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Transcript
Virtual laboratories for analysis and design of
civil engineering structures
S. Hernández, L.A. Hernández, A. Antón
E.T.S. Ingenieros de Caminos, Canales y Puertos,
Universidad de La Coruña, SPAIN
Abstract
Throughout the history of science and technology two alternative approaches,
namely experimental and analytical methods, have been used to produce new
advances. Empirical based research has asked continuously for more and more
sophisticated facilities and analytical work entered into computational
approaches since the developing of digital computers. In this paper a technique
linking both methodologies is presented, based on a combination of realistic
visualization models, advanced structural analysis and high performance
computers. Two examples, one corresponding to a bridge undergoing an
earthquake and another one devoted to the visualization of a digital model of the
Tacoma Narrows bridge and its aeroelastic response under wind loads are
presented to make clear the capabilities of this methodology.
1. Alternative approaches in science and technology
Knowledge adquisition in ancient times was based upon observation. But this
was long time ago. Since then, modern science and technology require more
sophisticated approaches to deal with current and futures challenges.
Mainstream approaches in nowadays research may be classified into
—Experimental techniques,
—Computational methods.
Both depend on observation. In experimental methods a lot of care need to
be done in setting up proper facilities to carry out experiments using appropriate
reduced models. On the other hand, the efficiency of computational methods
relay on the accuracy of the model and the capabilities of the numerical
techniques used in the analysis.
None of these approaches are completely independents. Both require to a
certain degree some external information in order to check out their credibility.
But this classification is instructive because emphasizes whether the main effort
is done in testing or in computer simulation.
This overview is also valid when explaining the tools used currently for
analysis and design of engineering structures. Bridges, dams, tall buildings,
power plants and offshore platform have been tested, analyzed by computer
programs or studied in both ways before being built.
2. Dynamic responses of civil engineering structures
Appropriate understanding of the dynamic behaviour of structures is very
important in civil engineering works. While small structures are mainly driven
by service loads, more important realizations require taking in account loadings
coming from earthquakes, wind or oceanwaves which are naturally dynamics.
The main classes of dynamic responses to be evaluated are:
—Frequencies and vibration modes,
—Time history of displacements,
—Time history of internal forces or stresses.
2.1. Conventional computer representation of dynamic responses
Computer evaluation of dynamic responses of structures is provided by
structural analysis of discretized FE or BE models. Figure 1 shows a structural
model and two vibration modes of a building.
a) Structural model
Figure 1. Dynamic response of a building
b) Vibration mode #1
c) Vibration mode #6
Figure 1. Dynamic response of a building (cont.)
In Figure 2 a finite element model of a suspension bridge and a time history
response of the vertical displacement of a node is presented.
a) Actual construction
Figure 2. Data visualization of a suspension bridge
b) Dynamic response
c) Structural model
Figure 2. Data visualization of a suspension bridge (cont.)
From these two examples can be concluded that graphical representation of
dynamic responses can not be obtained properly by the software used currently.
Vibration modes are represented by using very abstracts wireframe models and
time history responses are shown by means of curves in cartesian coordinates.
The lack of proper representation of dynamic responses has created the
necessity of using experimental facilities where reduced or real scale models are
subjected to dynamic loadings. This approach has been used widely in specific
types of actions as earthquakes or aeroelastic studies.
3. Testing facilities for dynamic responses
A brief description of testing facilities usually implemented to deal with the two
dynamic loadings before mentioned, namely earthquake or wind effects in
structures will follows:
• Shaking tables: They are composed by horizontal plates having several
degrees of freedom in order to represent vertical and horizontal ground
kinematics. The experiment is carried out by posing a reduced model of the
structure upon the table and imposing a time history of vertical and horizontal
displacements.
• Reaction walls: The aim of this testing device is to create horizontal forces
acting against the structure to be tested. Reaction walls are very useful to
represent earthquake actions on buildings. A picture of a reaction wall is shown
in Figure 3.
Figure 3. Reaction wall of Charles Lee Poweel Structural Research Lab
• Wind tunnels: Boundary layer wind tunnel facilities have been instrumental
in the developing of sound aeroelastic studies. Many important bridges, cooling
towers, communication towers or tall buildings have been tested under wind
flow provided by wind tunnel laboratories. Wind induced instabilities are
identified by creating a wind flow of increasing speed until the appearance of
instability in the reduced model of the structure tested. An example of a
structural model arranged for this class of experimental study is presented in
Figure 4.
Figure 4. Reduced model in a wind tunnel
These types of facilities have been very popular because the deficiencies of
conventional computational methods in dealing with appropriate representation
of dynamic responses. But on the other hand, construction of reaction walls,
shaking tables or wind tunnels is very expensive, they require very big volume
spaces, a delicate maintenance and an important number of technicians to take
care of the laboratories. Because of that an alternative to the experimental
approach based on the recent advances of high performance computers should
be very welcome. In the following a presentation about how this alternative may
be created, giving way to what can be defined as virtual laboratories for civil
engineering structures will be presented.
4. Fundamentals of virtual laboratories
This definition tries to define a kind of advanced visualization of structural
responses composed by three elements: an advanced visualization model, a
structural analysis software and a high performance computer.
ADVANCED
VISUALIZATION
MODEL
STRUCTURAL
ANALYSIS
SOFTWARE
HIGH
PERFORMANCE
COMPUTER
Figure 5. Virtual laboratories elements
The aim of a virtual lab is to represent in real time the behaviour of a future
construction, but instead of using the structural model an advanced visualization
model which shows the design very realistically is included in the procedure.
Visualization can be done
—in computer screens,
—with VR devices.
Additionally the virtual experiment can be stored with video recording
devices.
4.1. Advanced visualization models
The first step in this class of visualization is to create a computer representation
of the real construction, also denominated digital model.
A digital model of a construction is produced when all the geometrical
entities needed to identify it are defined and indicated as input data in the
computer. Points describing the construction can be linked by simple or
complex entities. The most common families of lines are Hermite curves, Spline,
Bezier, B-Spline or NURBS (Non-Uniform Rational B-Spline). Surfaces can be
approximated by Hermite patches, Bezier bicubic elements, and NURBS
surfaces. Surfaces can also be described by using polygonal fitting.
After the digital model is made, a representation of it can be presented on a
graphic display, a plotter or a printer. Computer aided drawing requires to place
any necessary point of the object on the graphic peripheral. This operation is
made by transforming a 3-D space into a 2-D space and it is made through
matrix operators [1-3].
The main difference between classical representation and computer aided
design is not the tool used to produce the drawing; the difference is deeper. In
classical representation the image of the object exists only in the mind of the
designer. To produce several views of it or just changing the scale of one
already made view is very time consuming.
In this approach an object visualization is defined by the following
parameters.
a) Stablishment of optical properties of the object’s surface
Colour, brightness, transparency and other optical properties must be set
prior to visualize the object. This properties can affect to the appearance of the
object as a whole, or they can vary along the object’s surface, being then defined
as textures.
b) Setting the lighting conditions
The number and type of light sources may be stated in order to evaluate their
influence in the object’s appearance. Most engineering works can be lit by using
a single parallel ray source associated to the sun.
c) Definition of scene properties
It is necessary to stablish how the object is to be viewed, in terms of relative
location between the object and the observer, kind of perspective, field of view,
etc. All these parameters are grouped in a camera model.
Other parameters such as fog, background, etc., are set in this point.
d) Choosing the shading model
The visualization process can give more or less realistic results depending on
the algorithms choosen to obtain the light intensity on every point considered of
an object surface, from fast procedures to obtain rough approximations to very
time consuming processes to get photorrealistic results.
The more stablished shading models are:
a) Flat shading: Shading function is evaluated only at one point for each
single triangle or quadrilateral element of the surfaces of the model. This simple
technique produces fair results for prismatic objects but leads to bad
visualizations for the curved ones.
b) Gouraud shading [4]: The shading function is evaluated at the vertices of
the polygons by first calculating the normal at these points and using the
expression of I. Then, the light intensity at any inner point is obtained by
bilinear interpolation.
c) Phong shading [5]: This technique uses the same kind of bilinear
interpolation indicated for Gouraud shading. But the approximation is applied to
the normal to the surface, instead of to the intensity light. Phong shading
produces the best quality of computer visualization.
Every shading technique intends to obtain the light intensity at a pixel of an
object for a given number of light sources and incident angles. Because of that
they are called local methods. Additionally, computer visualization requires
global methods accounting for the complete set of objects in a scene and the
ways they interfere each other.
a) Radiosity method [6-7]
b) Ray tracing method [8]
Many advantages can be obtained by using this techniques [9-10] and an
example of application of advanced visualization to bridge design is presented in
Figure 6.
a) Digital image
b) Real view of the bridge
Figure 6. Digital and real views of a bridge
4.2. Visualization of bridge displacement
To represent the deformation of a structure, it is necessary to modify the location
of all the vertices in the model that are to be moved. The variation of the
coordinates along the sequence of frames can be adapted to follow any desired
time line, being the time line curve, linear, or any other expression.
For very complex model shapes, it is very difficult to obtain de movement of
every single vertex in the model, but the displacement can be applied to another
simpler geometry that will respond to the movement in the same way that the
original geometry and can be used to deform clusters of vertices of the object
linearly with its own deformation. This concept is known as lattice.
Figure 7. Bridge model and associated lattice
To apply the lattice analogy to show the deformations of a bridge, several
hypothesis may be stated:
— Bridge displacements do not affect to the geometry of cross-section.
— Displacements of a cross section can be identified by three values:
horizontal and vertical displacements and twisting angle.
— Displacements of non-structural elements (lightposts, verandas, signs,
etc.) depend on the section on which they lay.
— Displacements of cables of suspension bridges are extrapolated from
deck movements.
Using these hypothesis, the information on the displacements of bridge can
be reduced to three values for each cross section, being the number of cross
section the same for both models, the one used for structural analysis and the
one used for visualization.
With all these considerations, the values for the displacements of every cross
section of the deck can be obtained from the structural analysis software [1112], and translated to the analogous sections of the lattice on the visualization
software [13].
Figure 8. Lattice deformation and bridge deformation
4.3. Structural analysis for dynamic responses
Current structural analysis is based on FE or BE structural models; for time
history approach modal analysis is the most common approach [14-16].
In case of bridges undergoing wind loads aeroelastic analysis need to be
carried out [17-21] in order to identify bridge deformation for each wind speed
and also the value of wind speed initiating flutter instability.
4.4. High performance computers
The concept of high performance computer is very problem dependant. Some
engineering problems may only require very fast CPU, but for virtual
laboratories applications computers needs to provide the following
characteristics:
—Fast CPU,
—Large RAM capacities for material textures and other material properties,
—High performance graphic engines for geometry operations.
Two examples are included in this paper showing the advantages of virtual
laboratories, all the analysis was carried out in SGI Onyx 2 machines and then
video recording of the computer animations was worked out. More powerful
machines would allow real time visualization of the dynamic responses of the
structures.
5. Application examples
5.1. Pedestrian bridge subjected to ground acceleration
The first example corresponds to a suspension bridge to be built in Spain. A
longitudinal view, the structural model and the visualization model are presented
in Figure 9.
a) Longitudinal view
b) Finite element based structural model
Figure 9. Suspension bridge in Spain
c) Visualization model
Figure 9. Suspension bridge in Spain (cont.)
The bridge was subjected to an earthquake of 30 sec. of duration defined by
the vertical ground acceleration values of Figure 10 at both ends of the bridge.
Figure 10. Values of vertical ground acceleration
Two pictures of the deformed shape of the bridge during the earthquake
appear at Figure 11.
Figure 11. Deformed shape of bridge during earthquake
A computer animation showing the bridge deformation along the earthquake
was recorder in NTSC format.
5.2. Aeroelastic analysis of the Tacoma Narrows bridge
The second example corresponds to the Tacoma Narrows built in 1940. This
structure was a suspension bridge which colapsed just few months after its
completion. Figure 12 shows a view of the bridge and the digital model
produced by computer.
a) View of the bridge
b) Digital model
Figure 12. Tacoma Narrows bridge
For this bridge visualization of a set of six vibration modes and bridge
deformation under several wind speeds was produced in a virtual laboratory
environment. Afterwards, bridge deformation under the wind speed arising
flutter instability was carried out.
Figure 13 shows a view of the bridge just before collapse and a digital image
obtained in this research that is very similar to the real picture.
a) Real view
b) Digital picture
Figure 13. Deformation of Tacoma bridge
A computer animation presenting bridge deformation under wind flow of
25%, 75% and 100% of flutter wind speed was produced.
6. Conclusions
Several conclusions can be drawn from the research presented:
—Conventional visualization is inefficient as a representation tool of
dynamic properties of structures, or time history responses.
—An environment composed by realistic visualization models, advanced
structural analysis and high performance computers can lead to an approach
giving presentations similar to real experimental facilities.
—Virtual laboratories are very well suited to visualize dynamic behaviour of
civil engineering structures.
Acknowledgement
Thanks are due to Mr. Ángel Sánchez, a Civil Engineer and Research Assistant
on the School of Civil Engineering for this work in the design and visualization
of the suspension bridge presented in Figure 9.
References
[1] Ferrante, A.J. and alt.; Computer Graphics for Engineers and Architects,
Elsevier, 1991.
[2] Rogers, D.F. and Adams, J.A.; Mathematical Elements for Computer
Graphics, McGraw-Hill, 1976.
[3] Rogers, D.F.; Procedural Elements for Computer Graphics, McGraw-Hill,
1985.
[4] Gouraud, H.; “Computer Display of Curved Surfaces”, IEEE Trans, C-20,
pp. 623-628, 1971.
[5] Bui-Tuong, Phong; “Illumination for Computer Generated Images”,
CACM, vol. 18, pp. 311-317, 1975.
[6] Goral, C., Torrance, K.E. and Greenberg, D.P.; “Modelling the Interaction
of Light between Diffuse Surfaces”, Computer Graphics, 18(3), pp. 212222, Proceedings of SIGGRAPH’84.
[7] Watt, A. and Watt, M.; Advanced Animation and Rendering Techniques,
Theory and Practice, Addison-Wesley, 1992.
[8] Kay, T.L. and Kajiya, J.T.; “Ray Tracing Complex Scenes”, Computer
Graphics, 20(4), pp. 269-278, Proceedings of SIGGRAPH’86.
[9] Hernández, S. & Hernández, L.A.; “Advanced Visualization and Computer
Animation in Engineering and Architectural Design”, Proc. of ICCE’96
International Conference on Civil Engineering. Bahrain, April, 1996.
[10] Hernández, L.A. & Hernández, S.; “Application of Digital 3D Models on
Urban Planning and Highway Design”, Third International Conference on
Urban Transport and the Environment, Acquasparta (Italy), 1997, pp. 391402, L.J. Sucharov and G. Bidini (eds.), Comp. Mech. Pub. 1997.
[11] COSMOS/M Finite Element Analysis System, Version 1.75. Manuals:
User guide, Basic Fea System, Advanced Modules, Command Reference.
SRAC, 1995.
[12] Romera, L.E. & Hernández, S.; Análisis estático y dinámico de estructuras
con el programa COSMOS/M, Universidad de La Coruña, 1998.
[13] MAYA 1.5, User’s Manual. Alias/Wavefront, 1999.
[14] Bathe, K.-J.; Finite Element Procedures in Engineering Analysis. Prentice
Hall, 1982.
[15] Hughes, T.J.R.; The Finite Element Method, Linear Static and Dynamic
Finite Element Analysis. Prentice Hall, 1987.
[16] Chopra, A.K.; Dynamics of Structures. Theory and Applications to
Earthquake Engineering. Prentice-Hall, 1995.
[17] Simiu, E. & Scanlan, R.H.; Wind Effects on Structures, Fundamentals and
Applications to Design. John Wiley & Sons, 1996.
[18] Jones, N.P. & Scanlan, R.H.; “Advances (and challenges) in the prediction
of long-span bridge response to wind” in Bridge Aerodynamics,
Proceedings of the International Symposium on Advances in Bridge
Aerodynamics, Copenhagen, Denmark, May 10-13, 1998, pp. 59-85, A.
Larsen & S. Esdahl (eds.), A.A. Balkema, 1998.
[19] Katsuchi, H., Saeki, S., Miyata, T. and Sato, H.; “Analytical assessment in
wind-resistant design of long-span bridges in Japan” in Bridge
Aerodynamics, Proceedings of the International Symposium on Advances
in Bridge Aerodynamics, Copenhagen, Denmark, May 10-13, 1998, pp. 8798, A. Larsen & S. Esdahl (eds.), A.A. Balkema, 1998.
[20] Hernández, S. & Jurado, J.A.; “A Review of the Theories of Aerodynamic
Forces in Bridges”. Fourth World Congress on Computational Mechanics,
Buenos Aires, Argentina, June 1998.
[21] Hernández, S. & Jurado, J.A.; “Design of Ultra Long Span Bridges with
Aeroelastic Constraints”, Optimization in Industry II, June 1999, Banff,
Canada.