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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 : 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 : 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  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 , and translated to the analogous sections of the lattice on the visualization software . 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  Ferrante, A.J. and alt.; Computer Graphics for Engineers and Architects, Elsevier, 1991.  Rogers, D.F. and Adams, J.A.; Mathematical Elements for Computer Graphics, McGraw-Hill, 1976.  Rogers, D.F.; Procedural Elements for Computer Graphics, McGraw-Hill, 1985.  Gouraud, H.; “Computer Display of Curved Surfaces”, IEEE Trans, C-20, pp. 623-628, 1971.  Bui-Tuong, Phong; “Illumination for Computer Generated Images”, CACM, vol. 18, pp. 311-317, 1975.  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.  Watt, A. and Watt, M.; Advanced Animation and Rendering Techniques, Theory and Practice, Addison-Wesley, 1992.  Kay, T.L. and Kajiya, J.T.; “Ray Tracing Complex Scenes”, Computer Graphics, 20(4), pp. 269-278, Proceedings of SIGGRAPH’86.  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.  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.  COSMOS/M Finite Element Analysis System, Version 1.75. Manuals: User guide, Basic Fea System, Advanced Modules, Command Reference. SRAC, 1995.  Romera, L.E. & Hernández, S.; Análisis estático y dinámico de estructuras con el programa COSMOS/M, Universidad de La Coruña, 1998.  MAYA 1.5, User’s Manual. Alias/Wavefront, 1999.  Bathe, K.-J.; Finite Element Procedures in Engineering Analysis. Prentice Hall, 1982.  Hughes, T.J.R.; The Finite Element Method, Linear Static and Dynamic Finite Element Analysis. Prentice Hall, 1987.  Chopra, A.K.; Dynamics of Structures. Theory and Applications to Earthquake Engineering. Prentice-Hall, 1995.  Simiu, E. & Scanlan, R.H.; Wind Effects on Structures, Fundamentals and Applications to Design. John Wiley & Sons, 1996.  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.  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.  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.  Hernández, S. & Jurado, J.A.; “Design of Ultra Long Span Bridges with Aeroelastic Constraints”, Optimization in Industry II, June 1999, Banff, Canada.