BOTTOM-UP MODELLING OF A CANTILEVER BEAM AND A PORTAL FRAME IN VIRTUAL REALITY (JELLY-SPINE MODEL)
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BOTTOM-UP MODELLING OF A CANTILEVER BEAM
AND A PORTAL FRAME IN VIRTUAL REALITY
(JELLY-SPINE MODEL)
S. Jankovic*, L. Jankovic**, A. H. C. Chan *, G. H. Little*
* School of Civil Engineering, University of Birmingham, Edgbaston, Birmingham
B15 2TT, United Kingdom
**InteSys Ltd, Birmingham Research Park, Vincent Drive, Edgbaston, Birmingham
B15 2SQ, United Kingdom
Tel: +44 (0)121 414 7028
e-mail: jankovic@civ-fs3.bham.ac.uk
ABSTRACT
The paper reports on creation of analogue models of rigid body in virtual reality using an
emergent, or bottom-up approach, in which the solution process is controlled by local
interaction of the structural components. Following the principles of this approach, the
Jelly-spine model was developed on the basis of interaction of rigid segments. The model
represents animation of entire process of structural behaviour from the original position
before application of the load until the final equilibrium state, after application of the
concentrated load. The Jelly-spine model was tested in the case of cantilever beam and
portal frame. The deflections of the both systems were compared with the results from
standard Finite Element Method software LUSAS. Results of this alternative approach to
structural analysis show that is possible to have analogue virtual reality models of the
beam and the portal frame, from which values of deflections could be obtained.
KEYWORDS
Bottom-up Modelling, Structural analysis, Virtual Reality, VRML
INTRODUCTION
The motivation for this work comes from discussions with practising engineers,
according to whom conventional structural analysis methods do not fully satisfy user
needs. Conventional analysis of structures is typically based on systems of algebraicequations that describe the entire modelled system, which is then solved by matrix calculus. This is a typical top-down approach, separate from the visualisation of the structural behaviour, and because of which visualisation is considered to be a problem in structural design. Modern finite element packages have visualisation facilities based on comparison of the undeformed and the deformed shape of the structure. The user always has to wait between two images for the calculation process to take place, and cannot visualize all structural behaviour dynamically. There are a lot of attempts to integrate visualisation and structural analysis software using high power hardware equipment (Rangaraju, 2001). This paper describes alternative (bottom-up approach) to structural analysis, which aims to integrate analysis and visualisation and create simulation of entire process of structural behaviour during the application of the load, using low cost virtual reality and inexpensive Pentium PCs. It was proved that very complex systems such as formations of birds, animals, or fish could be modelled by creating simple models of system components and making them interact (Reynolds, 1997). Inspired by more efficient bottom-up models in other disciplines the authors developed various models of trusses using the same approach and object-oriented languages VRML97 and JavaScript (Jankovic, 2000). This paper presents one of the attempts to model beams and portal frames. An early version of beam and portal frame models made out of continuous material was based on a box looking shape that had a point mass in each corner. Each corner was then made to interact with each other corner. The resultant interaction between the points created behaviour similar to lump of jelly, and this early model was named jelly-box. The model was extended to jelly-beam and jelly-portal frame by adding multiple segments. This approach was effectively the application of a truss analogy, and was not entirely satisfactory in terms of accuracy. Nevertheless, this attempt was a significant step in the field of geometry of bended rigid body in virtual reality. The next section will explain recent work on modelling the cantilever beam and portal frame, named the "Jelly-spine" model. DEVELOPMENT OF BOTTOM-UP MODELS OF CANTILEVER BEAM AND PORTAL FRAME (JELLY- SPINE MODEL) Following the principles of bottom-up approach, the Jelly Spine model has been developed as an assemblage of rigid segments connected to each other with a “box” which contains a bending stiffness and shear stiffness but has no mass. This is a dynamic model designed on the basis of interaction of rigid segments. Each segment is defined by displacement of centroid vi and rotation θi as shown in Fig. 1. The main concept for this simulation is first to start to calculate, for each segment, moments (Mi1 , Mi2 ), vertical forces (Fi1 , Fi2), acceleration and angular acceleration. The velocity and the angular velocity of each segment are calculated from acceleration and angular acceleration respectively in order to update the new position of each segment. This resulted with continuous animation, which contains every sequence of the structural behaviour of the
system during the application of the load. This process is repeated until the structure
reaches dynamic equilibrium state. The convergence to dynamic equilibrium state is
speeded up by the use of “kinetic damping”. The model has been developed using
programming languages VRML and JavaScript. Jelly-spine model contains Young’s
modulus for steel in order to simulate behaviour of structures that are made of real
material used in construction.
vi-1 Mi1
θi-1 vi
Fi1 θi Mi2 vi+1
Fi2 θi+1
Fig. 1 A segment “ i” of VR beam model with two neighbours segments connected by
boxes which contain a bending stiffness and a shear stiffness
RESULTS
On the basis of interaction of rigid segments, models of cantilever beam and portal frame
have been developed. Both models represent continuous simulation of the entire process
of structural behaviour during the application of load, from the original equilibrium state,
until final position of the structure. After application of concentrated load both systems
achieve dynamic equilibrium resulting from the interaction of segments. The deflection
of both systems in final equilibrium state was compared with LUSAS (FEA Ltd, 1999)
and results were almost identical. Figures of Jelly-spine models in this section present
images of cantilever beam and portal frame in final equilibrium state with displayed
deflections of discrete points. Other figures refer to undeformed and deformed images
from LUSAS, together with results of deflection.Simulation of structural behaviour of cantilever beam under concentrated load Fig. 2 shows cantilever beam in equilibrium state after application of the concentrated load of F = 5000 N at the end of the beam. Results of deflection of the cantilever beam obtained from LUSAS are shown in Fig. 3. Fig. 2 Jelly-spine model of cantilever beam with 10 segments under concentrated load of F = 5000 N at the end of the beam Fig. 3 Results of deflection of the cantilever beam obtained from LUSAS for the model shown in Fig. 2 The behaviour of Jelly-spine model of cantilever beam is realistic and similar to structural behaviour of the system in reality. The comparison between results shown in Fig. 2 and Fig. 3 is satisfactory in terms of accuracy.
Simulation of structural behaviour of portal frame under concentrated load at the top beam A portal frame has been developed on the same basis as the previous model of cantilever beam. Each element (two columns and top beam) has 10 segments. After application of concentrated load at the top beam, the system converges towards equilibrium with exact solution and shape of deflection. The speed of the execution is just a bit slower in comparison with the previous model of cantilever, due to a number of continuously displayed co-ordinates. The equilibrium state of Jelly-Spine model of the portal frame after application of concentrated load of F = 100000 N at the middle of the top beam is shown in Fig. 4. The numbers displayed next to the top beam in Fig. 4 are deflections in vertical, y – direction. Deflection in horizontal, x – direction of columns is displayed next to columns in Fig. 4. Results for vertical deflections of the top beam obtained from LUSAS are shown in Fig. 5. The LUSAS results for deflection of the columns in horizontal, x –direction, are shown in Fig. 6. Fig. 4 Jelly-spine model of portal frame in final equilibrium state after application of the vertical concentrated load at the top beam of F = 100000 N
Fig. 5 Vertical displacement of the top beam of the portal frame under vertical concentrated load at the top beam of F = 100000 N obtained from LUSAS The vertical displacements of columns in Jelly-spine model of portal frame are neglected in order to simplify the calculation process. The same assumption was not made in LUSAS model of portal frame. Like in the previous case of cantilever beam, the simulation that model of Jelly-spine of portal frame presents is realistic and similar to structural behaviour of the system in reality. The comparison between results shown in Fig. 4, and Fig. 5 and Fig. 6 is satisfactory in terms of accuracy.
Fig. 6 Horizontal displacement of the columns of the portal frame under vertical concentrated load at the top beam of F = 100000 N obtained from LUSAS CONCLUSIONS Conventional analysis of structures typically uses a top-down approach to modelling, where there is a global algorithm that controls the solution process. Being a system rather than a component based, this approach does not allow for an easy visualisation of the dynamic behaviour of the components and the entire system. The authors therefore believe that there is a need for better simulation and analysis tools for structural engineers to achieve better understanding of structural behaviour. Encouraged by development of bottom-up models of trusses, the authors developed dynamic models of cantilever beam and portal frame based on the interaction of rigid segments. These models achieved continuous animation of the entire dynamic process of structural behaviour during the application of the load, in low cost virtual reality. It therefore appears that integration of calculation and visualisation has been made possible using this approach. The deflection
of both systems in final equilibrium state was compared with LUSAS and results were almost identical. The results of this alternative (bottom-up) approach to structural analysis show that is possible to have analogue virtual reality models of cantilever beam and portal frame, from which displacements of structures could be obtained. The models have been developed using VRML and JavaScript programming languages, and inexpensive Pentium PCs. Future work will involve the creation of more complex structures. REFERENCES FEA Ltd (1999). LUSAS Examples. Version 13.2-0. Jankovic, S. et al. (2000). Bottom-up Virtual Reality Model of a Shallow Two-Bar Truss with Snap-Through Behaviour. In Proceedings of ACME2000, London 16-19 April 2000. Jankovic, L. et al. (2000) Structural Simulation Models that Build Themselves. International Journal of Simulation: Systems, Science & Technology. Vol. 1, No. 1, Dec. 2000. Jankovic, L et al. (2000) Can Bottom-Up Modelling In Virtual Reality Replace Conventional Structural Analysis Methods? In Proceedings of Construction Applications Of Virtual Reality, 4-5 September 2000, University of Teesside. Reynolds, C. W. (1987) Flocks, Herds, and Schools: A Distributed Behavioural Model. Computer Graphics. Vol.21, No.4. Rangaraju, N. and Terk, M. (2001) Framework for Immersive Visualization of Building Analysis Data. In Proceedings of Fifth International Conference on Information Visualisation, London, 25-27 July 2001. ACKNOWLEDGEMENTS This research is collaboratively funded by the UK EPSRC grant No. GR/M75273 and by the following industrial partners: WS Atkins Consultants Ltd, Oscar Faber Group Ltd, Maunsell Ltd, Halcrow Group Ltd, Mott MacDonald Ltd, Hyder Consulting Ltd, Ove Arup and Partners, Kvaerner Technology Ltd, O'Rourke & Son Ltd, and InteSys Ltd. Their support is gratefully acknowledged.
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