An interactive computer graphics processor is described that is capable of generating input to animate modal and transient vibrations of finite element models on an interactive graphics system. The results from NASTRAN can be postprocessed such that a three dimensional wire-frame picture, in perspective, of the finite element mesh is drawn on the graphics display. Modal vibrations of any mode shape or transient motions over any range of steps can be animated. The finite element mesh can be color-coded by any component of displacement. Viewing parameters and the rate of vibration of the finite element model can be interactively updated while the structure is vibrating

Lipman, Robert R.

English

NASA Technical Reports Server

Ns7-272 9
COMPUTER ANIMATION OF MODAL AND TRANSIENT VIBRATIONS
Robert R. Lipman
David W. Taylor Naval Ship Research and Development Center
Numerical Structural Mechanics Branch (Code 1844)
Bethesda, Maryland 20084-5000
SUMMARY
An interactive computer graphics postprocessor is described that is capable of generating input to
animate modal and transient vibrations of finite element models on an interactive graphics system. The
results from NASTRAN can be postprocessed such that a three-dimensional (3-D) wire-frame picture,
in perspective, of the finite element mesh is drawn on the graphics display. Modal vibrations of any
mode shape or transient motions over any range of time steps can be animated. The finite element
mesh can be color-coded by any component of displacement. Viewing parameters and the rate of vibra-
tion of the finite element model can be interactively updated while the structure is vibrating.
INTRODUCTION
As the computational power of computers has increased, the size of finite element models that an
engineer can analyze in a reasonable amount of time has also increased. Finite element models that are
analyzed overnight on an average computer can now be analyzed routinely in under an hour on a super-
computer. However, an engineer is still faced with the task of assimilating and drawing meaningful
conclusions from large amounts of output generated by the finite element analysis programs. Output
from these programs is presented as almost endless values of stress, strain, and displacement associated
with nodes and/or elements. The interpretation of the finite element results is made even more
difficult when real and imaginary values are considered. Structural deformations or color contours of
nodal results for various mode shapes or time steps can be plotted in addition to graphs of the response
of a finite element node versus time or frequency. However, the engineer is still depending on static
plots to understand the dynamic behavior of a structure.
A postprocessing computer program, CANDI (Color Animation of Nastran Displacements) for
NASTRAN finite element analysis results has been developed. CANDI generates input for an interac-
tive graphics system so that modal and transient vibrations of finite element models can be animated.
Providing the capability to animate finite element results has greatly improved the engineer's ability to
interpret dynamic results that were previously viewed with static plots.
Unfortunately, the black and white reproduction of this paper cannot show the color animation that
is generated by the hardware and software to be described. The reader will have to use his imagination.
HARD WARE
The hardware that is used to display the animation of finite element analysis results is an Evans &
Sutherland PS-330 interactive graphics system (ref. 1). The PS-330 has the ability to process a large
number of vectors, as would be dictated by complex finite element meshes, and to perform real-time
3-D interactive transformation of those vectors. The user can manipulate the PS-330 graphics display
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by means of a display data structure, a function network, and various input devices. The display data
structure represents the finite element mesh and transformations applied to the mesh for sealing, rota-
tion, translation, and other viewing purposes.
The function network represents a user-programmable system for describing the processing of
interactive input and output local to the PS-330. The function network determines the effect of input
from interactive devices on the display data structure (in the form of a finite element mesh). The user
interacts with the function network through programmable interactive control dials and function keys.
The display processor refreshes the screen image in real-time by traversing the display data structure
which the function network is potentially modifying.
The graphics display consists of a 19-inch color vector refresh display. Finite element meshes are
displayed in color or with depth-cueing. Depth-cueing enhances the illusion of depth and three dimen-
sions by drawing vectors lighter the "farther away" they are from the viewer. Also, to enhance the
illusion of three dimensions, perspective viewing of the finite element mesh is used.
FUNCTION NETWORKS
Function networks on the PS-330 are an example of data flow programming (ref. 2). An operator of
a data flow program is known as a function instance. The PS-330 has a predefined set of over 100 func-
tion instances such as add, multiply, and rotate. Each function has a fixed number of inputs and out.
puts with predefined meanings. Data flow programming is accomplished by creating function instances
and connecting inputs and outputs of the function instances to create the desired effect.
Function networks are data driven. A function becomes active only when data arrive at its inputs to
be processed. Once a function has executed its task, it becomes dormant again until another set of
input arrives. The entire function network is dormant until activity occurs at the interactive device to
which it is connected.
Figure 1 shows a small part of the function network used in the animation of finite element model
WS_ROT := F:CMUL;
WS_,MULX := F:MULC;
WS_XROT := F:XROTATE;
SEND 'X-ROT' TO < 1 >DLABEL 1;
CONNECT DIALS < 1 > :< 1 > WS__MULX;
SEND 180 TO <2>WS_MULX;
CONNECT WS_MULX < 1 > : < 1 >WS_XROT;
CONNECT WS_XROT< 1 > : <2 > WS_ROT;
CONNECT WS_ROT< 1 :> : < 1 >WS..ROT;
CONNECT WS_ROT< 1 > :WORLD .ROT;
Fig. 1. Rotation function network
vibrations. This part of the function network sets up a control dial to control the X rotation of the
finite element model on the display screen. Figure 2 shows a schematic of that function network. The
first three lines, of the rotation function network, instance (refer to) some of the PS-330 functions.
The fourth line sends a label to the LED lights on Control Dial 1. The fifth line connects the output of
the control dial to the first input of one of the function instances. The sixth line sends a constant value
of 180 to the second input of the same function instance. The remaining four lines connect the inputs
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WS.MtS.X WS.__OT IL WS_ROTDIALS<l>----4 I I
180------I F:MULC H F-._IOTATE H F.-CMUL WOlU.D£'OT
Fig. 2. Schematic of rotation function network
and outputs of the function instances in the correct manner. When the user rotates Control Dial 1, the
end result is that the finite element model on the display screen will rotate about the screen's X axis.
To animate modal or transient vibrations of finite element models, a function network must be
loaded into the PS-330. The basic function network used with CANDI sets up: (1) the control dials to
do rotations and translations of the finite element model about the X, Y, and Z axes, and (2) function
keys or control dials to both control the rate of vibration and cycle through the animation sequence.
For transient vibrations, the animation sequence consists of deformed shapes of the finite element
model over a range of time steps. For modal vibrations, the animation sequence consists of a
sinusoidal variation of the deformation of the finite element model.
In addition to controlling the function of the control dials and function keys, the function network
also contains the geometry of the finite element model that is to be animated. The geometry is written
in a vector list function. The vector list contains the necessary XYZ coordinate information to draw the
finite element mesh. A coordinate value in the vector list will be computed from the undeformed XYZ
coordinates of the finite element model plus the product of displacement of that coordinate and a scale
factor. An example of a vector list is shown in figure 3.
BEAM := VEC COLOR ITEM
P 1.000 0.000, 0.000 H=I20.
L 1.500
L 2.000
L 2.500
L 3.000
L 3.500
L 4.O00
L 4.500
L 5.OOO
0.000, 0.000 H=120.
0.000, 0.000 H=120.
0.000, 0.000 H=120.
0.000, 0.000 H=120.
0.000, 0.000 H=120.
0.000, 0.000 H=120.
0.000, 0.000 H=120.
0.000, 0.000 H=120.;
Fi& 3. Example vector list
The first line of the vector list establishes a name for the vector list function instance. The remain-
ing lines give the X-YZ coordinates of the finite element mesh. The "P" means move to that coordi-
nate. The "L" means draw to that coordinate. Associated with each coordinate is a color, "H=",
which is specified by a value between zero and 360. The colors blue, magenta, red, yellow, green, and
cyan have values of 0, 60, 120, 180,240, and 300, respectively. If a line has the same color specified at
the beginning and end, the entire line will be drawn with that single color. If the beginning and end of
a line have different color values, then the color of the line will change between the beginning and end
of the line. The finite element mesh can be color-coded by assigning a color value to each XYZ coordi-
nate according to a nodal value of displacement.
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Ratherthanhavethehost computer calculate the sinusoidal variation of the deformations for modal
vibrations, the function network computes the animation sequence locally on the PS-330 according to
the following equation (ref. 3):
F_:V, + DSF [ V,,sinO_- Vi,,,cosOi ]
where Fi is one frame in the animation sequence, Vs is the undeformed vector list, V_ is the real
deformation vector list, Vim is the imaginary deformation vector list, DSF is the deformation scale fac-
tor, and 01 is the angle for Fi. Usually a value of i between 12 and 16 is an acceptable number of
frames for smooth animation.
POSTPROCESSING OF NASTRAN RESULTS
The program CANDI can postprocess results from several different NASTRAN analyses: static,
eigenvalue, direct frequency response, direct transient response, and modal frequency response. (A
static analysis is handled in CANDI as a transient analysis with only one time step.) The NASTRAN
analysis must generate a file that CANDI will postprocess. To write out that file, DMAP ALTER state-
ments must be included in the NASTRAN executive control deck. Figure 4 shows an example of the
ALTER 83 $ Apr 86 Version
OUTPUT2 CASECC,BGPD T, ECT, LAMA,PPHIG $
ENDALTER $
Fig. 4. NASTRAN ALTER statments
ALTER statements required for an eigenvalue analysis. The data blocks that are written by these
ALTER statements contain the following information: CASECC - case control information, BGPDT-
XYZ nodal coordinates, ECT - element connectivity, LAMA - eigenvalues, and PPHIG - eigenvectors.
There are similar ALTER statements to write the appropriate data blocks for the other types of ana-
lyses.
The data block that contains nodal displacements, for example PPHIG, is only generated when plot-
ting is requested in the NASTRAN run. Therefore, plotting cards are required in the NASTRAN case
control deck. This displacement data block is used rather than other displacement data blocks within
NASTRAN, because the displacements are already in a basic XYZ cartesian coordinate system. Dis-
placement in other data blocks would have to be transformed to that system.
CANDI USAGE
GANDI is an interactive program that prompts the user for various inputs and generates undo-
formed shape and displacement vector lists. All possible responses are listed with each question. A
sample interactive session with CANDI is shown in figure 5. The user has many options to control the
parts of the finite element model to be written to the vector lists. Elements can be excluded by ele-
ment type or element identification number. Given a range of XYZ coordinate values, any element not
within that range can also be excluded. Elements can be color-coded by element type; for example,
plate elements may be green and solid elements cyan. The finite element mesh can also be color-coded
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by a nodal value of displacement. A user-modifiable deformation scale fac_r is computed. This scale
factor multiplies the real displacements so that their magnitude will be similar to the dimensions of the
finite element model. For a transient analysis, any range of time steps can be written to the displace-
ment vector list. For an eigenvalue or frequency response analysis, any frequency also can be written
to the displacement vector list.
D ISPLAYING THE ANIMATION
Before the finite element model vibrations can be animated, the function network that sets up the
function of the control dials and function keys must be sent from the host computer to the PS-330.
The definition of the control dials and function keys for modal vibrations is shown in figure 6 and, for
transient vibrations, in figure 7. Once either function network has been transmitted to the PS-330, the
undeformed shape and displacement vector lists can be sent to the PS-330 from the host computer.
Usually, the user will generate one undeformed shape and multiple displacement vector lists during one
interactive session with CANDI. To animate different displacement vector lists, the desired vector list
is downloaded to the PS-330. Once the required vector lists reside on the PS-330, the user has com-
plete control over the animation through the use of the control dials and function keys.
REFERENCES
1. "PS-300 User's Manual," Evans & Sutherland Computer Corporation, Salt Lake City, Utah, 1985.
2. McGraw, J.R., "Data Flow Computing - Software Development," in: IEEE Transactions on Cornpub
er6, Vol. C-29, No. 12, December 1980.
3. Ehlers, R., "Modal Vibration Simulation Package," Evans & Sutherland Computer Corporation, Salt
Lake City, Utah, 1984.
115
$ eandi
CANDI- Color Animation of Nastran DIsplacements
ENTER FILE NAME OF THE UT1 FILE ? fs.utl
COORDINATE LIMITS OF THE STRUCTURE
XMIN_2.39E+ 02 YMIN_--- 0.00E+ 00 ZMINP_ 1.03E+ 03
XMAX= 2.39E+ 02 YMAX_--- 2.39E+ 02 ZMAX= 1.38E+ 03
DO YOU WANT TO EXCLUDE ELEMENTS BY COORDINATE RANGES (Y/N) ? n
3 ELEMENT TYPES, CURRENTLY RECOGNIZED BY CANDI, WERE FOUND IN THE FEM.
180-CBAR 58-CQUAD2 53-CTRIA2
DO YOU WANT TO EXCLUDE ELEMENTS BY ELEMENT TYPE (Y/N) ? n
DO YOU WANT TO EXCLUDE ELEMENTS BY ELEMENT ID (Y/N) ? n
READING CBAR
READING CQUAD 2
READING CTRIA2
D O YOU WANT THE VECTOR LISTS TO BE WRITTEN
1 - COLOR CODED BY ELEMENT TYPE
2 - DEPTH CUED
?1
ENTER FILE NAME FOR THE UNDEFORMED FEM VECTOR LIST ? fs.und
WRITING VECTOR LIST
DO YOU WANT TO GENERATE ANY DISPLACEMENT VECTOR LISTS (Y/N) ? y
NUMBER OF SUBCASES _--- 1, SUBCASE IDS - 1
NUMBER OF EIGENVECTORS = 3 (MODE-FREQUENCY)
1-3.65E+01 2-3.83E+ 01 3-5.00E+ 01
ENTER A MODE NUMBER ? 2
ENTER FILE NAME FOR THE DISPLACEMENT VECTOR LIST ? fs.m2
ENTER NUMBER OF FRAMES OF ANIMATION ? 16
WRITING VECTOR LIST
MAXIMUM DEFORMATION = 1.1632E+ 00
DEFORMATION SCALE FACTOR = 2.0553E+ 01
DO YOU WANT TO WRITE ANOTHER DISPLACEMENT VECTOR LIST (Y/N) ? n
FORTRAN STOP
Fig. 5. Sample interactive session of CANDI
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CD(1) - X rotation
CD(2) - Y rotation
CD(3) - Z rotation
CD(5) - X translation
CD(6) - Y translation
CD(7) - Z translation
CD(8) - Scale
FK(1) - Start modal vibration
FK(2) - Stop modal vibration
FK(4) - Step through animation sequence
FK(5) - Slow down rate of vibration
FK(6) - Speed up rate of vibration
FK(9) - Reset all rotations and translations
FK(10) - Toggle on/off undeformed shape
FK(ll) - Toggle on/off coordinate axes
FK(12) - Calculate animation sequence from the undeformed
vector list and the displacement vector lists
Fig. O. Modal vibration control dial and function key definitions
Fig. 7.
CD(1) - X rotation
CD(2) - Y rotation
CD(3) - Z rotation
CD(4) - Control rate of vibration
CD(5) - X translation
CD(6) - Y translation
CD(7) - Z translation
CD(8) - Scale
FK(1) - Start/stop transient vibration
FK(9) - Reset all rotations and translations
FK(10) - Toggle on/off undeformed shape
FK(ll) - Toggle on/off coordinate axes
Transient vibration control dial and function key definitions
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Computer animation of modal and transient vibrations

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