZES 0.5 0.3 0.1
    BEGIN ARCLEN
     UPDATE
     BEGIN REGULA
      BEGIN SET
       NODES 1 3 5 7-13
       TYPE TRANSL
       DIRECT 5
       ALPHA 1.0
      END SET
     END REGULA
    END ARCLEN
   END EXPLIC
  END STEPS
END EXECUTE
*END

CMOD control    (syntax)

In CMOD Arc-length control the SET block defines related pairs of degrees of freedom (30.32). You may specify multiple SET blocks, one for each crack mouth.

SIDE1

defines the degrees of freedom along the first side of the crack mouth.

NODES

nodes1 is a series of node numbers.

TYPE

type1 specifies a degree of freedom type: TRANSL for translation or ROTATI for rotation.

DIRECT

dir1 is a direction number referring to table 'DIRECT'.

ALPHA

alpha1 and the direction determine the weight factors $\alpha_{{1}}^{}$ for each of the degrees of freedom.

SIDE2

defines the degrees of freedom along the second side of the crack mouth.

NODES

nodes2 is a series of node numbers. There must be just as much nodes along both sides of the crack mouth.

TYPE

type2 specifies a degree of freedom type: TRANSL for translation or ROTATI for rotation.

DIRECT

dir2 is a direction number referring to table 'DIRECT'.

ALPHA

alpha2 and the direction determine the weight factors $\alpha_{{2}}^{}$ for each of the degrees of freedom.

    (file.dcf)

*NONLIN
[ commands ]
BEGIN EXECUTE
 BEGIN LOAD
 LOADNR=2
  BEGIN STEPS
   BEGIN EXPLIC
    SIZES 0.5 0.3 0.1
    BEGIN ARCLEN
     UPDATE
     BEGIN CMOD
      BEGIN SET
       BEGIN SIDE1
        NODES  7
        TYPE   TRANS
        DIRECT 1
        ALPHA  1.0
       END SIDE1
       BEGIN SIDE2
        NODES  74
        TYPE   TRANS
        DIRECT 1
        ALPHA  -1.0
       END SIDE2
      END SET
      BEGIN SET
       BEGIN SIDE1
        NODES  9
        TYPE   TRANSL
        DIRECT 2      1
        ALPHA  0.8
       END SIDE1
       BEGIN SIDE2
        NODES  75
        TYPE   TRANSL
        DIRECT 1
        ALPHA  -0.9
       END SIDE2
      END SET
     END SELECT
    END ARCLEN
   END EXPLIC
  END STEPS
 END LOAD
END EXECUTE
*END

In the above example CMOD(1) is 1 x the translation in direction 1 of node 7 minus 1x the translation in direction 1 of node 74, CMOD(2) is 0.8 x the translation in direction 2 of node 9 minus 0.9 x the translation in direction 1 of node 75.

12.3.2.5 Automatic Adaptive Loading

The AUTOMA command causes automatic adaptive load increments. See §30.1.5.4 for background theory.

    (syntax)

SIZE=size

is the total load increment. [size=1 ]

MINSIZ=mins

is the lower limit of the step size, [mins=10^-4 ] relative to size.

MAXSIZ=maxs

is the upper limit of the step size, [maxs=1] relative to size.

CUTBCK=maxs

is the factor by which the step size is scaled down in case of non-convergence. [cutb=0.25]