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 has as options

*NLGEOM=YES

considers large displacements with small strains

 

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



The section keyword *STEP has no own data lines but has own keywords which are currently the following:

*STATIC

quasi-static computation

*SOLUTION TECHNIQUE

solver type for iterative solution of systems of nonlinear equations

*CONTROLS

iteration control

*DYNAMIC

dynamic computation with Newmark time integration

*DAMPING

Rayleigh damping parameters for Newmark time integration

*BOUNDARY

displacement boundary conditions for nodes

*AMPLITUDE

scaling function for loads, polyline defined in time

*CLOAD

concentrated loads on nodes

*DLOAD

distributed loads on elements

*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 keyword may have options and specific data lines which are described in the following. The following step keywords must at least be specified: (*STATIC or *DYNAMIC) and *BOUNDARY.

10.9.1 Options and Data of *STATIC

The step keyword *STATIC has as option

RIKS

arc length method is used for step size of load incrementation



separated by a comma. The data line describes the following data

$\Delta t$,

$t$,

$s$


with

$\Delta t$

time step for load incrementation (pseudo time)

$t$

time target in this step (should be larger than the target of a previous step)

$s$

prescribed scalar length of displacement vector – nodal displacements – in case of arc length method

 

(euclidian vector norm is used for $s$)

10.9.2 Options and Data of *DYNAMIC

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

$\Delta t$,

$t$


with

$\Delta t$

time step for load incrementation (real, physical time)

$t$

time target in this step (should be larger than the target of a previous step)

10.9.3 Options of *SOLUTION TECHNIQUE

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

TYPE=MODIFIED-NR

modified Newton-Raphson method

 

or

TYPE=QUASI-NEWTON

BFGS quasi Newton method



The step keyword *SOLUTION TECHNIQUE has no own data lines. Linear problems are treated like nonlinear problems but will generally stop after the first equilibrium iteration.

10.9.4 Options and Data of *CONTROLS

The step keyword *CONTROLS has as option

PARAMETERS=FIELD

 



separated by a comma. The data line describes the following data

$r_{tol}$

scalar tolerance for equilibrium iteration



An equilibrium iteration will stop in case the actual scalar equilibrium residual is lower than $r_{tol}$. A default value is used for $r_{tol}$ in case that a line *CONTROLS PARAMETERS=FIELD is not given.

The step keyword *CONTROLS has as further option

PARAMETERS=TIME INCREMENTATION

 



separated by a comma. The data line describes the following data

$niter$

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. A default value is used for $niter$ in case that a line *CONTROLS, PARAMETERS=TIME INCREMENTATION is not given.

10.9.5 Options and Data of *DAMPING

The step keyword *DAMPING introduces a Rayleigh damping into a dynamic calculation. It has as options

ALPHA=<value1>

The parameter <value1> describes factor for mass matrix

BETA=<value2>

The parameter <value1> describes factor for stiffness matrix



The values for ALPA, BETA are assumed as zero if not specified. The step keyword *DAMPING has no distinct data lines.

10.9.6 Options and Data of *AMPLITUDE

The step keyword *AMPLITUDE is used to define (pseudo-)time dependent boundary conditions or loadings. It has as option

*NAME=<name>

specifies a unique name which basically may be freely chosen (mandatory)



The data line describes a polyline with the following data

$t_0$,

$f_0$,

$t_1$,

$f_1$,

$t_ n$,

$f_ n$


with

$t_0$

time of initial supporting point

$f_0$

time of initial supporting point

$t_ i$

time of further supporting point

$f_ i$

time of further supporting point



with $t_{i} < t_{i+1}$. Supporting points are connected by straight lines. The number $n$ is not restricted.

10.9.7 Options and Data of *BOUNDARY

The section keyword *BOUNDARY has as options

*AMPLITUDE=<name>

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

*OP=NEW

currently not used (optional)



The following data lines describe as data

$i$,

$index_1$,

$index_ n$,

$u_ i$


whereby $index_ i$ indicates a nodal degree of freedom (ndof) and furthermore with

$i$

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 $index_1 \ldots index_ n$



For the meaning of a ndof indicated by $index_ i$ see Section 8 and Section 10.3. All dofs with $index_1<index_ i<index_ n$ are also constrained. Such a data line may be repeated as often as required for the same node or for further nodes.

The value of $u_ i$ is multiplied by the current value of the function defined with *AMPLITUDE=<name>. In case that *AMPLITUDE=<name> is not given a uniform increase starting with 0 and ending with 1 is assumed.

10.9.8 Options and Data of *CLOAD

The section keyword *CLOAD has as options

*AMPLITUDE=<name>

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



The following data lines describe as data

$i$,

$index$,

$P$


with

$i$

number of loaded node

$index$

index of degree of freedom (dof) to be loaded

$P$

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



For the meaning of a ndof indicated by $index_ i$ see Section 8 and Section 10.3. Such a data line may be repeated as often as required for the same node or for further nodes.

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 a uniform increase starting with 0 and ending with 1 is assumed.

10.9.9 Options and Data of *DLOAD

The section keyword *DLOAD has as options

*AMPLITUDE=<name>

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



The following data lines describe as data

<name>,

$index$,

$p$


with

<name>

name of set of loaded elements

 

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

$index$

index of degree of freedom (dof) to be loaded

$p$

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 SH4. Thus, an area loading for an element of type SH4 has to be divided by the particular thickness to determine the equivalent value $p$.

For the meaning of a dof indicated by $index$ see Section 8. Such 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 a uniform increase starting with 0 and ending with 1 is assumed.

10.9.10 Options and Data of *PRESTRESS

Prestressing currently is applicable to element types B23E, B23 only ($\rightarrow $ open issue). The section keyword *PRESTRESS has as options

NAME=<name1>

specifies a unique name which basically may be freely chosen (mandatory)

TYPE=POST-BONDED

indicates prestressing with subsequent bond after initial application (mandatory)

 

or

TYPE=POST-UNBONDED

indicates prestressing without subsequent bond after initial application (mandatory)

AMPLITUDE=<name2>

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



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

$pf_0$,

$A_ p$,

$E_ p$,

$f_{py}$,

$f_{pt}$,

$\epsilon _{pu}$,

$\alpha _ T$


with

$pf_0$

global load factor to yield the initial prestressing force from $pf_0 \cdot A_ p \cdot f_{py}$

$A_ p$

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 multiplied by the current value of the function defined with *AMPLITUDE=<name2>. In case that *AMPLITUDE=<name2> is not given a uniform increase starting with 0 and ending with 1 is assumed.

The following data lines describe the tendon profile with

$i$,

$pf_{i,1}$,

$z_{i,1}$,

$\varphi _{i,1}$,

$x$,

$plf_{i,2}$,

$z_{i,2}$,

$\varphi _{i,2}$


with

$i$

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

$pf_{i,j}$

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 $,\varphi _{i-1,2},\varphi _{i,1}$ mut not neccessarily 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 the step keyword *PRESTRESS with the options

NAME=<name1>

refers to a name of a prestressing (mandatory)

 

(the same name has to be defined within a preceding step section)

AMPLITUDE=<name2>

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



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

10.9.11 Options and Data of *EL FILE

The step keyword *EL FILE has as option

FREQUENCY=<value>

The parameter <value> gives the time interval for writing output files for element data, see Section 7



Following data lines

S

E


are currently not evaluated but should be given. Otherwise no output files will be written.

10.9.12 Options and Data of *NO FILE

The step keyword *NODE FILE has as option

FREQUENCY=<value>

The parameter <value> gives the time interval for writing output files for element data, see Section 7



The following data line

U


are currently not evaluated but should be given. Otherwise no output files will be written.

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