Dyna 1
Dyna 1
Dyna 1
Dynamic Analysis
SOFiSTiK 2016
DYNA
Dynamic Analysis
DYNA Manual, Version 2016-0
Software Version SOFiSTiK 2016
c 2015 by SOFiSTiK AG, Oberschleissheim, Germany.
Copyright
SOFiSTiK AG
HQ Oberschleissheim
Bruckmannring 38
85764 Oberschleissheim
Germany
Office Nuremberg
Burgschmietstr. 40
90419 Nuremberg
Germany
Front Cover
Project: MILANEO, Stuttgart, Germany | Client: Bayerische Hausbau and ECE | Architect: RKW Rhode Kellermann Wawrowsky
| Structural Engineering for Bayerische Hausbau: Boll und Partner | Photo: Dirk Mnzner
Contents | DYNA
Contents
Contents
Task Description
1-1
Theoretical Principles
2.1
Integration of the Equations of Motion . . . . . . . . . . . . .
2.2
Computation of the Eigenvalues and the Modal Damping
2.3
Modal Analysis for Time-dependent Loading . . . . . . . . .
2.4
Modal Excitation through Ground Acceleration . . . . . . .
2.5
Modal Analysis of a Steady-state Excitation . . . . . . . . .
2.6
Excitation through a Spectrum . . . . . . . . . . . . . . . . . .
2.7
Sign of corresponding forces . . . . . . . . . . . . . . . . . . .
2.8
Kinematic Constraints . . . . . . . . . . . . . . . . . . . . . . . .
2.9
Elastic Stiffnesses . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 Geometric Stiffness and P-delta . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
2-1
2-1
2-3
2-4
2-4
2-6
2-8
2-9
2-10
2-11
2-11
Literature
2-13
3-1
3-1
3-1
3-3
3-5
3-9
3-12
3-14
3-16
3-17
3-20
3-21
3-23
3-26
3-30
3-32
3-34
3-36
Input Description
3.1
Input Language . . . . . . . . . . . . . . . . . . . . .
3.2
Input Records . . . . . . . . . . . . . . . . . . . . . .
3.3
SYST System Parameters . . . . . . . . . . . . .
3.4
CTRL Calculation Parameters . . . . . . . . . .
3.4.1
SOLV Equation solver . . . . . . . . . . .
3.4.2
CORE Parallel computation control . .
3.5
GRP Selection of Element Groups . . . . . . .
3.6
MAT General Material Properties . . . . . . . .
3.7
BMAT Elastic Support / Interface . . . . . . . .
3.8
SMAT SBFEM - Material Properties . . . . . .
3.9
MASS Lumped Masses . . . . . . . . . . . . . .
3.10 EIGE Eigenvalues and Eigenvectors . . . . . .
3.11 MODD Modal Damping . . . . . . . . . . . . . . .
3.12 STEP Parameter of the Step-wise Integration
3.13 LC Load Case . . . . . . . . . . . . . . . . . . . . .
3.14 CONT Contact and Moving Load Function . .
3.15 HIST Results within Time . . . . . . . . . . . . .
SOFiSTiK 2016
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
DYNA | Contents
3.16
3.17
4
ii
Output Description
4.1
Nodes . . . . . . . . . . . . . . . . . . .
4.2
Cross Sections . . . . . . . . . . . . .
4.3
General Parameters . . . . . . . . . .
4.4
Elements . . . . . . . . . . . . . . . . .
4.5
Natural Frequencies . . . . . . . . . .
4.6
Load Cases, Functions and Loads
4.7
Displacements . . . . . . . . . . . . . .
4.8
Internal Forces and Moments . . . .
4.9
Time Variations . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3-39
3-45
4-1
4-1
4-1
4-1
4-2
4-2
4-2
4-3
4-3
4-3
SOFiSTiK 2016
Task Description
The program DYNA can be used for static and primarily for dynamic analysis
of three-dimensional structures. It can perform the following tasks (Special licenses may be needed):
Implicit direct integration of the equations of motion for structures with arbitrary damping
The static system is stored in the database after its generation e.g. by the program SOFiMSHA, SOFiMSHC or SOFiPLUS.
The following elements can be processed by DYNA:
Damping elements
Shell elements
3D-solid elements
For the explicit integration not all features are supported. Only the truss, cable,
SOFiSTiK 2016
1-1
spring and the 3D volume (BRIC) element are available. All interactions (Wind,
Loadtrain, Soil) are not available. But geometric and material nonlinearity are
supported.
The results of the dynamic analysis including the mode shapes are stored in the
database as displacements and stresses with a load case number.
The mode shapes can also be transferred from the database after a calculation
with the program ASE.
For the purposes of a dynamic analysis, the program may output the maximal
and the minimal of all displacements, velocities or accelerations as well as internal forces and moments, and eventually the time variation of selected degrees
of freedom or internal forces and moments.
For speed reasons almost all algorithms follow what is called IN-CORE solutions. The size of the problem is therefore limited by the amount of available
main memory. Modal solutions transferring the eigenvalues from ASE are not
subjected to this limitations.
1-2
SOFiSTiK 2016
Theoretical Principles
(2.1)
where
u
displacement
mass
viscous damping
stiffness
p(t)
external loading
The method of finite elements replaces the continuous vector fields by discrete
displacement, velocity and acceleration vectors. The material properties are
converted to mass, damping and stiffness matrices:
mj j + cj j + kj j = p (t)
(2.2)
2.1
For the most general approach the direct integration of the differential equations
a second discretisation in time has to be applied. The first step is to subdivide
the time in discrete time steps. Then the simplest form is to assume a constant
SOFiSTiK 2016
2-1
0) +
(t)
= (t
t t0
t
0 + t) (t
0 )]
[ (t
(2.3)
According to the Newmark method the following expressions hold for the velocity and the displacement at the end of the time interval t :
(t + t) = (t)
(t + t)]
+ t [(1 ) (t)
+
(2.4)
(t + t)]
(t + t) = (t) + t (t)
+ t 2 [(1/ 2 ) (t)
+
(2.5)
Then we have the choice between five different possibilities to select how or for
which time t + t the equilibrium equation is fulfilled.
Wilson-Theta-Method ( 1.37)
This value is a modification of the Newmark method where the numerical
damping enlarges the period to a greater extent, but keeps the amplitudes
to a higher accuracy. In the literature the parameter is given as but this
has been changed to avoid conflicts with the next method.
2-2
SOFiSTiK 2016
degrading the order of accuracy. It is especially suited for non linear problems. The value is taken from the input value as = ( 1.0). Thus
we have a formal equivalent to the Crank-Nicholson method (see program
HYDRA)
Modal Analysis
The system of equations to be solved can be significantly simplified if the
solution is calculated in the subspace of a few eigenvectors. This requires
knowledge of the eigenvalues and the eigenvectors, the calculation of which
is relatively extensive. But then it is possible to integrate the linear equations
exactly. Nonlinear effects may be treated in a simplified way if the modes
contain the nonlinear displacement possibilities.
2.2
k Vj = 0
6= j
(2.6a)
6= j
(2.6b)
By use of these conditions both the mass and the stiffness matrix in the eigenvalue space become pure diagonal matrices. In order for the damping matrix
to become diagonal too, damping must be diagonal itself or proportional to the
mass and/or the stiffness matrix:
c=m+bk
(2.7)
A decoupled system can be solved in such case yielding the natural frequencies as well as the generalised masses (M), the modal damping (d) and the
SOFiSTiK 2016
2-3
V Tn
V Tn
V Tn
(2.8a)
k V n = Mn
2
(2.8b)
(2.8c)
(2.8d)
c V n = 2 d Mn
p(t)
The mode shapes are scaled in such a way that Mn become equal to 1.0. When
(2.7) is used, the resulting modal damping d (Lehrs damping factor) is also a
diagonal matrix:
dn =
1
2
+ b n =
(2.9)
In a complex system the individual elements may have quite different damping
properties. The proportionality of the damping is then no longer given and the
damping matrix Cn does not become a diagonal matrix. In that case there are
three possibilities:
2.3
As long as the conditions (2.6)-(2.7) are fulfilled, the equation of motion can be
solved decoupled and integrated exactly. The solution at each time moment
results from superposition of the computed mode shapes.
2.4
2-4
SOFiSTiK 2016
(2.10)
The vector r defines the displacements of the individual nodes, when the base
point is subjected to a unit displacement. Excitations at particular base points
can be defined by this vector as well. The vector can be defined through the input
of its individual components or it can be read from the database (e.g. influence
line of the reaction force).
Applying equation (2.8d) to the load vector (2.10) one can obtain the modal
loads, which can also be represented as the product of the acceleration with the
so-called participation factors L.
(t)
P = V Tm p(t) = Lm
(2.11)
0.00
1.00
2.00
7.00
7.00
6.00
6.00
5.00
5.00
4.00
4.00
3.00
3.00
1.00
0.00
1.00
1.00
2.00
2.00
1.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
It is very important to keep in mind, that those modal loads describe the participation of the eigenforms and thus may have quite different values. If we consider
for example the first three modes of a column with an intermediate support:
1.00
0.00
1.00
we obtain for a horizontal acceleration the modal loads with different signs and
the largest contribution from the third Eigenform:
Mode
1
2
3
R*V-Factor
-2.278E+00
9.226E-01
2.747E+00
SOFiSTiK 2016
[o/o]
30.4
5.0
44.3
2-5
4
6.345E-08 0.0
5 -6.505E-01 2.5
------------------------Qu.Sum
1.401E+01 82.2
The sum of the squares of the participation factors represents the mass of the
system in the activated direction. The number of eigenvectors used in practical
analyses should be such that at least 90 percent of the total mass is taken into
account.
Many design codes use equivalent loads to calculate the forces and moments
for every mode. They are given by the relation:
HE, = M
L
M
S,
(2.12)
The given formula respective the load vector is a very nice picture if we have only
one principal mode. However if we have multiple modes and multiple directions,
we encounter a severe problem. Beside the inefficient evaluation of all those
data there is no such thing like an unfavourable load in a single node. Even the
maximum obtained acceleration is not a suitable measure for an unfavourable
action on any member.
As DYNA calculates the forces and moments of the Eigenforms in a much more
efficient and mathematical correct way, those bulk values are not available for
the user. However the resultant forces of those, the base shear is evaluated and
superposed like all other results according to the definitions of CTRL STYP.
If the user wants to see those load vectors in detail he may use SOFiLOAD
and the command ACCE NODE LINF i where i is the load case number of the
corresponding eigenform and an acceleration has to be defined from the value
2 times the modal response (Y ) taken from the DYNA results printout.
2.5
(2.13)
2-6
T p0
2
sn ( t )
2
1 r 2 + 4 (d r)2
(2.14)
SOFiSTiK 2016
where
r=
= + rctn
2dr
1 r2
(2.15)
These classical response functions have a region below the resonance frequency where the structure follows the loading with a dynamic enlarging factor
and a region above the resonance where it is no longer possible for the structure
to follow the loading, yielding in a steady decay of the counter phase response
until zero for high frequencies.
These response functions yield the true response including the shift of the resonance peak due to damping effects. All frequencies used in DYNA are always
there for those of the undamped oscillation.
The oscillation contains an additional r-multiple component, introduced through
the starting conditions and gradually reduced due to damping. The superposition of these oscillations results in a floating effect, which can be accurately
registered by time integration. DYNA can selectively omit this component or add
it if its unfavourable.
An accurate calculation of the maximum stressing taking into consideration the
phase shift can be carried out only for the final transient oscillation state by
neglecting the transient components. In all other cases only a statistical super-
SOFiSTiK 2016
2-7
2.6
In this case the factors f(t) with unknown phase shift are defined by their maximum value only, and they are usually prescribed in tables as functions of natural
frequency and damping. In order to compute the response frequency and damping are interpolated from the spectra.
For an earthquake analysis the response spectra define the acceleration dependant of the Perios and Damping or the behaviour factor.
For the wind the response is obtained by a background and a resonance response. While the dynamic response is obtained from a normalized power
spectrum, the background contribution is always assumed to be 1.0, as this
is on the safe side and is appropriate if the coherence effects are introduced by
the loading itself.
q=
S
v
u
t
1+
2
2
1 X + 2 X 2 + 3 X 3
(1 + b X c )d
L
z
X=
=
or
m
V
V
2
(2.16)
(2.17)
(2.18)
rX X
q j qj
3
8 d dj d + r dj r 2
j =
2
1 r 2 + 4d dj r 1 + r 2 + 4 d2 + dj2 r 2
(2.19)
(2.20)
For the case of shear within a quadratic section it can be easily shown, which
error is introduced by the SRSS Method. The acceleration in X-direction exits
the two diagonal Eigenforms with the same amount of 25 % of the total shear.
2-8
SOFiSTiK 2016
Eigenfor m 2
a
=
Eigenfor m 1
+
Eigenfor m 1
Eigenfor m 2
The SRSS-Method yields 35 % for all 4 walls, while the CQC Method will give
50 % for the x-walls and zero for the y-walls which is the correct value.
The
same method may be also used for the directional superposition for the most
unfavourable direction. Three load cases with accelerations in orthogonal directions may be analyzed together in a single DYNA run and combined with the
SRSS method. The correct sign of the corresponding forces will yield correct results, while the method used in other programs with independent extreme values
may yield results considerably to large.
2.7
For every type of superposition yielding only positive values, the sign of the
corresponding forces and moments should not be neglected. Although it is quite
common to use positive values for all results, this is not true and uneconomical
in most cases.
For example if we look at a plane horizontally loaded framework, the internal
forces and moments vary depending on the sign of the horizontal force, yet in
every case it has to be observed that the sign of the moment and normal force
in one of the column are identical, while different in the other one.
SOFiSTiK 2016
2-9
If we extremize for the maximum moment, then the associated normal forces
must have different signs. Exactly this is available from the mode shapes. If we
now assemble the maximum moment of different mode shapes, then we should
thus always add the mode shapes only completely with a global factor. When
we intend to add the absolute values, then it is sufficient that all mode shapes
are either added or subtracted according to the sign of the leading force. So we
are replacing the rule of combination
SUMj =
X
sj
(2.21)
by the general form for the vector of internal forces and for the maximum value
of force j:
SUM =
+1, s 0
j
(2.22)
1, s < 0
j
The same can be used for the method SRSS (Square Root of Sum of Squares)
the rule:
v
uX
sj 2
SUMj = t
(2.23)
is replaced through
SUM =
sj
= qP
2
sj
(2.24)
Last but not the same can be done for the CQC-method. In any case the leading
force value will be positive thence it must be introduced as an alternating load in
the final design superposition.
2.8
Kinematic Constraints
2-10
SOFiSTiK 2016
can lead also to oscillation of solution through violation of the discrete maximum
principle at small time steps that perform disturbingly. But as these matrices
are not always acceptable, the user therefore can switch to the use of a diagonalised mass matrix, which then requires special care in the description of the
constraints.
When modelling rigid floor disks one should place the reference node as close
as possible to the gravity or the shear centre in order to get the most realistic
results.
Kinematic constraints increase the band width considerably. The memory capacity can thus be quickly exceeded in cases of large systems or strongly recursive kinematic constraints.
2.9
Elastic Stiffnesses
DYNA employs very compact formulations of the element stiffnesses. The spring
and boundary elements are in the classical form given and do not distinguish
from those ones in programs ASE or STAR2.
The beam element is a real finite element with a displacement accretion with
Hermitical function of second redundancy (therefore cubical polynomials). That
is considered at:
The element always produces however only internal forces and moments for
internal sections if requested bei CTRL BEAM 1. Deformations along the beam
element will never be calculated.
The QUAD shell element corresponds to the simple accretion without nonconforming parts. (Hughes and/or Bathe-Dvorkin)
2.10
For beam and truss elements a load case can be read, which can be used
for the determination of the geometric stiffnesses. The second order theory
effects are exact in those cases where the axial force does not change due to
SOFiSTiK 2016
2-11
geometric nonlinear effects. Thus this approach includes not only but exceeds
the so called P-delta effects. The eigenfrequency of member with tension will
thereby increase, while those of members under compression will decrease until
they reach the value of zero for the buckling load.
For cable elements the complete separation of geometric stiffness is not always
a good approach, as this might generate negative eigenvalues in a buckling
analysis. On the other side a buckling factor is defined as the factor of the
loading. So it is generally foreseen for cables to split the prestress in two parts.
One part is included in the general stiffness (this is the value defined with the
element itself) and the difference from the actual primary estate to that general
value is then used to form the geometric stiffness for the buckling analysis. If that
general value is not defined and option CTRL PLC does not select otherwise,
the primary estate will be taken as general prestress.
2-12
SOFiSTiK 2016
Literature | DYNA
Literature
[1] Timothy A. Davis. Ldl: a consise sparse cholesky factorization package.
http://www.cise.ufl.edu/research/sparse/ldl, 2003-2012.
[2] F.P. Mller. Baudynamik. Betonkalender, Teil II, 1978.
SOFiSTiK 2016
2-13
DYNA | Literature
2-14
SOFiSTiK 2016
Input Description
3.1
Input Language
The input is made in the CADINP language (see general manual SOFiSTiK:
Basics).
Three categories of units are distinguished:
mm
[mm]
[mm] 1011
3.2
Input Records
Items
SYST
TYPE
NCS
PROB
CTRL
OPT
VAL
VAL2
GRP
NO
VAL
MODD
MAT
BMAT
SMAT
PHYS
CS
PLC
STAT
CS
FACS
HING
RADA
RADB
FACP
FACM
WIND
LMAX
NCSP
NO
MUE
GAM
GAMA
ALFA
EY
MXY
OAL
OAF
SPM
TITL
NO
CT
CRAC
YIEL
MUE
COH
DIL
GAMB
REF
MREF
NO
LC
EX
EY
EZ
RHOX
RHOY
SOFiSTiK 2016
3-1
Record
MASS
EIGE
Items
RHOZ
ALF
BET
NO
MX
MY
MZ
MXY
MXZ
MYZ
MB
NEIG
TYPE
NITE
MITE
MXX
MYY
MZZ
LMIN
STOR
LC
DEL
LCUP
MODD
NO
STEP
DT
INT
BET
THE
EIGB
EIGT
EIGS
DTF
STHE
LC
NO
FACT
DLX
DLY
DLZ
MODB
TITL
CONT
TYP
REF
NR
TMIN
LCUV
LCUT
TYPE
FROM
TO
STEP
RESU
LCST
XREF
YREF
ZREF
DUMP
EXTR
TYPE
MAX
MIN
STYP
ACT
ECHO
OPT
VAL
LCUR
HIST
The records HEAD, END and PAGE are described in the general manual
SOFiSTiK: Basics.
A description of each record follows:
3-2
SOFiSTiK 2016
3.3
SYST
Item
Description
Unit
Default
TYPE
Type of System
REST use existing main system
SECT use subsystem of section SNO
Section number
LT
REST
LT
LT
LINE
CS
PLC
STAT
State of analysis
SERV serviceability
ULTI
ultimate limit
CALC general nonlinear
LT
SNO
PROB
PHYS
The system for the analysis has to exist in the database. DYNA can use also
the FE-meshes of a specific section. This may be selected with SYST SECT
nnn, where nnn is the number of that section. The FE-system of the sections is
saved in separate data base in a sub-directory.
The geometric type of the analysis may be linear or according 2nd order theory
(small deformations, but stress induced geometric stiffness and 3rd order theory
(large deformations but small strains). The stresses for the geometric stiffness
are taken from the primary load case. Thus without a primary load case the
analysis is always linear, with a primary load case the default is TH2. Option
TH3 is currently only available for explicit integration.
The physical type of the analysis may be linear or including the nonlinear properties of the spring elements and/or the full material non linearity (explicit inte-
SOFiSTiK 2016
3-3
gration only). The definition of the state presets the selection of stress strain
laws and safety factors according to the INI-file of the selected design code.
The analysis uses the properties for construction stage CS and the stresses and
deformations according CTRL PLC from load case PLC.
3-4
SOFiSTiK 2016
3.4
CTRL
Item
Description
Unit
Default
OPT
Calculation parameter
LT
VAL
V2
V3
V4
V5
V6
V3
SOFiSTiK 2016
axial force
bending moments
3-5
+4 =
V4
2=
RLC
torsion
do not set the general prestress value for cables
from the primary load case for buckling eigenvalues.
suppress the coordinate update
Displacements (default)
+2 =
Results of elements
+4 =
+8 =
CONT
WARP
BETA
+4 =
+8 =
+12 =
deactivation
1=
activation
no, the 2nd order Saint Venant theory for torsion is applied
1=
yes, unless the section is warp free. (CM 0.) The initial
stress stiffness for lateral torsional buckling is applied.
2=
3-6
save
SOFiSTiK 2016
1=
superposition
The estimate of the buckling length will be saved only for those beam
elements where the estimate is less than the limit value LMAX specified in record GRP. It has to be marked however, that there are many
cases not applicable for a buckling length approach and that the second order analysis will be more suitable in most cases.
QUAD
BRIC
SPRI
MCON
1=
nonconforming elements
2=
3=
1=
nonconforming elements
+2 =
+32 =
+64 =
2=
3=
Hint
Rotational masses for torsion are always referred on the shear
centre. A constraint rotation must be considered therefore with
the definition of the cross section.
CCON
HLC
SRES
Steady-state response
SOFiSTiK 2016
3-7
STYP
0=
1=
2=
ADD
SUM
BLEV
3-8
Height ordinate of a layer for which the resultant base shear should
be calculated during the response spectra evaluation (may be defined multiple times). The resulting Moment is always taken to the
reference of the origin of the global coordinate system to allow the
superposition of different levels.
SOFiSTiK 2016
3.4.1
SOLV
Description
VAL
Unit
Default
For solving the equation systems of the Finite-Element problem, SOFiSTiK provides a number of solvers. Which solver is used best depends highly on the type
of the system and requires knowledge of relevant system parameters. Following
types are available:
The advantage of the direct solvers is especially given in case of multiple right
hand sides, as the effort for solving them is very small compared to the triangulization of the equation system. Thus they are the first choice for any dynamic
analysis or in case of many load cases.
In order to minimize computational effort, the solvers need an optimized sequence of equation numbers. This optimization step is usually performed during
system generation. The programs SOFIMSHA/C by default always create a sequence which is suitable for the direct sparse solver (3). The solvers (1) or (2)
however require a skyline oriented numbering which may be obtained using the
option (CTRL OPTI 1) or (CTRL OPTI 2) during system generation. The correct
SOFiSTiK 2016
3-9
setting will be checked and a warning will be issued in case a correct numbering
is not available.
The iterative (CTRL SOLV 2) and the parallel sparse solver (CTRL SOLV 4) can
be run in parallel providing an additional reduction in computing time. A parallelization basically requires a license of type HISOLV. More information about
parallelization can be found in subsection 3.4.2 describing the input parameter
(CTRL CORE).
The equation solvers are selected using the parameter (CTRL SOLV). The first
value defines the type of the solver, followed by optional additional parameters.
Direct Skyline Solver (Gauss/ Cholesky)
SOLV
VAL
Description
Unit
Default
Description
Unit
Default
V2
V3
V4
Type of preconditioning:
0
Diagonal Scaling (not recommended)
1
Incomplete Cholesky
2
Incomplete Inverse
V5
V6
The iterative solver uses a conjugate gradient method in combination with preconditioning. For the preconditioning, following variants are supported:
3-10
SOFiSTiK 2016
For any kind of preconditioning the number of matrix entries taken into account
during preconditioning can be reduced either by giving a relative threshold value
at V5 or via a maximum bandwidth size at V6. The optimum choice depends on
the type of the structure and may only be found by some tests.
Hint
The correctness of the solution of the iterative solver depends primarily on
the tolerance threshold. Therefore, changing the default setting V3 is not
recommended. In any case the analyst should carry out a proper assessment of the computation results.
Description
Unit
Default
SOFiSTiK 2016
3-11
SOLV
WERT
Description
Unit
Default
This solver PARDISO uses processor optimized high performance libraries from
the Intel Math Kernel Library MKL. It usually provides the least computing times.
It does not require an a priori optimization of the equation numbers during system generation. Hence, the equation optimization in SOFiMSHA/C could also
be deactivated using (CTRL OPTI 0) in order to save memory during system
generation. On the other hand however, this solver does not allow reusing the
factorized stiffness matrix in other programs. Thus, a usage in combination with
the program ELLA is not possible.
3.4.2
CORE
Description
VAL
Unit
Default
SOFiSTiK supports parallel computing for selected equation solvers. Additionally, some programs offer parallel element processing capabilities independent
of the chosen equation solver (CTRL SOLV).
Activation of parallel computing
By default parallel computing is triggered automatically where it is feasible.
Parallel computing requires corresponding harware and operation system support. In addition, availability of an adequate SOFiSTiK license is obligatory.
Hint
Parallel computing requires availability of a HISOLV license (ISOL granule).
3-12
SOFiSTiK 2016
CTRL SOLV
Serial
Parallel
n.a.
Iterativ
SOFiSTiK 2016
HISOLV HISOLV
n.a.
HISOLV HISOLV
3-13
3.5
Description
NO
Group number
VAL
Selection
OFF
YES
FULL
SOIL
GRP
Unit
Default
LT
FULL
CS
do not use
use, but do not print
use and print the results
elements define boundary to halfspace for SBFEM
Number of the construction stage
FACS
1.0
HING
Lt16
RADA
1/ sec
0.0
RADB
sec
0.0
MODD
Modal damping
0.0
FACP
1.0
FACM
1.0
WIND
LMAX
NSCP
All elements are used if nothing is input. When there is input, only the specified
groups get activated. This effect has to be especially taken care of, if only some
groups get a damping assigned to.
The elements of a group can be provided with two damping types. the value
RADA represents an external damping proportional to the mass and thus the
excursion (e.g. air or water). The value RADB represents an internal damping
proportional to the stiffness (material damping).
The geometric initial stress stiffness will not be multiplied with the factor RADB in
general. Only for the cable the prestress defined with the element is contributing
3-14
SOFiSTiK 2016
to the damping.
C
RADA m
RADB K
kNsec/ m
1/ sec Nsec2 / m
sec kN/ m
For a modal analysis it is possible to specify a modal damping for every group.
This value is then converted using the element masses to an approximate equivalent modal damping of the total eigenform.
More explanations for the damping you will find at MODD
The description of the half space with the Scaled Boundary Element Method
(SBFEM) allows to define the respective static and dynamic properties of the
infinite space accounting for the radiation damping properties. GRP selects the
boundary elements of a 2D Analysis or the QUAD elements of a 3D analysis
defining the boundary of the half space. The local z axis must show into the
direction of the half space. Without definition of NSCP the scaling point will be
located on the upper center of all soil interface nodes.
SOFiSTiK 2016
3-15
3.6
MAT
Item
Description
Unit
Default
NO
Material number
Elastic modulus
kN/ m2
MUE
0.2
Shear modulus
kN/ m2
Bulk modulus
kN/ m2
GAM
Specific weight
kN/ m3
25
GAMA
kN/ m3
ALFA
1/ rK
E-5
EY
kN/ m2
MXY
MUE
OAL
deg
deg
1.0
Lt32
OAF
SPM
TITL
Material name
Materials which can be used for SVAL or QUAD and BRIC elements may be
defined with the record MAT and MATE. The number of the material must not be
used for other materials.
The differences between the two records are mainly the used dimensions. MATE
is analogue to CONC,STEE etc. (MPa) and has additional strength values, while
MAT uses (kN/m2 ) analogue to NMAT. MAT has older item names for the orthotropic parameters.
3-16
SOFiSTiK 2016
3.7
BMAT
Item
Description
Unit
Default
NO
Material number
kN/ m3
0.
CT
kN/ m3
0.
CRAC
kN/ m2
0.
YIEL
kN/ m2
MUE
COH
Cohesion of interface
kN/ m2
DIL
Dilatancy coefficient
0.
GAMB
t/ m2
TYPE
Reference
LT
PESS
PAIN
HALF
CIRC
SPHE
NONE no reference
MREF
NO
Reference dimension
(thickness H or radius R)
SOFiSTiK 2016
3-17
others, ignores the shear deformations of the supporting medium. The bedding
effect may be attached to beam or plate elements, but in general it will be used
as an own element. (see SPRI, BOUN, BEAM or QUAD and the more general
description of BORE profiles)
The determination of a reasonable value for the foundation modulus often
presents considerable difficulty, since this value depends not only on the material parameters but also on the geometry and the loading. One must always
keep this dependance in mind, when assessing the accuracy of the results of an
analysis using this theory.
The subgrade parameters C and CT will be used for bedding of QUAD elements
or for the description of support or interface conditions. A QUAD element of a
slab foundation will thus have a concrete material and via BMAT the soil properties attached to the same material number. The value C is than acting in the
main direction perpendicular to the QUAD surface in the local z-direction, while
CT is acting in any shear direction in the QUAD plane.
If subgrade parameters are assigned to the material of a geometric edge (GLN),
spring elements will be generated along that edge based on the width and the
distance of the support nodes.
Instead of a direct value you may select a reference material and a reference dimension for some cases with constant pressure based on the elasticity modulus
and the Poisson ratio [1] :
Planar layer with horizontal constraints e.g. for modeling elastic support by
columns and supporting walls (plane stress condition):
Cs =
1
(1 + )(1 )
Ct =
E
H
1
2(1 + )
(3.1)
E
H
(1 )
(1 + )(1 2)
Ct =
E
H
1
(1 + )
(3.2)
Planar layer with horizontal constraints for settlements of soil strata (plane
strain condition):
Cs =
E
R
2
(1 + )(1 )
(3.3)
Circular hole with radius R in infinite disk with plane strain conditions (bedded
pipes or piles):
3-18
SOFiSTiK 2016
Cs =
(1 + )(1 2)
Ct = Cs
(3.4)
E
R
Ct = Cs
(1 + )
(3.5)
Including a dilatancy factor describing the volume change induced by shear deformations, we have for the bedding stresses the following equations depending
on the normal and transverse displacements:
= Cs (s + DL t )
= Ct t
(3.6)
Yield load:
Upon reaching the yield stress, the principal deformation component of the interface increases without an
increase of the stress.
Friction/cohesion:
Defining a friction and/or a cohesion coefficient, the lateral shear stress can not become larger than:
Friction coefficient * normal stress + Cohesion
Please note, that before reaching this limit the stiff-ness
CT will produce the shear stress only if a deformation
is present.
If the principal interface has failed (CRAC), then the lateral bedding acts only if
0.0 has been entered for both friction- coefficient and cohesion.
The non-linear effects can only be taken into account by a non-linear analysis.
The friction is an effect of the lateral bedding, while all other effects act upon the
principal direction.
SOFiSTiK 2016
3-19
3.8
SMAT
Item
Description
Unit
Default
NO
Material number
LC
Characteristic Length
EX
EY
EZ
RHOX
RHOY
RHOZ
ALF
Inhomogenity of elasticity
BET
Inhomogenity of density
E = Ere E
= re
3-20
||
Lc
||
Lc
+ Ey
+ y
|y|
Lc
|y|
Lc
+ Ez
+ z
|z|
(3.7)
Lc
|z|
Lc
(3.8)
SOFiSTiK 2016
3.9
Description
NO
MASS
Unit
Default
Node number
MX
Translational mass
0.
MY
Translational mass
MX
MZ
Translational mass
MX
MXX
Rotational mass
tm2
0.
MYY
Rotational mass
tm2
0.
MZZ
Rotational mass
tm2
0.
MXY
Rotational mass
tm2
0.
MXZ
Rotational mass
tm2
0.
MYZ
Rotational mass
tm2
0.
MB
Rotational mass
tm2
0.
SOFiSTiK 2016
3-21
ues MX till MZ, with default value of 1.0, are then the factors for the individual
directions of the mass components which are generated from the loads in the
dead weight direction. If other load directions are to be converted to masses as
well, these directions have to be specified additionally at NO encoded with the
addend 10000 for the X direction, 20000 for the Y direction and 30000 for the Z
direction. The input
MASS -12
creates translational masses from all loads of load case 12 in the direction of the
dead weight. By contrast the input
MASS -30012 0.1 0.05 0.1
MASS -20013 0.0 0.1 0.0
creates masses (t) in the x and z direction from all PZ loads (kN) of load case
12. Only half of the mass is activated in the y direction, however. The second
input processes PY loads of the load case 13.
Masses can get also a factor with MASS. For this purpose the literal FACT has
to be input for NO. This can be reasonable particularly for larger systems, where
it is favourable to suppress many low frequencies which are not essential for the
analysis. With the input
MASS FACT MZ 0.01
3-22
SOFiSTiK 2016
3.10
Description
NEIG
TYPE
MITE
LMIN
Eigenvalue shift
STOR
EIGE
Unit
Default
LT
SIMU
1/ sec2
NEIG
LC
LCUP
NITE
The input of EIGE requests calculation of the eigenvalues and the mode shapes.
If the eigenvectors have been already computed, one must enter TYPE REST.
Special attention must be paid to this when importing eigenvalues from program
ASE.
Eigenvalues and forms may represent dynamic vibration modes or buckling
eigenforms. While the first uses a well defined positive definite mass matrix,
the second problem may encounter indefinite geometric stiffness matrices (negative Eigenvalues) and establish problems. Only SIMU and RAYL have some
provisions for that type of problem. In any case you should start with a few
Eigenvalues in those cases.
All the eigenvectors have to be simultaneously in storage, therefore in cases of
large problems sufficient memory should be provided. The mode shapes can be
stored in the database similarly to static load cases and can be then represented
graphically as deformed structure.
SOFiSTiK 2016
3-23
A modal evaluation of forces is possible only when all required mode shapes
have been stored also as stresses or forces of the elements.
On the other side also computed influence areas for the processing of selective
foot point excitation or other special cases may be introduced into the analysis.
In this case the numbers of these load cases have to follow the eigenform load
cases immediately and may be requested through the explicit input of LCUP.
The eigenvalue problem can be shifted by one value. This finds application in
structures that are not supported (zero eigenvalue is the smallest value) as well
as in checking the number of eigenvalues by means of a Sturm sequence. The
number of skipped eigenvalues is manifested during the shift by the number of
sign changes of the determinant.
The choice of method for the eigenvalue analysis depends on the number of
the eigenvalues. The simultaneous vector iteration is used in most cases. The
number of iterations can be reduced when a somewhat expanded subspace is
used for the eigenvalue iteration. For that reason the default value for NITE is
the minimum between NEIG+2 and the number of unknowns. The iteration is
terminated when the maximum number of iterations (default max (15, 2 NTE))
is reached or when the highest eigenvalue has only changed by a factor less
than 0.00001 compared to the previous iteration.
The method of Lanczos is significantly quicker than the vector iteration, when
a large number of eigenvalues is sought. A good accuracy is achieved when
the number of vectors NITE is at least double the number of sought eigenvalues (default). In case of NITE=NEIG, by contrast to vector iteration, the higher
eigenvalues are usually worthless.
The method of Rayleigh is especially useful if only few eigenvalues are required
and if there are also negative Eigenvalues. As it uses the iterative solver it
requires a special license ISOL and a skyline optimization (CTRL OPTI 1) but
can handle very large systems with least memory requirements.
If a primary load case is selected with CTRL PLC, the geometric initial stiffness is
included in the eigenvalue analysis. So you will get the frequency zero if you are
approaching a buckling case.
In that case you may however evaluate the buckling eigenform directly via TYPE
BUCK (or more specific BULL, BUSI or BURA). For lateral torsional buckling
BURA is the best method in general to suppress the negative eigen values.
3-24
SOFiSTiK 2016
Number of
Eigenvalues
Range of
Eigenvalues
multiple
Eigenvalues
missing
Eigenvalues
negative
Eigenvalues
Memory
requirement
Speed
Vektoriteration
Lanczos
Rayleigh
moderate
high
few
Ritz-Step
problematic
yes
no problems
yes
sometimes
problems
yes
very rare
rare
very rare
yes
only positive
moderate
high
small
moderate
fast
variable
SOFiSTiK 2016
3-25
3.11
Item
Description
NO
MODD
Unit
Default
all
1/ sec
sec
The damping may be specified within the GRP record with different values for
each group. When using direct integration, these values will become effective
in just this way. For a modal analysis however the modal damping will be calculated, following the computation of the eigenvalues, from the defined damping
values by a diagonalisation process. Each Eigenform will then have one distinct
modal damping value.
However the modal damping (Lehrs damping factor), can also be defined separately for each mode by three independent parts (direct value of D, mass proportional A and stiffness proportional B). The values are stored in the database.
The definition of this value will overwrite any damping definitions in the GRP
record or from explicit damper elements!
As the values in the literature are mostly given as modal damping values or
logarithmic decrements we will give some important formulas:
d =
=D+
1
2
(3.9)
In the next pictures you will see the influence of the factors A and B depending on
the eigenfrequencies of a SDOF-oscillator. The damping is shown as logarithmic
decrement ,describing the ratio of two consecutive amplitudes A1 and A2.
logarithmic dekrement
3-26
= og
A1
A2
(3.10)
SOFiSTiK 2016
Verschiebun
g SY [mm]
A1
1600.00
0
A2
1400.00
0
1200.00
0
1000.00
0
800.00
0
600.00
0
400.00
0
200.00
0
Zeit
0.00
0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
[sec]
1-2
Prestressed concrete
0.8
0.4
Hint
MODD have to be specified as absolute value or with an explicit unit [%] !
For a direct integration without eigenvalues, there is no modal damping, thus it
is necessary to convert a given damping value to the parameters A and B. The
conversion of parameters A and B can be seen from the next picture.
SOFiSTiK 2016
3-27
50
B = 0.001
45
B = 0.002
40
B = 0.005
35
A = 0.1
30
A = 0.2
Dekremente [%]
25
A = 0.5
20
A = 1.0
15
10
0
0.5
10
20
50
Eigenfrequenzen [Hz]
B=2
1 2 2 1
2 2 1 2
2 2 1 1
2 2 1 2
(3.11)
(3.12)
If the damping at the start of the interval should be equal to the damping at the
end of the interval and by converting to the standard frequencies = 2 we
have:
A = 4
B=
1 2
1 + 2
1
(1 + 2 )
(3.13)
(3.14)
Example: A structural steel with bolted connections should have a mean modal
damping of 0.01 between 2 Hertz and 10 Hertz. We thus have a decrement of
2 = 2 0.01 = 0.063 i.e. the amplitude of a free oscillation should reduce
3-28
SOFiSTiK 2016
by 6.3 % from peak to peak within the range from 2 Hertz to 10 Hertz.
Factor ( 22 1 2) is given by
2 1
A = 4 0.01
B=
0.01
2 + 10
2 10
2 + 10
(102)
102 22
= 0.083. Thus:
= 0.21
(3.15)
= 0.000266
(3.16)
0.0525
0.0105
0.021
from B
0.0105
0.0525
0.026
total
0.0630
0.0630
0.047
i.e. at the bounds of the interval we have the desired damping, but between we
have a little bit less. For 5.0 Hertz we have only d = 0.047.
For a direct integration there is an additional numerical damping effect possible
with the selection of the integration constant BET, DEL and THE. The default
(BET = 0,25; DEL = 0,5; THE = 1) will not have any damping effect. The same is
valid for modal analysis there is also no damping effect, because the equations
are integrated exactly.
SOFiSTiK 2016
3-29
3.12
Description
STEP
Unit
Default
10
DT
0.1
INT
/ LT
1/ sec
0.
sec
0.
BET
1/4
1/2
DEL
THE
1.
EIGB
Hz
EIGT
Hz
EIGS
Hz
DTF
STHE
1.4
STEP N > 0
Analysis of a time segment with duration N DT by direct (Newmark-Wilson)
or analytical modal integration. When N <1 is input, DT is interpreted as total
time and the individual time step becomes N DT .
THE < 1.0 for the Hughes-Alpha method (0.7 < THE < 1.0)
3-30
SOFiSTiK 2016
the literal STIM or SFRE is given, the load is normalised to a constant displacement instead of the acceleration. If the literal VTIM or VFRE is selected,
the normalisation is based on a constant velocity.
STEP N < 0
Analysis of a transient steady-state condition taking phase shifts into consideration. Referred to the eigen period if DT not given.
A suitable size of the time step depends on the frequency of the expected response. In case of the direct method components with periods smaller than
about ten times the time step are damped out of the solution. A comparison
analysis should be performed if in doubt with a step approximately equal to one
fourth of the initial time step.
It should be taken care of the fact, that the standard Newmark-Method has no
numerical damping. Thus small errors may amplify easily. Those errors may
be introduced by a time step chosen to small together with consistent mass
matrices. In that or other cases the integration constant should be modified, eg.:
SOFiSTiK 2016
3-31
3.13
LC Load Case
Description
NO
LC
Unit
Default
FACT
1.0
DLX
0.0
DLY
0.0
DLZ
0.0
MODB
TITL
Lt32
Transient analysis
During a time variation analysis (STEP N > 0) all the selected load cases
and their functions define the time dependence of the loading and the starting time. All functions act with their loads simultaneously upon the structure.
DYNA allows the extra definition of a contact condition CONT for a moving
load.
2.
If spectra are defined, DYNA computes by double interpolation of all the spectra
a system response, which is then superimposed by statistical methods according to the input for CTRL STYP.
For a modal analysis the general case is to apply the same load vector for all
eigenforms. However if every eigenform should obtain a separate loading as in
a modal wind analysis, the item MODB allows to specify the load case number
for the loading to the first eigen form. All following eigenforms will be associated
to the consecutive load case numbers.
3-32
SOFiSTiK 2016
SOFiSTiK 2016
3-33
3.14
CONT
Item
Description
Unit
Default
TYPE
LT
REF
NR
Travel speed
m/ sec
YEX
Local Eccentricity
0.0
TMIN
sec
0.0
LCUV
LCUT
LCUR
3-34
SOFiSTiK 2016
SOFiSTiK 2016
3-35
3.15
HIST
Item
Description
Unit
Default
TYPE
LT
FROM
TO
FROM
INC
Increment or Identifier
/ Lt
RESU
Output request
LT
PRIN
LCST
XREF
0.
YREF
0.
ZREF
or dP/P width
0.
DUMP
Lt48
The record HIST requests the time history of particular values. These will be
saved into the database for the presentation with DYNR, but it is also possible
to print the values directly or to save them to an external dump file. Up to 32
values can be addressed per input record.
The computed maximum and minimum values of the curves will be printed in
any case.
Table 3.21: Possible literals for TYPE
TYPE
Meaning
UX, UY, UZ
U-X
3-36
U-
U-Z
Displacements
SOFiSTiK 2016
TYPE
U-RX
Meaning
U-RY
U-RZ
Rotations
VX, VY, VZ
V-X
V-Y
V-Z
Velocities
V-RX
V-RY
V-RZ
Angular velocity
AX, AY, AZ
AX
AY
AZ
Accelerations
ARX
ARY
ARZ
Angular acceleration
PT
PX
PY
PZ
PT/P
DP/P
SP
SPX
SPY
SPZ
SPRX
SPRY
SPRZ
TRUS
CABL
BEAM
VY
VZ
MT
MY
MZ
SIG
TAU
SIGV
QUAD
MXX
MYY
VXX
VYY
NXX
NYY
MXY
Shell moments
Shell shear forces
NXY
BRIC
TXX
TYY
TZZ
Stresses of 3D continuum
TXY
TXZ
TYZ
DSX
DSY
DSZ
DSRX
DSRY
DSRZ
SOFiSTiK 2016
3-37
For the beam results XREF is used to define the section where the results are
evaluated. A negative definition is taken as the ratio of the section to the total
beam length, thus a value of -1.0 selects the end of the beam.
For the stresses INC is used to define the identifier of the stress point (SPT)
within the section where the stresses should be evaluated.
The spring force ratios may be useful for vehicle-structure-interaction. They are
defined as follows:
PT/P
DP/P
The ratio of the difference of the main forces of two springs to the
mean value of the same spring forces:
P
P
3-38
P1 P2
P1 + P2
(3.17)
INC=0
INC>0
SOFiSTiK 2016
3.16
EXTR
Item
Description
Unit
Default
TYPE
Structural magnitude
LT
MAX
MIN
LT
CQC
0
STYP
print only
sum of values
SUM
SRSS
CQC
SRS1
harmonised SRSS
LT
The following literals are possible for TYPE. The values of the first line activate
all possible internal forces and moments as maximum value only. No corresponding internal forces are computed in this case.
SOFiSTiK 2016
3-39
TYPE
Designation
Displacement
Velocity
Acceleration
TYPE
Designation
BEAM
Normal force
VY
Shear force Vy
VZ
Shear force Vz
MT
Torsional moment
MY
Bending moment My
MZ
Bending moment Mz
MB
Warping moment
MT2
TYPE
Designation
TRUS
3-40
SOFiSTiK 2016
TYPE
Designation
CABL
TYPE
Designation
SPRI
PT
PTX
PTY
PTZ
Spring moment
SP
SPX
SPY
SPZ
SPRX
SPRY
SPRZ
SOFiSTiK 2016
3-41
TYPE
Designation
QUAD
MXX
MYY
MXY
VXX
VYY
NXX
NYY
NXY
NZZ
TYPE
Designation
BRIC
TXX
TYY
TZZ
TXY
TXZ
TYZ
3-42
SOFiSTiK 2016
TYPE
Designation
RSET
RS1
RS2
RS31
The maximum values are stored in the database, if a load case number is input
for MAX and/or MIN. For nodal values (U,V,A) only the maximum values are
output as default. Use ECHO DISP, VELO or ACCE to see all nodal results.
SOFiSTiK 2016
3-43
3-44
SOFiSTiK 2016
3.17
ECHO
Item
Description
Unit
Default
OPT
LT
FULL
LT
FULL
ELEM
Elements
Natural frequencies
LOAD
Loads
DISP
Displacements
VAL
VELO
Velocities
ACCE
Accelerations
STAT
FULL
NO
No output
YES
Regular output
FULL
Extensive output
EXTR
Extreme output
The name ECHO must be repeated in each record to avoid confusion with similar
record names (e.g. CROS).
The default value is NO for NODE, CROS, and ELEM; for all others it is YES.
The warning no. 10918 (No convergence of the iterative equation solver in load
vector) for convergence checks can be switched off with ECHO STAT NO.
SOFiSTiK 2016
3-45
3-46
SOFiSTiK 2016
Output Description
4.1
Nodes
The nodes are output by use of ECHO NODE YES only. The table includes the
coordinates and constraints, and by ECHO NODE FULL the equation numbers of
the freedom degrees as well.
4.2
Cross Sections
The table of the cross sections appears after request by ECHO SECT and contains
the following value:
CROSS SECTIONS
A
Ay
Az
It
Iy
Iz
Elastic modulus
Shear modulus
Da
Di
Rho
Mass density
4.3
General Parameters
At the beginning of a dynamic analyses appears a table CONTROL INFORMATIONS with the general parameters. These are:
SOFiSTiK 2016
4-1
4.4
Elements
The tables of beam elements and spring or truss elements as well as lumped
masses and damping elements appear upon request by ECHO ELEM. They contain for each element the participating nodes, the length, the spring stiffnesses,
the local axis directions and the mass components.
In the table of the total masses, the first line has the sum of the nodal masses,
i.e. the rotational masses are only the rotational inertias of the nodes. However
the following rows contain the ordinates of the global centre of gravity and the
total rotational inertia of all translatoric masses measured to this centre as a 3x3
matrix.
4.5
Natural Frequencies
After the first computation of the natural frequencies the program outputs the
error in the eigenvalues along with the number of the required iterations. The
rest of the output is controlled by ECHO EIGE as follows:
ECHO EIGE YES
For a uniform ground acceleration in the three coordinate directions the modal
contributions may be evaluated (columns f-XX, f-YY and f-ZZ). Taken as percentage of the total mass this gives a criteria for a sufficient number of eigenvalues.
The eigenvectors are normalised with respect to the masses (equation 2.8 of
the theoretical principles). The internal forces and moments of the eigenvectors
are usually to be understood as an indication of the stressing type. The absolute
value depends on the normalisation and it can take considerably large values.
4.6
The table of functions and loads is always introduced before the description of
the function, followed by the loads of this load case.
The generalised loads of the individual modes and the sum of their squares are
output in the case of a modal loading.
4-2
SOFiSTiK 2016
There is a second value printed, which may be used to integrate the square of
Eigenvalues for only parts of the structure via special load patterns.
4.7
Displacements
The displacements of the individual load cases are output by static analysis.
In case of dynamic analysis the maximum displacements, velocities and accelerations can be output for all nodes. There result two lines per node with the
minimum and maximum values as well as the corresponding time values if a
time analysis was carried out. In case of stochastic or steady-state excitation
the extreme values were computed by statistical methods or by analysis of one
period of the steady-state excitation.
4.8
The internal forces of the individual load cases are output by static analysis.
The maximum values are calculated for all internal forces and moments specified by EXTR along with the other corresponding values. The given time value
holds for the whole line. In case of stochastic or steady-state excitation the
extreme values were computed by statistical methods.
4.9
Time Variations
The time variation of the structural magnitudes specified with HIST is presented
lastly. This can take the form of a table, a printer graph and/or a curve in the
database for further processing with DYNR. The nodes or elements addressed
by each HIST record are output in a general graph. Time is plotted in the longitudinal direction of the paper, while the various magnitudes are plotted in the
transverse direction. A common scale for all involved magnitudes is selected for
each plot. The curves are marked by numbers or letters.
SOFiSTiK 2016
4-3