10.9 Step Section

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A section starting with *STEP defines a type of computation, corresponding loading and boundary conditions to be applied on the model defined in the previous sections.

The section keyword *STEP may have as option

*NLGEOM=YES

considers large displacements with small strains

 

(currently implemented for element types B23E, B23, T2D2, SH4)



The section keyword *STEP has no own data lines but has sub-keywords which are currently as follows:

*STATIC

quasi-static computation disregarding mass inertia

*DYNAMIC

dynamic computation with Newmark time integration

*DAMPING

Rayleigh damping parameters for Newmark time integration

*SOLUTION TECHNIQUE

solver type for iterative solution of systems of nonlinear equations

*CONTROLS

equilibrium iteration control

*AMPLITUDE

scaling function for boundary conditions / loads – polyline defined in time

*BOUNDARY

displacement boundary conditions for nodes

*CLOAD

concentrated loads on nodes

*DLOAD

distributed loads on elements

*TEMPERATURE

temperature at nodes as cause of temperature stresses

*PRESTRESS

prestressing data

*EL FILE

output related to elements

*NODE FILE

output related to nodes



A step section has to closed by *END STEP as the last line. Further step sections may follow. Computations are applied in a sequence as defined by the sequence of step sections.

Each step sub-keyword may have options and specific data lines which are described in the following.

*STATIC

The step sub-keyword *STATIC has as data line

$\Delta t_1$,

$t_1$,

$\Delta t_2$,

$t_2$,

…,

$\Delta t_n$,

$t_n$



with at least a first pair $\Delta t_1, t_1$ and

$\Delta t_i$

pseudo-time increment up to time target $t_i$

$t_i$

pseudo-time target with $t_{i}>t_{i-1}$

 

$t_n$ is the final time target of actual step

 

final time target should be smaller than first target in a following step (if there is one)



This step sub-keyword may have an option – separated by a comma – to activate arc-length control

ARCLENGTH=s



with

$s$

prescribed scalar length – euclidean vector norm – of nodal displacement increment vector

 

nodal displacement increment vector is the difference relating to subsequent instants of time

 

an appropriate value for $s$ may be determined by checking the execution report, see Section 12.2, with a $Delta t$ prescribed in a preceding computation

 

the preceding data line is ignored if the arclength control is activated



See also the the Book, Appendix A.4 for the arclength method

*DYNAMIC

The step sub-keyword *DYNAMIC has no options. The data line describes the following data

$\Delta t$,

$t$



with

$\Delta t$

time increment

$t$

time target of actual step



A variable time increment within a dynamic step is not considered as appropriate.
A dynamic step may be connected with a Rayleigh damping, see the following.
See the Book 4.10 for dynamics.

*DAMPING

The step sub-keyword *DAMPING introduces a Rayleigh damping into a dynamic calculation. This builds a damping matrix from a linear combinations of the mass matrix and the stiffness matrix and might avoid artificial high frequency oscillations.
*DAMPING has as options

ALPHA=$\alpha $

The parameter $\alpha $ gives the scaling factor for the mass matrix

BETA=$\beta $

The parameter $\beta $ gives the scaling factor for the stiffness matrix



The values for $\alpha ,\beta $ are assumed as zero if not specified.
If specified in a static step, *DAMPING is ignored.

*SOLUTION TECHNIQUE

Default method for solution of systems of equations is the Newton-Raphson method in case that *SOLUTION TECHNIQUE is not specified. Alternative methods may be used with the step sub-keyword *SOLUTION TECHNIQUE with the options

TYPE=MODIFIED-NR

modified Newton-Raphson method

or

TYPE=QUASI-NEWTON

BFGS quasi Newton method



Linear problems are treated like nonlinear problems but will generally stop after the first equilibrium iteration, see the following *CONTROLS.

See the Book Appendix A.1 for solution methods.

*CONTROLS

The step sub-keyword *CONTROLS contrls iterations parameters and has as options – separated by a comma

ITOL=$r_{tol}$

scalar tolerance for equilibrium iteration

 

an equilibrium iteration will stop in case the actual scalar equilibrium residual is lower than $r_{tol}$

and

NITER=

  \[ niter \]    

maximum number of equilibrium iterations with a time increment or loading step

 

iteration will stop upon this criterion, irrespectively whether the equilibrium iteration tolerance is reached or not



Default values $r_{tol}=1 \cdot 10^{-3}$ and $niter=10$ are used in case *CONTROLS is not specified. It is highly recommended to try different values (e.g. $1 \cdot 10^{-3} \ldots 1 \cdot 10^{-6}$) if a new problem is started to check convergence of equilibrium iterations.
These criteria are also used for linear problems, but the iteration will stop after the first iteration with $r \approx 0$.

*AMPLITUDE

The step sub-keyword *AMPLITUDE may be used to define (pseudo-)time dependent scaling factors for boundary conditions or loadings. It has as mandatory option

*NAME=<name>

specifies a unique name which may be freely chosen



The data line describes a polyline with the following data – in one line not interrupted with CR!

$t_0$,

$f_0$,

$t_1$,

$f_1$,

$t_n$,

$f_n$


with

$t_0$

time of initial supporting point

$f_0$

value of initial supporting point

$t_i$

time of further supporting point

$f_i$

value of further supporting point



with $t_{i} < t_{i+1}$. Supporting points are connected by straight lines. The number $n$ or line length, respectively, is not restricted.
If $t>t_n$ the corresponding value $f$ is linearly extrapolated from the last two pairs.
Prescribed loadings and nonzero boundary conditions are scaled with (pseudo-)time value $t$ in case *AMPLITUDE is not specified.

*BOUNDARY

The step sub-keyword *BOUNDARY defines boundary conditions. There must be sufficient boundary conditions to prevent rigid body motions. It may have as options

*AMPLITUDE=<name>

refers to a name of an amplitude defined with the step keyword *AMPLITUDE within the current step section (optional)

*OP=ADD

data of following date lines are added to final values of previous step

 

in case there is a previous step and boundary conditions are defined for the same degrees of freedom



The data lines describe as data

$i$,

$index_1$,

$index_n$,

$u_i$


with (dof is degree of freedom)

$i$

number of node to be constrained

$index_1$

index of 1st dof to be constrained

$index_n$

index of last dof to be constrained

$u_i$

value of prescribed displacements of dofs defined by $index_1 \ldots index_n$

 

$u_i=0$ is for a fixed zero displacement



For the type of a dof indicated by $index_i$ see Section 7 and Section 10.3.
All dofs with $index_1<index_i<index_n$ are also constrained.
Use $index_1=index_i$ in case only dof is constrained, i.e. two integers must always be given (exactly four items per data line).
A data line may be repeated as often as required for the same node or for further nodes.

The value of $u_i$ is scaled by the current value of the function defined with *AMPLITUDE=<name>. In case that *AMPLITUDE=<name> is not given a non-zero $u_i$ is scaled with the (pseudo-)time value.

*CLOAD

The section sub-keyword *CLOAD may define concentrated loadings and may have as options

*AMPLITUDE=<name>

refers to a name of an amplitude defined with the step keyword *AMPLITUDE within the current step section



The data lines describe as data

$i$,

$index$,

$P_i$


with

$i$

number of loaded node

$index$

index of degree of freedom (dof) to be loaded

$P_i$

value of prescribed concentrated load of dof defined by $index$



For the type of a ndof indicated by $index_i$ see Section 7 and Section 10.3.
A data line may be repeated as often as required for the same node or for further nodes.

The value of $P_i$ is scaled by the current value of the function defined with *AMPLITUDE=<name>. In case that *AMPLITUDE=<name> is not given $P_i$ is scaled with the (pseudo-)time value.

*DLOAD

The section sub-keyword *DLOAD may define distributed loadings and may have as option

*AMPLITUDE=<name>

refers to a name of an amplitude defined with the step keyword *AMPLITUDE within the current step section



The data lines describe as data

<name>,

$index$,

$p_i$


with

<name>

name of set of loaded elements, see Section 10.3

 

the same name also has to be defined within an element section

$index$

index of degree of freedom (dof) to be loaded

$p_i$

value of prescribed distributed load of dofs defined by <index> and $index$



A distributed loading is distributed over a length for element types B..., T..., over an area for element types CP..., SB3 and over a volume for the element type SH3, SH4. Thus, an area loading for an element of type SH4 has to be divided by the particular thickness to determine the equivalent value $p_i$.
For the type of a dof indicated by $index$ see Section 7.
A data line may be repeated as often as required for more element sets.
The value of $p$ is multiplied by the current value of the function defined with *AMPLITUDE=<name>. In case that *AMPLITUDE=<name> is not given $T$ is scaled with the (pseudo-)time value.

*TEMPERATURE

The step sub-keyword *TEMPERATURE may define temperatures at nodes. Temperatures may induce stresses.

It may have as option

*AMPLITUDE=<name>

refers to a name of an amplitude defined with the step keyword *AMPLITUDE within the current step section



The data lines describe as data

$i$,

$T_1$,

$T_2$


with

$i$

number of node with temperatureto be constrained

$T_1$

temperature at lower edge $z_1$ of beam, see Fig. 1

$T_2$

temperature at upper edge $z_2 > z_1$

 

temperature is linearly interpolated in between along the cross section



Regarding the beam’s longitudinal direction temperatures are linearly interpolated between nodes on the left hand and right hand side. Regarding enhanced beam elements, see Section , a temperature definition for the additional node is ignored.
The value of $T$ is multiplied by the current value of the function defined with *AMPLITUDE=<name>. In case that *AMPLITUDE=<name> is not given $p_i$ is scaled with the (pseudo-)time value.

See the Book 4.6 for temperature effects with beams.

*PRESTRESS

The step sub-keyword *PRESTRESS may define a prestressing of elements.

It must have the options

NAME=<name1>

specifies a unique name which may be freely chosen

TYPE=POST-BONDED

indicates prestressing with subsequent bond after initial application

or

TYPE=POST-UNBONDED

indicates prestressing without subsequent bond after initial application



It may have an option

AMPLITUDE=<name2>

refers to a name of an amplitude defined with the step keyword *AMPLITUDE within the current step section



The first data line describes the following general properties of tendon and its material with

$\alpha _{p0}$,

$A_p$,

$E_p$,

$f_{py}$,

$f_{pt}$,

$\epsilon _{pu}$,

$\alpha _T$


with

$\alpha _{p0}$

factor for the nominal prestressing force $F_{p0}=\alpha _{p0} \cdot A_p \cdot f_{py}$

 

$\alpha _{p0}<1$ with $\alpha _{p0}\approx 0.6 \ldots 0.8$ according to common standards

$A_p$

cross section area

$E_p$

initial Young’s modulus

$f_{py}$

yield stress

$f_{pt}$

failure stress

$\epsilon _{pu}$

strain corresponding to $f_u$

$\alpha _T$

thermal expansion coefficient



The value of the prestressing force is scaled by the current value of the function defined with *AMPLITUDE=<name2>. In case that *AMPLITUDE=<name2> is not given the nominal prestressing force $F_{p0}$ is scaled with the (peseudo-)time value. Anyway, the scaling factor should not exceed a value of 1.

The following data lines describe the tendon profile with

$i$,

$\alpha _{pi,1}$,

$z_{i,1}$,

$\varphi _{i,1}$,

$x$,

$\alpha _{pi,2}$,

$z_{i,2}$,

$\varphi _{i,2}$


with

$i$

number of a finite element defined in the element section, see 10.3

$\alpha _{pi,j}$

factor to adapt the initial prestressing to the respective element

 

$j=1$: at the element’s start node, $j=2$ at the element’s end node

 

(may be used to, e.g., model frictional losses)

$z_{i,j}$

height coordinates of tendon in element $i$ with respect to reference axis

$\varphi _{i,j}$

inclinations of tendon in element $i$ with respect to reference axis (counterclockwise positive)

$x$

not used (for compatibility with the data of the start node)



The tendon profile is interpolated with a cubic spline within an element on base of values $z_{i,1},z_{i,2},\varphi _{i,1},\varphi _{i,2}$. The values of $z_{i-1,2},z_{i,1}$ and $\varphi _{i-1,2},\varphi _{i,1}$ must not necessarily be same for an element $i-1$ followed by an element $i$, although same values generally make more sense. Furthermore, an element within a structure must not have a prestressed preceding element or prestressed following element.

There may as much data lines for tendon profiles as required.

Prestressing is firstly applied as unbonded in that step where it is defined with that data as is described before. It is applied in following steps again using the step sub-keyword *PRESTRESS within the respective *STEP-section with the options

NAME=<name1>

refers to a name of a prestressing defined in a preceding step (mandatory)

AMPLITUDE=<name3>

refers to a name of an amplitude defined with the step keyword *AMPLITUDE within the current step section (optional)



General and geometric data lines must not be repeated. The value of nominal prestressing force $F_{p0}$ is scaled by the current value of the function defined with *AMPLITUDE=<name3>. The *AMPLITUDE may be omitted and the nominal prestressing force is scaled by the (pseudo-)time, but this is not appropriate regarding the actual application of prestressing. It should be hold constant during service accomplished by a constant $f$-value, see *AMPLITUDE-definition.

Prestressing is applied as unbonded in case it has initially defined with TYPE=POST-UNBONDED or alternatively as bonded in case it has initially been defined with TYPE=POST-BONDED.

See the Book 4.8 for prestressing of beams.

*EL FILE

The step sub-keyword *EL FILE initiates ASCII-output related to integrations points of elements and must have as option

FREQUENCY=<value>

The parameter <value> defines the output time interval



Details for element data are given in Section 12.3.

*NODE FILE

The step sub-keyword *NODE FILE initiates ASCII-output related to nodes and must have as option

FREQUENCY=<value>

The parameter <value> defines the output time interval



Details for nodal data are given in Section 12.4

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