COSMOSFFE Frequency
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1
Introduction
Introduction
COSMOSFFE Frequency is a fast, robust, and accurate finite element program
for the analysis of dynamic structural problems. The program exploits a new
technology developed at Structural Research for the solution of large systems
of simultaneous equations using sparse matrix technology along with iterative
methods combined with novel database management techniques to substantially
reduce solution time, disk space, and memory requirements.
COSMOSFFE Frequency has been written from scratch using state of the art
techniques in FEA with two goals in mind: 1) to address basic design needs, and 2)
to use the most efficient possible solution algorithms without sacrificing accuracy.
The program is particularly suitable to solve large problems.
COSMOSFFE Frequency is not meant to be a replacement for DSTAR, the
COSMOSM conventional dynamic structural analysis module. The capabilities
of FFE Frequency are a subset of the capabilities of DSTAR. Problems that can
be solved by FFE Frequency can also be solved by DSTAR. The advantage is
that FFE Frequency for the class of problems it supports is far superior in terms of
robustness, speed, and use of computer resources. Clear messages of unsupported
capabilities and options are given whenever encountered. Appendix A gives a list of
error messages along with suggestions to fix the problem.
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COSMOSFFE Frequency
Theoretical Background
Frequency Analysis (Modal Analysis)
The computation of natural frequencies and mode shapes is known as modal or
normal modes analysis. The finite element system of equations for dynamical
systems can be written as:
where [M] is the mass matrix, and [C] is the damping matrix. For free vibrations,
the above equation takes the form:
When undamped linear elastic structures are initially displaced into a certain shape,
they will oscillate indefinitely with the same mode shape but varying amplitudes.
The oscillation shapes are called the mode shapes and the corresponding frequencies
are called natural frequencies. The term modal analysis has been used throughout
this manual for the study of natural frequencies and mode shapes. For undamped
linear elastic structures, the above equation reduces to:
With no externally applied loads, the structure is assumed to vibrate freely in a
harmonic form defined by:
which leads to the eigenvalue problem:
where
ω is the natural frequency and φ is corresponding mode shape of the structure.
Brief Overview
Element Library
•
Two and three dimensional trusses (TRUSS2D and TRUSS3D)
•
Spring and mass elements (SPRING and MASS)
•
Three dimensional beam elements (BEAM3D)
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Chapter 1 Introduction
•
First and second order triangular plane stress, plane strain and axisymmetric
elements (TRIANG)
•
First and second order quad plane stress, plane strain and axisymmetric
elements (PLANE2D)
•
First order triangular and quad shell elements (SHELL3 and SHELL4)
•
First and second order hexahedral elements (SOLID)
•
First and second order tetrahedral elements (TETRA4 and TETRA10)
Displacement Constraints
•
Displacement constraints in the global Cartesian, cylindrical, and spherical
coordinate systems
•
Displacement constraints in any local Cartesian, cylindrical, or spherical
coordinate system
Material Properties
In this release only isotropic materials are supported. Use DSTAR for orthotropic or
anisotropic materials.
Analysis Capabilities
Analysis options are specified through the
A_FEEFREQ
(Analysis > Frequency/
Buckling >
FFE Frequency Options
) command. The following choices are
available:
1. Element order in analysis:
•
Use first order elements with first order mesh
•
Use second order elements with first order mesh
•
Use first order elements with second order mesh
•
Use second order elements with second order mesh
2. Number of natural frequencies to be calculated.
3. Lower bound of the desired frequency range.
4. Upper bound of the desired frequency range.
5. Rigid connection flag which controls the continuity between solid and shell and
solid and beam elements connected to each other. You may choose rigid or
hinge connection along the interface.
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COSMOSFFE Frequency
Results
•
Mode shape plots.
•
Frequency lists.
The output file (problem-name.out) contains frequency results and useful infor-
mation on resources used during analysis.
Consistent Systems of Units
In COSMOSM modules including FFE Frequency, you are free to adopt standard or
non-standard systems of units, but you are responsible for consistency and the
interpretation of the units of results. The table below shows consistent standard
systems of units for the physical quantities used in the FFE Frequency module.
Table 1-1. Table of Consistent Units for COSMOSFFE Frequency
* Units are consistent with the COSMOSM material library.
1 FPS refers to the U.S. customary system of units.
2 SI refers to the International system of units.
3 MKS refers to the Metric system of units.
4 CGS refers to the French system of units.
Description
COSMOS
Name
* FPS
1
(gravitational)
* SI
2
(absolute)
* MKS
3
(gravitational)
CGS
4
(absolute)
Measure
Length
X, Y, Z
in
m
cm
cm
Material Properties
Elastic
Modulus
EX, EY, EZ
lbs/in
2
Newton/m
2
or Pascal
kg/cm
2
dyne/cm
2
Shear Modulus
GXY, GYZ,
GXZ
lbs/in
2
N/m
2
or Pa
kg/cm
2
dyne/cm
2
Poisson's Ratio
NUXY, NUYZ,
NUXZ
in/in
(no units)
m/m
(no units)
cm/cm
(no units)
cm/cm
Mass
Density
DENS
lbs sec
2
/in
4
kg/m
3
kg
sec
2
/cm
4
g/cm
3
Loads and Boundary Conditions
Translational
Displacements
UX, UY, UZ
in
m
cm
cm
Rotational
Displacements
RX, RY, RZ
radians
radians
radians
radians
Results
Frequency
FREQ
Hz or rad/sec Hz or rad/sec Hz or rad/sec Hz or rad/sec
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2
Element Library
Introduction
This chapter lists the elements currently supported by COSMOSFFE Frequency.
Most of 2D and 3D continuum elements are programmed on first and second order
hierarchical basis. You may mesh your model with linear or parabolic elements but
you can still control the order to be used in the analysis through the
A_FFEFREQ
(Analysis > Frequency/Buckling >
FFE Frequency Options
) command. As an
example, you may mesh your model with TETRA10 elements but specify first
order in the
A_FFEFREQ
command (equivalent to TETRA4). In this case the
middle node information for elements on the boundary will still be used for the
geometry. Similarly, you may define TETRA4 elements in GEOSTAR and specify
second order in the
A_FFEFREQ
command.
Plane 2D Continuum Elements
•
First order (3-node) triangular plane stress elements (TRIANG)
•
Second order (6-node) triangular plane stress elements (TRIANG)
•
First order (3-node) triangular plane strain elements (TRIANG)
•
Second order (6-node) triangular plane strain elements (TRIANG)
•
First order (3-node) triangular axisymmetric elements (TRIANG)
•
Second order (6-node) triangular axisymmetric elements (TRIANG)
•
First order (4-node) quadratic plane stress elements (PLANE2D)
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COSMOSFFE Frequency
•
Second order (8-node) quadratic plane stress elements (PLANE2D)
•
First order (4-node) quadratic plane strain elements (PLANE2D)
•
Second order (8-node) quadratic plane strain elements (PLANE2D)
•
First order (4-node) quadratic axisymmetric elements (PLANE2D)
•
Second order (8-node) quadratic axisymmetric elements (PLANE2D)
Continuum 3D Solid Elements
•
First order (8-node) hexahedral elements (SOLID)
•
Second order (20-node) hexahedral elements (SOLID)
•
First order (8-node) pentahedral elements (SOLID with a face collapsed to an
edge)
•
Second order (20-node) pentahedral prism-shaped elements (SOLID with a face
collapsed to an edge)
•
First order tetrahedral elements (TETRA4)
•
Second order tetrahedral elements (TETRA10)
Structural Elements
•
Two and three dimensional truss elements (TRUSS2D and TRUSS3D)
•
Three dimensional beam elements (BEAM3D)
•
First order triangular (3-node) shell elements (SHELL3)
•
First order quad (4-node) shell elements (SHELL4)
✍
The elements given above are to be defined using the
EGROUP
(Propsets >
Element Group
) command shown in the Table 2-1. The Table also lists other
commands for the manipulation of the associated element properties. These
commands can be issued by following the menu path given in the table between
parenthesis.
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Chapter 2 Element Library
Table 2-1. Commands for Element Group Definition, Modification, and Listing
Every element has several analysis and modeling options (maximum of eight
entries), designated as OP1, …, OP8. When you execute the
EGROUP
command,
you are prompted for these options with description relevant to the selected element
type.
The following figure shows pictorial representations of all elements available in the
COSMOSFFE Frequency module. COSMOSM User’s Guide (Volume 1) presents a
detailed description of all elements in Chapter 4, Element Library.
The
RCONST
(Propsets >
Real Constant
) command should be used to specify the
cross-sectional dimensions of some elements such as thickness for SHELL3
elements. Material properties may be specified using
MPROP
,
PICK_MAT
, or
R_MATLIB
commands found in the Propsets menu. The
R_MATLIB
command
requires the installation of the InfoDex Mil 5 material library.
Command
Function
Comments
EGROUP (Propsets >
Element Group)
Defines element groups and
the associated element
analysis options.
The maximum number of
element groups permitted in a
model is 20.
EPROPSET (Propsets >
New Property Set)
Assigns the existing element
group, material property, and
real constant groups as well as
element coordinate system to
newly created elements.
EPROPCHANGE
(Propsets > Change
El-Prop)
Changes the association
between element groups, real
constants sets, and material
property sets.
EGLIST (Edit > LIST >
Element Groups)
Lists specified element groups
and the associated element
analysis options.
The on-screen listing can be
piped to a text file if desired,
using the LISTLOG (Control >
MISCELLANEOUS > List
Log) command.
EGDEL (Edit > DELETE
> Element Groups)
Deletes specified element
groups and the associated
element analysis options.
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COSMOSFFE Frequency
Figure 2-1. Supported Elements
3 - Node Thin
S he ll
Element: SHELL3
Nodes: 3
4 - Node S he ll
Element: SHELL4
Nodes: 4
4 - Node P la ne or
Ax is y mme t ric
Q ua drila t e ra l
Element: PLANE2D
Nodes: 4
8 - Node P la ne or
Ax is y mme t ric
Q ua drila t e ra l
Element: PLANE2D
Nodes: 8
6 - Node P la ne or
Ax is y mme t ric
Tria ngle
Element: TRIANG
Nodes: 6
3 - Node P la ne or
Ax is y mme t ric
Tria ngle
Element: TRIANG
Nodes: 3
8 - Node S olid
Element: SOLID
Nodes: 8
2 0 - Node S olid
Element: SOLID
Nodes: 20
Trus s / S pa r
Element: TRUSS2D or
TRUSS3D
Nodes: 2
Be a m
Element: BEAM2D or
BEAM3D
Nodes: 2 or 3
Firs t O rde r
P ris m- S ha pe d S olid
Element: SOLID
Nodes:
S e c ond O rde r
P ris m- S ha pe d S olid
Element: SOLID
Nodes:
4 - Node
Te t ra he dra l S olid
Element: TETRA4
Nodes: 4
1 0 - Node
Te t ra he dra l S olid
Element: TETRA10
Nodes: 10
Line a r S pring
Element: SPRING
Nodes: 2
Conc e nt ra t e d
Ma s s
Element: MASS
Nodes: 1
8 with a face
collasping to
an edge
20 with a face
collasping to
an edge
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Chapter 2 Element Library
Top and Bottom Faces of Shell Elements
Only the mid surface of a shell element is shown in GEOSTAR. Each shell element
has a top and a bottom face determined by the order of the connectivity in the
element definition. Shell elements must be aligned properly for the stress results to
be averaged correctly. Use the
ELIST
(Edit > LIST >
Elements
) command to list
the connectivity of elements. The direction of the thumb when using the right-hand
rule points to the direction of the top face.
Figure 2-2. Top and Bottom Faces of Shell Elements
Elements generated by meshing a surface will have their top face in the direction of
the outside normal of the surface determined by the right-hand rule. The direction
of the outer contour of a region is used to determine the top face of elements
generated by meshing regions. The
ACTMARK
(Control > ACTIVATE >
Entity
Mark
) command may be used to show the parametric directions of surfaces.
ACTMARK
may also be activated from the
STATUS1
table.
✍
Full integration is always used for the TRIANG, PLANE2D, SOLID, TETRA4,
and TETRA10 elements. The corresponding option in the element group
definition is ignored. Results from FFE Frequency should compare with results
from DSTAR when the full integration option is used.
Visualizing Shell Faces
Use the
SHADE
command (Display > DISPLAY OPTIONS > Shaded Element
Plot) and plot elements. See Help for this command for the details. You may also
use the
ALIGNSHELL
command (Meshing > ELEMENTS > Align Shell Elements)
to align shell elements automatically.
S HE LL4
S HE LL4
S HE LL3
S HE LL3
1
3
2
Top face (Face 5) is
directed towards you.
Bottom face (Face 5) is
directed towards you.
Bottom face (Face 5) is
directed towards you.
Top face (Face 5) is
directed towards you.
1
2
3
3
4
2
1
3
2
4
1
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COSMOSFFE Frequency
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3
Input Data
Introduction
Proper modeling and analysis specifications are crucial to the success of any finite
element analysis. Irrespective of the type of analysis, numerical solution using
finite element analysis requires complete information of the model under con-
sideration. The finite element model you submit for analysis must contain all the
necessary data for each step of numerical simulation - geometry, elements, loads,
boundary conditions, solution of system of equations, visualization and output of
results, etc. This chapter attempts to conceptually illustrate the procedure for
building a model for analysis in the COSMOSFFE Frequency module.
The COSMOSM User Guide (Volume 1) presents in-depth information on the pre-
and postprocessing procedures in GEOSTAR. This chapter therefore will not repeat
the information here but will offer a brief overview of those commands which are
relevant to the COSMOSM FFE Frequency module.
For a detailed description of all commands, refer to the on-line help or the
COSMOSM Command Reference Manual (Volume 2).
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COSMOSFFE Frequency
Modeling and Analysis Cycle in the
COSMOSFFE Frequency Module
The basic steps involved in a finite element analysis are:
1. Create the problem geometry.
2. Define the appropriate element group.
3. Define material properties.
4. Define real constants for truss, beam, plane stress and shell elements.
5. Mesh the desired part of geometry with appropriate type of elements.
6. Repeat steps 2 through 5 as desired if needed.
7. Merge coinciding nodes along the common boundaries of different geometric
entities using the
NMERGE
(Meshing > Nodes >
Merge
) command.
8. Apply constraints on the finite element model.
9. Use the
A_FFEFREQ
(Analysis > Frequency/Buckling >
FFE Frequency
Options
) command to specify desired options including element order and
number of frequencies. If you have solid and shell or beam elements in your
model, decide whether a rigid or hinged connection is to be used along the
interface.
10. Submit the completed finite element model for analysis using the
R_FREQUENCY
(Analysis > Frequency/Buckling >
Run Frequency Analysis
)
command.
11. Use the Results menu to postprocess the results. Results may be displayed in
text or graphical formats. Use the
LISTLOG
(Control > Miscellaneous >
List
Log
) command to direct list screens to a file.
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Chapter 3 Input Data
✍
R_FREQUENCY
runs either DSTAR or FFE Frequency. The following factors
determine which one will run:
1. If you have not issued the
A_FREQUENCY
nor the
A_FFEFREQ
commands,
R_FREQUENCY
will run DSTAR (the direct solver).
2. If both of the two commands have been issued, the later one will determine
which solver to run. DSTAR will run if
A_FREQUENCY
has been issued later,
and FFE Frequency if
A_FFEFREQ
has been issued later.
3. If only one of the two commands has been issued, then DSTAR will run if
A_FREQUENCY
has been issued, and FFE Frequency will run if
A_FFEFREQ
has been issued.
These steps can be schematically represented as shown in the figure below.
Figure 3-1. Finite Element Modeling and Analysis Steps
Preprocessing refers to the operations you perform prior to submitting the model
for analysis. Such operations include defining the model geometry, mesh genera-
tion, applying boundary conditions, and other information needed. The term
analysis in the above figure refers to the phase of specifying the analysis options
and executing the actual analysis. Postprocessing refers to the manipulation of the
analysis results for the visualization and interpretation in graphical and tabular
environment.
The commands summarized in the table below provide you with information on the
input of element groups, material properties, loads and boundary conditions,
analysis options, and output specifications.
START
PREPROCESSING
POSTPROCESSING
STOP
Analysis and
Design Decisions
Problem Definition
ANALYSIS
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COSMOSFFE Frequency
Table 3-1. Commands for FFE Frequency Analysis
Frequency Analysis Options
The
A_FFEFREQ
command is used to specify several frequency analysis options to
be used for subsequent analysis. The syntax and help for the
A_FFEFREQ
and
R_FREQUENCY
commands are given below.
Function
Using COSMOSM Menu
Typing the Command
Property
Definition
Propsets
> Element Group
> Material Property
> Real Constant
> Pick Material Lib
> User Material Lib
> Material Browser
> AISC Sect Table
> Change El-Prop
> New Property Set
> Beam Section
. . .
EGROUP
MPROP
RCONST
PICK_MAT
USER_MAT
R_MATLIB
PICK_SEC
EPROPCHANGE
EPROPSET
BMSECDEF
Boundary
Conditions
LoadsBC
> STRUCTURAL
> DISPLACEMENT
. . .
. . .
D_ commands for prescribed displacements
Model
Verification
Meshing
> ELEMENTS
> Check Element
Analysis
> Data Check
> Run Check
. . .
. . .
E_CHECK
. . .
DATA_CHECK
R_CHECK
Specifying
Analysis
Options
Analysis
> Frequency/Buckling
> FFE Frequency
Options
. . .
. . .
A_FFEFREQ
Executing
Frequency
Analysis
Analysis
> Frequency/Buckling
> Run Frequency
Analysis
. . .
. . .
R_FREQUENCY
Post-
processing
Results
> PLOT
> Deformed Shape
> LIST
> Frequency
. . .
. . .
DEFPLOT
. . .
FREQLIST
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Chapter 3 Input Data
The A_FFEFREQ Command
Geo Panel: Analysis > Frequency/Buckling > FFE Frequency Options
The
A_FFEFREQ
command specifies analysis options for frequency analysis
using the FFE Frequency module. Note that the
A_FREQUENCY
command
specifies analysis options for frequency analysis using the DSTAR module. The
most recently issued command out of the two commands (
A_FREQUENCY
and
A_FFEFREQ
) determines whether the
R_FREQUENCY
command will run DSTAR
or FFE Frequency. The default is to run DSTAR.
Entry and Option Description
element-order
Order of the element to be used. In spite of the element group name in the
database, you may specify through this option whether first (linear) or second
(parabolic) elements will be used. As an example, if you define TETRA4
elements and use second order, middle nodes on straight edges will be consid-
ered during analysis. On the other hand you may define TETRA10 elements and
specify to use first order.
first
use first order for continuum elements.
second
use second order for continuum elements.
(default is second)
number of frequencies
Number of natural frequencies to be calculated. Enter 0 if unknown number of
frequencies is to be calculated in a given range.
N;
calculate N natural frequencies.
0;
calculate all frequencies in the specified range.
lower bound value
Lower bound of the frequency range. This option is currently not used, it is
always set to zero.
(default is 0)
upper bound value
Upper bound of the frequency range. Enter 0 if you specified the number of fre-
quencies to be calculated.
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COSMOSFFE Frequency
rigid connections flag
This flag controls the continuity between solid and shell or beam elements
connected to each other. Solid elements like TETRA4, TETRA10), and SOLID
do not have explicit rotational degrees of freedom (DOF). Rotations of solid
elements can be expressed in terms of the translational DOF. Beam and shell
elements on the other hand have explicit rotational DOF.
Traditionally, you need to introduce some coupling constraints when connecting
such incompatible elements to ensure continuity. This flag, when active, takes
care of this condition automatically and rigid connections between all such
incompatible elements in the model are assumed.
When you want to specify hinge connections or you need to compare
COSMOSFFE results to results from traditional finite element systems which
assume hinge connections between solid and shell or beam elements, you must
turn this flag off before running the analysis.
YES; activate
rigid
connections.
NO;
deactivate rigid connections.
(default is YES)
✍
Notes:
1. Either the number of frequencies or the upper limit must be non-zero.
2. The actual number of frequencies calculated will be the number specified + 1
if the specified number is not zero. If the number of frequencies is set to zero,
all frequencies in specified range + 1 frequency (outside range) will be
calculated.
The R_FREQUENCY Command
Geo Panel: Analysis > Frequency/Buckling > Run Frequency Analysis
The
R_FREQUENCY
command performs dynamic analysis to calculate frequencies
and mode shapes. The command runs FFE Frequency if the
A_FFEFREQ
com-
mand has been issued and was not followed by the
A_FREQUENCY
command. On
the other hand, the command runs DSTAR module if the
A_FFEFREQ
command
has not been issued or was issued but followed by the
A_FREQUENCY
command.
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Chapter 3 Input Data
✍
Notes:
1. Use flags specified by the
A_FREQUENCY
command or the
A_FFEFREQ
command depending on your choice of solver.
2. Recommended steps for performing analysis:
a. Create the model.
b. Plot, list and examine the model.
c. Execute the
R_CHECK
(Analysis >
Run Check
) command to check input
data.
d. Issue the
A_FFEFREQ
(Analysis > Frequency/Buckling >
FFE Frequency
Options
) command to specify the element order and frequency number
flags or the
A_FREQUENCY
(Analysis > Frequency/Buckling >
Frequency
Analysis Options
) command to specify DSTAR options. Use equivalent
commands for other types of analyses.
e. Issue the
R_FREQUENCY
(Analysis > Frequency/Buckling >
Run
Frequency Analysis
) command to perform dynamic analysis. Use the
equivalent command for other types of analyses.
f. If the run is not successful, a clear message will be given. For FFE
messages, refer to Appendix A of this manual for explaining and fixing the
problem. The message is also written to the output file (extension OUT).
3. The command will calculate frequencies and mode shapes.
Postprocessing
An output file (problem-name.OUT) is generated by FFE Frequency. The file is an
ASCII file that can be viewed and edited as desired. The results in the database can
be viewed in both text and graphical formats in GEOSTAR. The following table
gives a brief description of the postprocessing commands related to FFE Frequency.
Table 3-2. Postprocessing Commands Related to FFE Frequency
Command *
Description
DEFPLOT (Results, Plot, Deformed Shape)
DISPLOT (Results, Plot, Displacement)
DISLIST (Results, List, Displacement)
FREQLIST (Results, List, Displacement)
LISTLOG (Control, Miscellaneous, List Log)
Plots mode shapes
Plots displacement contours of mode shapes
Lists mode shapes
Lists natural (resonance) frequencies
Can be used to write the list screens to a file
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COSMOSFFE Frequency
Verification of Model Input Data
Avoiding errors in the modeling and input data is important. Some of the errors can
be detected by plotting the model in various views, listing the elements, nodes,
element groups, material properties and real constant sets, and plotting or listing
loads and constraints. For small problems, it is often easier to perform these checks
to see if all required input data have been properly generated and defined. However,
you may still miss some errors that are not easily identifiable. For these types of
situations and also for larger problems, it is preferred to perform model checks in
an automated environment.
The
R_CHECK
(Analysis >
Run Check
) command performs rigorous checks on
the validity, compatibility, and completeness of the input data and gives messages
for any warnings and errors encountered. The
ECHECK
(Meshing > Elements >
Check Element
) performs a quick check on the elements in the model and deletes
any degenerate elements.
You are strongly recommended to run the
R_CHECK
command and fix all errors
before submitting the model for analysis.
Note that the
R_CHECK
command is a general model verification tool. You may
still find some errors that are not detected by the use of this command. In most
cases, the error messages either printed on the screen or written to the output file
(problem_name.CHK) provide further information as to the nature of errors and
their remedies. In addition, the FFE Frequency module will give you clear
messages if any problems are encountered during the analysis process. Refer to
Appendix A for more information about error messages.
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Examples
Introduction
This chapter presents step-by-step examples for performing frequency analysis
using the FFE Frequency module. The examples discussed in this chapter are
practical problems that demonstrate the savings in time and resources when
using FFE Frequency compared to using the conventional solvers. Chapter 5
includes a number of small size problems that demonstrate most of the capabilities
of FFE Frequency and that are suitable for verification purposes and academic
studies.
The input files for the examples in this chapter and the verification problems
in Chapter 5 are compressed in the archive file FFEPROBS.LZH in your
COSMOSM directory. It is suggested to create a new subdirectory and extract
the input files.
Table 4-1. Frequency Examples
Analysis of a Bridge.
(See page 5-2.)
FFEFX1.GEO
Analysis of an Airplane Entertainment TV Casing.
(See page 5-7.)
FFEFX2.GEO
In
de
x
In
de
x
Chapter 4 Examples
4-2
COSMOSFFE Frequency
Model Information
Length Units:
Feet (ft)
Element Type:
Shell, Beam
Number of Elements:
352
Number of Corner Nodes:
255
Number of Degrees of Freedom:
1530
The bridge is made of a combination of Beam and Shell elements as shown in the
figure. The span of the bridge is 1000 feet long and it is rigidly supported by 4
points at each end of the bridge.
The finite element model and
its boundary conditions have
already been completed.
The file needed to create
the geometry is called
FFEFX1.GEO and may
be retrieved from the
FFEPROBS.LZH file in your
COSMOSM directory. You
could read in the FFEFX1.GEO
file, or you may choose to input
the commands and construct the
database step-by-step by issuing
the commands.
Loading GEO File
1. Start GEOSTAR. The Open Problem
Files dialog box opens.
2. Type the problem name, for example,
bridge in the File Name field, and
Example 1 – Analysis of a Bridge
See
Page
5-2
Figure 4-1. Model of Bridge
In
de
x
In
de
x
COSMOSFFE Frequency
4-3
Chapter 4 Examples
click OK. It is recommended that you save the
problem to a working directory different from
where COSMOSM is installed.
3. From the File menu, choose Load. The FILE
dialog box opens.
4. Click the Find button by the Input Filename field.
5. Navigate to the directory where you retrieved the
FFEPROBS.LZH archive file.
6. Choose FFEFX1.GEO and click OK.
7. Click OK in the FILE dialog box. The model will
be created and displayed on the screen.
Specifying Analysis Option
Now the model has been created, we are ready to
specify analysis options and run the analysis.
1. From the ANALYSIS menu, select
Frequency/
Buckling
,
FFE Frequency Option
or type
A_FFEFREQ
command at the GEO> prompt in the
GEO panel. The
A_FFEFREQ
dialog box opens.
2. From the Element Order drop-down menu, choose
Second.
3. Enter 30 in the Number of Frequencies field.
4. Click the OK button.
✍
It is always recommended to use the second order
option for more accurate solutions.
In
de
x
In
de
x
Chapter 4 Examples
4-4
COSMOSFFE Frequency
Running Frequency Analysis
1. From the ANALYSIS menu, select
Frequency/Buckling
,
Run Frequency
or type R_Frequency at the GEO >
prompt.
The COSMOSFFE Frequency Solver
window will open and the program starts
the analysis. You will see the progress of
the analysis procedure. After finishing the
analysis, FFE Dynamic gives control back
to GEOSTAR to continue with
postprocessing.
Postprocessing
All postprocessing commands are included in the Results menu.
Listing Frequencies
1. From the RESULTS menu, choose
List
,
Natural Frequency
. The FREQLIST
window opens and lists all the frequencies.
In
de
x
In
de
x
COSMOSFFE Frequency
4-5
Chapter 4 Examples
Plotting Mode Shape
1. From the RESULTS menu, choose
Plot
,
Deformed Shape
. The
DEFPLOT dialog box opens.
2. Enter 1 in the Mode
Shape Number field.
3. Click OK. The Scale
Factor will be displayed
in the field.
4. Click OK again. The
mode shape is plotted.
Animating Deformed
Shape
1. From the RESULTS
menu, select
Plot
,
Animate
. The ANIMATE
dialog box opens.
2. Set the Mode Shape Number to 1.
Figure 4-3.The fundamental Mode Shape of Bridge
In
de
x
In
de
x
Chapter 4 Examples
4-6
COSMOSFFE Frequency
3. Click OK. The program will calculate and display the scale factor.
4. Click OK again. The animation is generated on the screen.
5. Press Esc key to stop the animation.
6. Click OK to abort the Animate command.
7. Repeat the above steps to animate other mode shapes.
✍
You can save the animation in the AVI format by selecting YES from the Save
and play as AVI pull-down menu.
✍
You may activate the element shading using the
SHADE
(Display > Display
Option >
Shaded Element Plot
) command and accept all default entries.
In
de
x
In
de
x
COSMOSFFE Frequency
4-7
Chapter 4 Examples
Model Information
Length Units:
Inches (in)
Element Type:
Shells
Element Order:
First
Number of Elements:
796
Number of Corner Nodes:
850
Number of Degrees of Freedom:
5100
In this example, you will perform a
frequency analysis of an entertainment
casing. The finite element mesh of the
model is shown below.
The file needed to create the geometry is
called FFEFX2.GEO and may be retrieved
from the FFEPROBS.LZH file in your
COSMOSM directory. You could read in
the FFEFX2.GEO file, or you may choose
to input the commands and construct the
database step-by-step by issuing the
commands.
Loading GEO File
1. Start GEOSTAR. The Open Problem
Files dialog box opens.
2. Type the problem name, for example,
Casing in the File Name field, and
click OK. It is recommended that
you save the problem to a working
directory different from where
COSMOSM is installed.
3. From the FILE menu, choose
Load
. The FILE dialog box opens.
Example 2 – Analysis of an Airplane
Entertainment TV Casing
See
Page
5-2
Figure
4-9.
Meshed Model with
Boundary Conditions
In
de
x
In
de
x
Chapter 4 Examples
4-8
COSMOSFFE Frequency
4. Click the Find button by the Input
Filename field.
5. Navigate to the directory where
you retrieved the FFEPROBS.LZH
archive file.
6. Choose FFEFX2.GEO and click
OK.
7. Click OK in the FILE dialog box.
The model will be created and displayed on the screen.
Specifying Analysis Option
Now the model has been created, we are ready to specify analysis options and run
the analysis.
1. From the ANALYSIS menu, select
Frequency/Buckling
,
FFE Frequency
Option
or type
A_FFEFREQ
command at the GEO> prompt in the GEO panel.
The A_FFEFREQ dialog box opens.
2. From the Element Order drop-down menu, choose Second.
3. Enter 5 in the Number of Frequencies field.
4. Click the OK button.
✍
It is always recommended to use the second order option for more accurate
solutions.
In
de
x
In
de
x
COSMOSFFE Frequency
4-9
Chapter 4 Examples
Running Frequency Analysis
1. From the ANALYSIS menu, select
Frequency/Buckling
,
Run Frequency
or type
R_FREQUENCY
at the GEO>
prompt.
The COSMOSFFE Frequency Solver
window will open and the program starts
the analysis. You will see the progress of
the analysis procedure. After finishing the
analysis, FFE Dynamic gives control back
to GEOSTAR to continue with
postprocessing.
Postprocessing
All postprocessing commands are included in the Results menu.
Listing Frequencies
1. From the RESULTS menu, choose
List
,
Natural
Frequency
. The FREQLIST window opens and
lists all requested frequencies.
Plotting Mode Shape
1. From the RESULTS menu, choose
Plot
,
Deformed Shape
. The DEFPLOT
dialog box opens.
2. Enter 1 in the Mode Shape Number field.
In
de
x
In
de
x
Chapter 4 Examples
4-10
COSMOSFFE Frequency
3. Click OK. The default scale Factor will be displayed in the field.
4. Click OK again. The mode shape is plotted.
5. Repeat the above steps to generate other mode shapes.
Figure 4-3. Mode Shapes of Casing
In
de
x
In
de
x
COSMOSFFE Frequency
4-11
Chapter 4 Examples
Animating Deformed Shape
1. From the RESULTS menu, select
Plot
,
Animate
. The ANIMATE
dialog box opens.
2. Set the Mode Shape Number to 1.
3. Click OK. The program will
calculate and display the default
scale factor.
4. Click OK again. The animation is
generated on the screen.
5. Press Esc key to stop the animation.
6. Click OK to abort the Animate
command.
7. Repeat the above steps to animate other mode shapes.
✍
You can save the animation as AVI format by selecting YES from the Save and
play as AVI pull-down menu.
✍
You can activate the element shading using the
SHADE
(Display > DISPLAY
OPTION >
Shaded Element Plot
) command.
In
de
x
In
de
x
4-12
COSMOSFFE Frequency
In
de
x
In
de
x
COSMOSFFE Frequency
5-1
5
Verification Problems
Introduction
This chapter includes a set of verification problems that check various elements and
features of the FFE Frequency module. The problems are carefully selected to
check the numerical answers versus theoretical results.
The input files for theses verification problems are compressed in an archive file
called “...\Vprobs\FFE” in your COSMOSM directory.
To extract the input files for the verification problems:
1. Create a new working directory.
2. Copy the FFEPROBS.BAT batch file from COSMOSM directory to that
directory.
3. Double-click the FFEPROBS.BAT to extract all the input files.
To run a verification problem:
1. Start GEOSTAR and create a new problem.
2. From the File menu, choose Load to import the GEO file.
In
de
x
In
de
x
Chapter 5 Verification Problems
5-2
COSMOSFFE Frequency
The table below lists the verification problems in this chapter.
Table 6-1. List of Verification Problems
Problem
Element
Title
FFEF1
TRUSS, MASS
Natural Frequencies of a Two-Mass Spring
System
(See page 5-3.)
FFEF2
PLANE2D
Frequencies of a Cantilever Beam
(See page 5-4.)
FFEF3
BEAM3D
Frequency of a Simply Supported Beam
(See page 5-5.)
FFEF4
BEAM3D
Natural Frequencies of a Cantilever Beam
(See page 5-6.)
FFEF5
BEAM3D, MASS
Frequency of a Cantilever Beam with Lumped
Mass
(See page 5-7.)
FFEF6
SHELL4
Dynamic Analysis of a Simply Supported Plate
(See page 5-8.)
FFEF7
SHELL4
Frequencies of a Cylindrical Shell
(See page 5-9.)
FFEF8
SHELL4
Symmetric Modes and Natural Frequencies
of a Ring
(See page 5-10.)
FFEF9
SHELL3
Eigenvalues of a Triangular Wing
(See page 5-11.)
FFEF10
BEAM3D
Vibration of an Unsupported Beam
(See page 5-12.)
FFEF11
SOLID
Frequencies of a Solid Cantilever Beam
(See page 5-13.)
FFEF12
TRUSS2D
Natural Frequency of Fluid
(See page 5-14.)
FFEF13A, B, C, D,
E, F, & G
PLANE2D, SOLID,
TRIANG, TETRA10
Dynamic Analysis of Cantilever Beam
(See page 5-15.)
FFEF14
SHELL4
Natural Frequencies of a Simply-Supported
Square Plate
(See page 5-16.)
In
de
x
In
de
x
COSMOSFFE Frequency
5-3
Chapter 5 Verification Problems
TYPE:
Mode shape and frequency, truss and mass element (TRUSS3D, MASS).
REFERENCES:
Thomson, W. T., “Vibration Theory and Application,” Prentice-Hall, Inc.,
Englewood Cliffs, New Jersey, 2nd printing, 1965, p. 163.
PROBLEM:
Determine the normal modes and natural frequencies of the system shown below for
the values of the masses and the springs given.
MODELING HINTS:
Truss elements with very small density are used as springs. Two dynamic degrees of
freedom are selected at nodes 2 and 3 and masses are input as concentrated masses
at nodes 2 and 3.
Figure FFEF1-1
FFEF1: Natural Frequencies of a Two-Mass
Spring System
(See
page
5-2.)
GIVEN:
m
2
= 2m
1
= 1 lb-sec
2
/in
k
2
= k
1
= 200 lb/in
k
c
= 4k
1
= 800 lb/in
COMPARISON OF RESULTS:
F
1
, Hz
F
2,
Hz
Theory
2.581
8.326
COSMOSFFE
2.581
8.326
Problem Sketch
2
k
1
k
c
k
m
1
m
2
1st
D.O.F.
2nd
D.O.F.
1
2
3
4
X
1
2
3
Y
Finite Element Model
5
4
In
de
x
In
de
x
Chapter 5 Verification Problems
5-4
COSMOSFFE Frequency
TYPE:
Mode shape and frequency, plane element (PLANE2D).
REFERENCE:
Flugge, W., “Handbook of Engineering Mechanics,” McGraw-Hill Book Co.,
Inc.,
New York, 1962, pp. 61-6, 61-9.
PROBLEM:
Determine the fundamental frequency, f, of the cantilever beam of uniform cross
section A.
Figure FFEF2-1
FFEF2: Frequencies of a Cantilever Beam
(See
page
5-2.)
GIVEN:
E
= 30 x 10
6
psi
L
= 50 in
h
= 0.9 in
b
= 0.9 in
A
= 0.81 in
2
ν
= 0
ρ
= 0.734E-3 lb sec
2
/in
4
COMPARISON OF RESULTS
F
1
, Hz
F
2
, Hz
F
3
, Hz
Theory
11.79
74.47
208.54
COSMOSFFE
11.72
73.14
206
y
x
Finite Element Model
L
Problem Sketch
Front View
Cross
Section
b
h
In
de
x
In
de
x
COSMOSFFE Frequency
5-5
Chapter 5 Verification Problems
TYPE:
Mode shapes and frequencies, beam element (BEAM3D).
REFERENCE:
Thomson, W. T., “Vibration Theory and Applications,” Prentice-Hall, Inc.,
Englewood Cliffs, New Jersey, 2nd printing, 1965, p. 18.
PROBLEM:
Determine the fundamental frequency, f, of the simply supported beam of uniform
cross section A.
GIVEN:
E
= 30 x 10
6
psi
L
= 80 in
ρ
= 0.7272E-3 lb-sec
2
/in
4
A
= 4 in
2
I
= 1.3333 in
4
h
= 2 in
ANALYTICAL
SOLUTION:
F
i
=
(i
π)
2
(EI//mL
4
)
(1/2)
i
= Number of frequencies
COMPARISON OF RESULTS:
FFEF3: Frequency of a Simply Supported Beam
(See
page
5-2.)
F
1
, Hz
F
2
, Hz
F
3
, Hz
Theory
28.78
115.12
259.0
COSMOSFFE
28.78
114.3
242.7
Figure FFEF3-1
1
2
3
1
2
Y
3
4
4
5
X
6
Finite Element Model
L
h
Problem Sketch
In
de
x
In
de
x
Chapter 5 Verification Problems
5-6
COSMOSFFE Frequency
TYPE:
Mode shapes and frequencies, beam element (BEAM3D).
REFERENCE:
Thomson, W. T., “Vibration Theory and Applications,” Prentice-Hall, Inc.,
Englewood Cliffs, New Jersey, 2nd printing, 1965, p. 278, Ex. 8.5-1, and p. 357.
PROBLEM:
Determine the first three
natural frequencies, f, of a
uniform beam clamped at
one end and free at the
other end.
GIVEN:
E
= 30 x 10
6
psi
I
= 1.3333 in
4
A
= 4 in
2
h
= 2 in
L
= 80 in
ρ
= 0.72723E-3 lb sec
2
/in
4
COMPARISON OF RESULTS:
FFEF4: Natural Frequencies of a Cantilever Beam
(See
page
5-2.)
F
1
, Hz
F
2
, Hz
F
3
, Hz
Theory
10.25
64.25
179.9
COSMOSFFE
10.24
63.95
178.5
L
h
Problem Sketch
1 2 3 4
19
1 2
18
X
Z
Y
20
Finite Element Model
Figure FFEF4-1
In
de
x
In
de
x
COSMOSFFE Frequency
5-7
Chapter 5 Verification Problems
TYPE:
Mode shape and frequency, beam and mass elements (BEAM3D, MASS).
REFERENCE:
William, W. Seto, “Theory and Problems of Mechanical Vibrations,” Schaum’s
Outline Series, McGraw-Hill Book Co., Inc., New York, 1964, p. 7.
PROBLEM:
A steel cantilever beam of
length 10 in has a square cross-
section of 1/4 x 1/4 in A weight
of 10 lbs is attached to the free
end of the beam as shown in the
figure. Determine the natural
frequency of the system if the
mass is displaced slightly and
released.
GIVEN:
E
= 30 x 10
6
psi
W = 10 lb
L
= 10 in
COMPARISON OF RESULTS:
FFEF5: Frequency of a Cantilever Beam with
Lumped Mass
(See
page
5-2.)
F, Hz
Theory
5.355
COSMOSFFE
5.359
L
W
Problem Sketch
Y
X
1
2
3
1
3
4
2
Finite Element Model
Figure
In
de
x
In
de
x
Chapter 5 Verification Problems
5-8
COSMOSFFE Frequency
TYPE:
Mode shapes and frequencies, shell element (SHELL4).
REFERENCE:
Leissa, A.W. “Vibration of Plates,” NASA, sp-160, p. 44.
PROBLEM:
Obtain the first natural
frequency for a simply
supported plate.
GIVEN:
E
= 30,000 kips
ν
= 0.3
h
= 1 in
a
= b = 40 in
ρ
= 0.003 kips sec
2
/in
4
NOTE:
Due to double symmetry in geometry and the required mode shape, a quarter of the
plate is taken for modeling.
COMPARISON OF RESULTS:
FFEF6: Dynamic Analysis of a Simply Supported
Plate
(See
page
5-2.)
F, Hz
Theory
5.94
COSMOSFFE
5.929
Z
Y
X
h
b
a
Problem Sketch and Finite Element Model
Figure FFEF6-1
In
de
x
In
de
x
COSMOSFFE Frequency
5-9
Chapter 5 Verification Problems
TYPE:
Mode shapes and frequencies, shell element (SHELL4).
REFERENCE:
Kraus, “Thin Elastic Shells,” John Wiley & Sons, Inc., p. 307.
PROBLEM:
Determining the first three
natural frequencies.
GIVEN:
E
= 30 x 10
6
psi
ν
= 0.3
ρ
= 0.00073 (lb-sec
2
)/in
4
L
= 12 in
R
= 3 in
t =
0.01
in
NOTE:
Due to symmetry in geometry and the mode shapes of the first three natural
frequencies, 1/8 of the cylinder is considered for modeling.
COMPARISON OF RESULTS:
FFEF7: Frequencies of a Cylindrical Shell
(See
page
5-2.)
F
1
, Hz
F
2
, Hz
F
3
, Hz
Theory
552
736
783
COSMOSFFE
539.6
710.2
779.9
t
L
R
Problem Sketch
and Finite Element Model
Figure FFEF7-1
In
de
x
In
de
x
Chapter 5 Verification Problems
5-10
COSMOSFFE Frequency
TYPE:
Mode shapes and frequencies, shell element (SHELL4).
REFERENCE:
Flugge, W. “Handbook of Engineering Mechanics,” First Edition, McGraw-Hill,
New York, p. 61-19.
PROBLEM:
Determine the first two natural
frequencies of a uniform ring in
symmetric case.
GIVEN:
E
= 30E6 psi
ν
= 0
L
= 4 in
h
= 1 in
R
= 1 in
ρ
= 0.25E-2 (lb sec
2
)/in
4
COMPARISON OF RESULTS:
FFEF8: Symmetric Modes and Natural
Frequencies of a Ring
(See
page
5-2.)
F
1
, Hz
F
2
, Hz
Theory
135.05
134.92
COSMOSFFE
134.8
720.1
Z
h
L
Y
X
R
Problem Sketch
Figure FFEF8-1
In
de
x
In
de
x
COSMOSFFE Frequency
5-11
Chapter 5 Verification Problems
TYPE:
Mode shapes and frequencies, triangular shell elements (SHELL3).
REFERENCE:
“ASME Pressure Vessel and Piping 1972 Computer Programs Verification,” ed. by
I. S. Tuba and W. B. Wright, ASME Publication I-24, Problem 2.
PROBLEM:
Calculate the natural
frequencies of a triangular
wing as shown in the figure.
GIVEN:
E
= 6.5 x 10
6
psi
ν
= 0.3541
ρ
= 0.166E-3 lb sec
2
/in
4
L
= 6 in
Thickness = 0.034 in
COMPARISON OF RESULTS:
Natural Frequencies (Hz):
FFEF9: Eigenvalues of a Triangular Wing
(See
page
5-2.)
Frequency
No.
Reference
COSMOSFFE
1
55.9
55.76
2
210.9
206.5
3
293.5
285.5
Finite Element Model
Problem Geometry
L
Figure FFEF9-1
In
de
x
In
de
x
Chapter 5 Verification Problems
5-12
COSMOSFFE Frequency
TYPE:
Mode shapes and frequencies, rigid body modes, beam element (BEAM3D).
REFERENCE:
Timoshenko, S. P., Young, O. H., and Weaver, W., “Vibration Problems in
Engineering,” 4th ed., John Wiley and Sons, New York, 1974, pp. 424-425.
PROBLEM:
Determine the elastic and
rigid body modes of vibration
of the unsupported beam
shown below.
GIVEN:
L
= 100 in
E
= 1 x 10
8
psi
r
= 0.1 in
ρ
= 0.2588E-3 lb sec
2
/in
4
ANALYTICAL SOLUTION:
The theoretical solution is given by the roots of the equation Cos KL Cosh KL = 1
and the frequencies are given by:
COMPARISON OF RESULTS:
NOTE:
First two modes are rigid body modes.
FFEF10: Vibration of an Unsupported Beam
(See
page
5-2.)
fi
= Ki
2
(EI/
ρA)
(1/2)
/(2
π)
i
= Number of natural frequencies
K
i
= (i + 0.5)
π/L
A
= area of cross-section
ρ
= Mass Density
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Theory F, Hz
0
0
11.07
30.51
59.81
98.86
Theory (ki)
(0)
(0)
(4.73)
(7.853)
(10.996) (14.137)
COSMOSFFE F, Hz
0
0
10.92
29.82
57.94
94.94
Figure FFEF10-1
1
1
2
3
15 16
2
Finite Element Model
15
L
Problem Sketch
In
de
x
In
de
x
COSMOSFFE Frequency
5-13
Chapter 5 Verification Problems
TYPE:
Mode shapes and frequencies, hexahedral solid element (SOLID).
REFERENCE:
Thomson, W. T., “Vibration Theory and Applications,” Prentice-Hall, Inc.,
Englewood Cliffs, N. J., 2nd printing, 1965, p.275, Ex. 8.5-1, and p. 357.
PROBLEM:
Determine the first
three natural
frequencies of a
uniform beam
clamped at one
end and free at
the other end.
GIVEN:
E
= 30 x 10
6
psi
a
= 2 in
b
= 2 in
L
= 80 in
ρ
= 0.00072723
lb-sec
2
/in
4
COMPARISON OF RESULTS:
FFEF11: Frequencies of a Solid Cantilever Beam
(See
page
5-2.)
F
1
, Hz
F
2
, Hz
F
3
, Hz
Theory
10.25
64.25
179.91
COSMOSFFE
10.24
63.81
177.4
L
x
y
z
Problem Sketch
b
a
Finite Element
Model
Figure FFEF11-1
In
de
x
In
de
x
Chapter 5 Verification Problems
5-14
COSMOSFFE Frequency
TYPE:
Mode shapes and frequencies, truss elements (TRUSS2D).
REFERENCE:
William,
W.
Seto,
“Theory and Problems of Mechanical
Vibrations,”
Schaum’s
Outline Series, McGraw-Hill Book Co., Inc., New York, 1964, p. 7.
PROBLEM:
A manometer used in a fluid mechanics laboratory has a uniform bore of cross-
section area A. If a column of liquid of length L and weight density
ρ
is set into
motion, as shown in the figure, find the frequency of the resulting motion.
NOTE:
The mass of fluid is lumped at nodes 2 to 28. The boundary elements are applied at
nodes 6 to 24.
Figure FFEF12-1
FFEF12: Natural Frequency of Fluid
(See
page
5-2.)
GIVEN:
COMPARISON OF RESULTS
A
= 1 in
2
ρ = 9.614E-5 lb sec
2
/in
4
L
= 51.4159 in
E
= 1E5 psi
F, Hz
Theory
0.617
COSMOSM
0.6172
y
y
y
Problem Sketch
Finite Element Model
1.0"
10"
10"
X
Y
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COSMOSFFE Frequency
5-15
Chapter 5 Verification Problems
TYPE:
Mode shapes and frequencies, multifield elements, 4- and 8-node PLANE2D, 6-
node TRIANG, TETRA10, and 8- and 20-node SOLID.
PROBLEM:
Compare the first two natural frequencies of a cantilever beam modeled by each of
the above element types.
GIVEN:
E
= 10
7
psi
ρ
= 245 x 10
–3
lb-sec
2
/in
4
b
= 0.1 in
h
= 0.2 in
L
= 6 in
n
= 0.3
COMPARISON OF RESULTS:
The theoretical solutions for the first and second mode are: 181.17 and 1136.29 Hz.
FFEF13A, FFEF13B, FFEF13C, FFEF13D,
FFEF13E, FFEF13F: Dynamic Analysis of
Cantilever Beam
(See
page
5-2.)
Input File
Element
1st Mode
Difference
(%)
2nd Mode
Difference
(%)
FFEF13A
PLANE2D 4-node
180.49
0.37
1118.17
1.59
FFEF13B
PLANE2D 8-node
178.91
1.24
1107.59
2.52
FFEF13C
TRIANG 6-node
180.52
0.36
1121.60
1.29
FFEF13D
TETRA10
182.64
0.81
1139.23
0.26
FFEF13E
SOLID 8-node
180.98
0.10
1121.70
1.28
FFEF13F
SOLID 20-node
179.78
0.77
1112.17
2.12
b
L
h
Problem Sketch
Figure FFEF13-1
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Chapter 5 Verification Problems
5-16
COSMOSFFE Frequency
TYPE:
Frequency analysis, SHELL4 elements.
PROBLEM:
Natural frequencies of a simply-supported plate are calculated. Utilizing the
symmetry of the model, only one quarter of the plate is modeled and the first three
symmetric modes of vibration are calculated. The mass is lumped uniformly at
master degrees of freedom.
Theoretical results can be
obtained from the equation:
ω
mn
= r
2
D/L
2
U
∗
(m
2
+ n
2
)
Where:
D = Eh
3
/12(1 -
ν
2
)
U =
ρh
FFEF14: Natural Frequencies of a Simply-
Supported Square Plate
(See
page 5-
2.)
GIVEN:
L
= 30 in
h
= 0.1 in
ρ
= 8.29 x 10
-4
(lb sec
2
)/in
4
ν
= 0.3
E
= 30.E6 psi
ANALYTICAL
SOLUTION:
COMPARISON OF RESULTS:
Normalized mode shape displacements for the nodes
connected by the rigid bar.
Natural Frequency (Hz)
First
Second
Third
Theory
5.02
25.12
25.12
COSMOSM
5.023
25.11
25.11
Total Mass =
ρ
∗
ν
=
8.29
∗
10
-4
∗
0.1
∗
30
∗
30 =.07461
Lumped Mass at Master Nodes =.07461/64 = 1.16E-3
L
Problem Sketch
961
931
1
31
Simply
Supported
Plate
Figure
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COSMOSFFE Frequency
A-1
A
Troubleshooting
Introduction
When you use the COSMOSFFE Frequency module, you may sometimes come
across the following error messages, listed alphabetically. Diagnostics and
corrective measures for each error message are provided.
PROBLEM:
Bonding is not supported
You have specified bonding of two bodies in your model using the
BONDDEF
command. Bonding is not supported in this version of FFE Thermal. Delete
bonding or use the conventional HSTAR module.
PROBLEM:
Cannot restart because previous results are not compatible
Some changes in the model were introduced after the results existing in the
database have been calculated. Use the
RESTART
(Analysis >
Restart
) com-
mand to deactivate the restart option and try again.
PROBLEM:
Cannot restart without previous results
You have activated the restart option for transient thermal analysis. Results of
the analysis were not found in the database. Use the
RESTART
(Analysis >
Restart
) command to deactivate the restart option and try again.
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Appendix A Troubleshooting
A-2
COSMOSFFE Frequency
PROBLEM:
Cannot restart without results for the starting point
You have activated the restart option for transient thermal analysis. Results of
the analysis at the starting solution step were not found in the database.
PROBLEM:
Coordinate system <number> is referenced but not defined
Define the missing coordinate system and try again or modify your input such
that the named coordinate system is not referred to.
PROBLEM:
Degenerate element <number>
Degenerate elements were detected in your model. Degenerate elements are bar
elements with 0-length, area elements with 0-area, or solid elements with 0-vol-
ume. Use the
ECHECK
(Meshing > ELEMENTS >
Check Element
) command
to correct the problem and automatically delete bar elements whose length is
less than
PTTOL
, area elements whose area is less than
PTTOL
square, and solid
elements whose volume is less than
PTTOL
cubed. The point tolerance is
defined by the
PTTOL
(Geometry > POINTS >
Merge Tolerance
) command.
PROBLEM:
Element <number> has unsupported type
The given element is associated with an element group that is not supported in
this release of FFE Thermal. Use the conventional solver, or redefine the ele-
ment group if possible.
PROBLEM:
Element <number> is pyramid shaped, which is not supported
The named element belongs to a SOLID element group. The nodes defining a
face of the solid have collapsed to a single location. This type of collapsed ele-
ment is not currently supported by FFE Thermal. This element may have been
defined manually or resulted from the parametric meshing of a volume with a
collapsed face. Delete the mesh, define a TETRA4, or TETRA10 element
group, and use automatic meshing instead of parametric meshing. Prism-shaped
elements are automatically supported by FFE Thermal.
PROBLEM:
Error while closing a temporary file
An I/O error occurred while closing a temporary file.
PROBLEM:
Error while positioning a temporary file
An I/O error has occurred while reading information from a temporary working
file.
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COSMOSFFE Frequency
A-3
Appendix A Troubleshooting
PROBLEM:
Error while reading file <filename>
An I/O error has occurred while reading from the named file which is part of the
COSMOSM database. The file may have been corrupted. Check the integrity of
your hard disk, reconstruct the model by creating a new problem and using the
FILE
(File >
Load...
) command, and try again.
PROBLEM:
Error while reading from a temporary file
An I/O error has occurred while reading information from a temporary working
file.
PROBLEM:
Error while writing to a temporary file
An error occurred while writing data to the temporary file. Check the available
disk space, and the integrity of your system, especially the hard disk. Recon-
struct the database and try again.
PROBLEM:
Error while writing to file <filename>
An error occurred while writing data to the named file. Check the integrity of
your system, especially the hard disk. Reconstruct the database and try again.
PROBLEM:
File <filename> does not contain necessary data
The named file name does not contain the expected data in the expected format.
Either the file is corrupted, overwritten, or created by a different COSMOSM
version.
PROBLEM:
File <filename> has invalid format
The format of the data in the named file is not as expected. Either the file is cor-
rupted, overwritten, or created by a different COSMOSM version.
PROBLEM:
Improper
axisymmetric
model
The defined axisymmetric model is improper. Axisymmetric elements must be
defined in the global X-Y plane with the Y-axis as the axis of symmetry.
PROBLEM:
Improper mesh near element <number>
The mesh elements are not compatible in the neighborhood of the named ele-
ment. This can be the result of improper node merging, invalid parametric tetra-
hedral mesh, or invalid manually created elements.
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Appendix A Troubleshooting
A-4
COSMOSFFE Frequency
PROBLEM:
Improper mesh, properties, or boundary conditions
Either the mesh, material properties, or boundary conditions of the model have
been improperly defined. Use the
R_CHECK
(Analysis >
Run Check
) com-
mand to check the elements. Also list and examine the material properties and
boundary conditions.
PROBLEM:
Incompatible
element groups
The generated mesh connects elements with incompatible element groups to
each other. Try to use other alternatives such that connected elements have com-
patible degrees of freedom.
PROBLEM:
Internal error # <number>
An internal error has occurred. Record the error number and report to S.R.A.C.
PROBLEM:
Invalid combination of first and second order elements
First order (linear) and second order (parabolic) elements are connected to each
other resulting in incompatible common edges. An example is connecting
TETRA4 elements to TETRA10 elements. Use the
ECHANGE
(Meshing >
Ele-
ment Order
) command to fix the problem by raising the order of first order ele-
ments or lowering the order of second order elements. It is recommended,
though not necessary to change the element group(s).
PROBLEM:
Invalid curve
An invalid temperature or time curve has been found. Verify your input. The
ACTXYPRE
(Display XY PLOTS >
Activate Pre-Proc
) and
XYPLOT
(Display
XY PLOTS >
Plot Curves
) commands may be used to plot time and tempera-
ture curves. Redefine the invalid curves using the
CURDEF
(LoadsBC > FUNC-
TION CURVE > Time/Temp Curve) command and try again. A corruption in
the database is possible.
PROBLEM:
Invalid order of nodes for element <number>
The number of nodes used to define the specified element is invalid. Use the
(Edit > LIST >
Element Groups
) and
ELIST
(Edit > LIST >
Elements
) com-
mands to find the error. The
R_CHECK
(Analysis >
Run Check
) command will
also detect such errors.
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COSMOSFFE Frequency
A-5
Appendix A Troubleshooting
PROBLEM:
Invalid time interval for the analysis <start>, <end>
The time interval specified for the transient thermal analysis is invalid. Use the
TIMES
(LoadsBC > LOAD OPTIONS >
Time Parameter
) command to correct
the error.
PROBLEM:
Maximum number of nonlinear iterations <number> exceeded
The maximum allowable number of nonlinear iterations has been exceeded
without conversion. Check your input. Allow a higher number of iterations if no
errors are found. Use a smaller time interval for transient analysis.
PROBLEM:
Not enough boundary conditions
None or inadequate boundary conditions specified. Use commands in the
LoadsBC > HEAT TRANSFER menu to check your input. Specify more bound-
ary conditions and try again.
PROBLEM:
Out of memory or swap space
Available virtual memory is not sufficient to run this problem.
On UNIX systems contact your system administrator to increase size of the
swap space.
PROBLEM:
Too many time steps
The number of time steps for transient thermal analysis exceeded the maximum
allowed number which is currently 2400.
PROBLEM:
Unable to create a temporary file
FFE Thermal could not create a temporary file. Check the integrity of your sys-
tem and verify that adequate disk space is available.
PROBLEM:
Unable to create file <filename>
FFE Thermal could not create the named file. Check the integrity of your sys-
tem and verify that adequate disk space is available.
PROBLEM:
Unable to open file <filename>
FFE Thermal could not open the named file which is part of the COSMOSM
database. The file may have been deleted. Check the integrity of your hard disk,
reconstruct the model by creating a new problem and using the
FILE
(File >
Load...
) command.
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Appendix A Troubleshooting
A-6
COSMOSFFE Frequency
PROBLEM:
Unable to open problem database
FFE Thermal could not open the database for this problem. Verify that the data-
base files for this problem exist in the proper path and directory specified and
that the correct version is being used. Also check the integrity of your system
and verify that adequate disk space is available.
PROBLEM:
Unexpected end of file while reading <filename>
An end-file mark was found before reading all needed data from the named file.
Check related input, fix the problem if any, and try again. Regenerate the file if
possible, check the integrity of your system and reconstruct the database
through the
FILE
(File >
Load...
) command if the problem could not be fixed
otherwise.
PROBLEM:
You are not authorized to use this type of analysis
You are not authorized to use this type of analysis. Use the
PRODUCT_INFO
(Control > MISCELLANEOUS >
Product Info
) command to get a list of the
modules you are authorized to use. Contact S.R.A.C.
PROBLEM:
Zero or negative cross section area for element <number>
The cross sectional area of the specified element is zero or negative. Use the
ELIST
(Edit > LIST >
Elements
) command to find the associated real constant
set and then use the
RCLIST
(Edit > LIST >
Real Constants
) command to list
the cross sectional area. Use the
RCONST
(Propsets >
Real Constant
) com-
mand to specify a positive value.
PROBLEM:
Zero or negative heat conductivity for element <number>
The heat conductivity specified for this element is zero or negative. Use the
ELIST
(Edit > LIST >
Elements
) command to find the associated material prop-
erty set and then use the
MPLIST
(Edit > LIST >
Material Props
) command to
list the material properties in the associated set. Use the
MPROP
(Propsets >
Material Property
) command to specify a positive value.
PROBLEM:
Zero or negative real constant for radiation link element <number>
An invalid value has been specified in the real constant associated with the spec-
ified element. Use the
ELIST
(Edit > LIST >
Elements
) command to find the
associated real constant set and then use the
RCLIST
(Edit > LIST >
Real
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COSMOSFFE Frequency
A-7
Appendix A Troubleshooting
Constants
) command to list the set and check your input for the radiating sur-
face area, the view factor, emissivity, and the Stefan-Boltzman constant. Use the
RCONST
(Propsets >
Real Constant
) command to fix the error.
PROBLEM:
Zero or negative thickness for element <number>
The thickness of the specified element is zero or negative. Use the
ELIST
(Edit >
LIST >
Elements
) command to find the associated real constant set and then
use the
RCLIST
(Edit > LIST >
Real Constants
) command to list the thickness.
Use the
RCONST
(Propsets >
Real Constant
) command to specify a positive
value.
PROBLEM:
Zero or negative time increment
The time increment specified by the
TIMES
command is invalid. Use the
TIMES
(LoadsBC > LOAD OPTIONS >
Time Parameter
) command to specify a posi-
tive value.
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COSMOSFFE Frequency
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COSMOSFFE Frequency
I-1
Index
A
A_FEEFREQ 1-3
Align Shell Elements 2-5
analysis options 3-5, 4-8
anisotropic 1-3
axisymmetric 2-1
B
basic steps 3-2
beam elements 2-2
BEAM3D 1-2
bottom face 2-5
D
damping matrix 1-2
DSTAR 3-5
E
EGROUP 2-3
eigenvalue problem 1-2
element order 1-3, 3-5, 4-3, 4-8
error messages 3-8, A-1
F
FFE Frequency Options 1-3, 3-2,
3-5
full integration 2-5
H
hexahedral 2-2
I
isotropic 1-3
L
lower bound 1-3
lower bound value 3-5
M
MASS 1-2
mass matrix 1-2
material properties 2-3
mid surface 2-5
modal analysis 1-2
mode shape 4-5, 4-9
mode shapes 1-2, 3-6
N
natural frequencies 1-2, 1-3
number of frequencies 3-5, 3-6,
4-3, 4-8
O
orthotropic 1-3
output file 3-7
P
pentahedral 2-2
plane strain 2-1
plane stress 2-1
PLANE2D 1-3, 2-1
R
R_MATLIB 2-3
RCONST 2-3
Real Constant 2-3
rigid connection 1-3
rigid connections flag 3-6
Run Check 3-8
S
second order 4-3, 4-8
SHADE 2-5
shell elements 2-2
SHELL3 1-3
SHELL4 1-3
SOLID 1-3, 2-2
sparse matrix 1-1
SPRING 1-2
step-by-step examples 4-1
stress results 2-5
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Document Outline
- COSMOSFFE Frequency Analysis Module
