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For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. Emergent Modelling for Structural Design L. Jankovic*, S. Jankovic**, A. H. C. Chan**, G. H. Little** *School of Computer Science **School of Civil Engineering University of Birmingham Edgbaston, Birmingham B15 2TT, United Kingdom 1. ABSTRACT Conventional structural analysis and design methods typically use a top-down approach to modelling, where there is a global algorithm that controls the solution process. Consequently the real time interaction with the model could become impractical due to its computational intensity. This paper describes an alternative approach to structural analysis, which draws its inspiration in behavioural models of animal movement. These models achieve a considerably complex behaviour based on a relatively simple bottom-up modelling approach. The application of behavioural modelling methods to structural analysis is described, and advantages and limitations of this approach are discussed. 2. INTRODUCTION This paper reports on research into optimisation of efficiency of computational processes in structural analysis. It first explains why the optimisation is needed and gives an overview of the current methods. It then focuses on an alternative approach to structural analysis using principles of Complexity, and in particular the principles of behavioural modelling of animal movement, to achieve optimisation. The development of these alternative models is described, and the results of operation and validation are reported on. 2.1 Current solution methods Conventional analysis and design of structures is based on describing the structure as a system of algebraic equations, and solving the system simultaneously by iteration. Although the definition of the equations is based on Newton's laws of motion, the solution method usually requires a simplification of the system of equations in order to be able to calculate the solution. Furthermore, the solution process is typically based on matrix manipulation and inversion. Each structural component is defined with a stiffness matrix that is obtained by a Finite Element Method to calculate the solution (Fig. 1a). The complexity of the matrix increases proportionally with the number of components (Fig. 1b, Fig1c). It can be argued that the matrix calculus is an artificial process that is somewhat removed from the underlying physical system that it describes. 2.2 User needs The motivation from this work comes from discussions with practising engineers, according to whom conventional structural analysis methods do not fully satisfy user needs. These methods are based on solving systems of simultaneous differential equations that are separate from the visualisation of the structure. Consequently, they do not allow for a time efficient dynamic review of the design in progress, and for an easy assessment of implications of late design changes. Being an iterative process, the analysis and design are time consuming for engineers, and the results are difficult for clients to visualise. For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. a) Structural component b) Simple structure c) Complex structure Fig. 1 Current solution methods 2.3 An alternative approach It was therefore decided to look for an alternative, more efficient approach to analysis that would better satisfy the user needs. The new approach had to integrate analysis and visualisation in the real time, and to rely on a much more efficient method for analysis of complex behaviour that will avoid the use of a globally controlled solution method and a system of simultaneous algebraic equations. It appeared that virtual reality modelling in VRML was the most suitable and inexpensive medium for creation of analogue models of structures. This would allow for development of simple component models and an easy implementation of Newton's laws of motion on a component level. The question was then how to obtain an efficient system model from the simple component models. The inspiration was found in the field of complexity, and in particular, in the behavioural modelling of animal movement. 2.4 Complexity According to Langton (1992), order and chaos are two opposite states of systems consisting of a number of components. These systems are sensitive to initial conditions, and can consequently develop different behaviour. For instance, a chaotic pendulum, shown in Fig. 2, will behave totally differently, depending on how it started, and Newton's laws alone are not sufficient to predict its behaviour, as exact initial conditions and repeatable arithmetic is required. Fig. 2 Chaotic pendulum. Newton's Laws alone are not sufficient to predict its behaviour The transition between the order and the chaos is defined as the "edge of chaos" or "complexity". Systems at the edge of chaos exhibit complex behaviour and are called complex systems. These systems have a tendency to develop a behaviour that is unexpected from the rules that define the For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. system components. Through this unexpected behaviour a complex system appears to self- organise. This self-organising behaviour is called emergent behaviour. There are many examples of systems with emergent behaviour: crystal formations, molecules, flocks of birds, multi-cellular organisms, Darwinian natural selection, and others. None of these examples have been modelled successfully with deterministic (top-down) models, but have been modelled very successfully with emergent, bottom-up models. 2. 5 Behavioural models Behavioural models of animal movement are probably the best known models of complex systems. The first behavioural model was created by Reynolds (1987), who developed an emergent model of a flock of artificial birds called "boids". He 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. Tu and Terzopoulos (1994), who looked into the processes for creation of behavioural models, further developed this approach. According to Reynolds (1987), there are only three rules for each boid: • Separation: steer to avoid crowding local flockmates • Alignment: steer towards the average heading of local flockmates • Cohesion: steer to move toward the average position of local flockmates Fig. 3 An emergent model of a flock of boids (left) and school of fish (right) developed in VRML97 and JavaScript The complexity of system models achieved with this approach is considerably disproportional to the simplicity of the component models (Fig. 3). This was the main motivation to attempt to apply similar principles to structural analysis. 2.6 Transfer of behavioural modelling principles to structures In order to facilitate the transfer of behavioural modelling principles to structures, the essence of behavioural models, and the essence of structures had to be identified. From the analysis of existing behavioural models it was found that their essence is in: 1. Multiple components 2. Simple rules for individual components 3. Local interaction between the components 4. Global model emerges from the local interaction without explicit programming For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. Similarly, the essence of structures can be described as follows: 1. Multiple components 2. Simple rules for individual components: Newton's laws of motion 3. Local interaction between the components Thus the first three aspects of behavioural models are also present in structures. The question is whether the fourth aspect would also occur, i.e. whether the global model of a structure would emerge from the local interaction of the components without explicit programming. The answer to this question could only be given by experimental research, which involved development, testing, and validation of models of structures created on the basis of transfer of the essence of the behavioural modelling principles. This is reported in the remainder of the paper. 3. DEVELOPMENT AND TESTING OF EMERGENT MODELS OF STRUCTURES 3.1 Development of emergent models of trusses 3.1.1 Model Description A model of a simple triangle truss was developed using VRML97 and JavaScript (Fig. 4), and consisting of joints and bars as main components. Following the principles of structural dynamics, the assumption was made that the mass of the truss was concentrated only in the joints. The joints and the bars were modelled as separate, independent components, each considered as an object in terminology of the object-oriented programming. The objects were connected through inputs and Fig. 4 A bottom-up model of a triangle truss in VRML and JavaScript #Component prototype PROTO Component [ #PROTOtype declaration eventIn SFSomething protoEventIn eventOut SFSomething protoEventOut ] { #PROTOtype definition DEF protoNode someNode { DEF someSubNode someOtherNode {} } #The script inside the prototype is mapped #to PROTOtype inputs, outputs, and internal #nodes using IS and USE Script { eventIn SFSomething scriptEventIn IS protoEventIn eventOut SFSomethingscriptEventOut IS protoEventOut field SFNode scriptNode USE protoNode url "javascript: scriptNode.someSubNode = someValue; " } } Fig. 5 VRML and JavaScript pseudo code for component model architecture For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. outputs only, in a similar way in which they are connected in reality. The bars were modelled as weightless springs. A viscous damping mechanism was adopted, and the damping force modelled to act in the opposite direction to the joint's velocity. Each component was defined on the basis of the Newton's laws of motion. 3.1.2 Component Model Architecture The component architecture involved the use of PROTO(types) and Scripts (Fig. 5). The component PROTO was responsible for dealing with external components and the Script inside the PROTO was responsible for implementation of simple rules that determined the component behaviour. Fig. 6 System Model Architecture The parameters and variables from the PROTO interface declaration were mapped to the Script parameters and variables. This enabled the prototype inputs to access the Script inside the PROTO directly. All components of the emergent model were created by a process of instantiation (creation of working copies) of the same PROTO. #Environment Transform{ #instantiation of Components children [ DEF Component1 Component{ #instantiation parameters here } DEF Component2 Component{ #instantiation parameters here } ] DEF Starter TimeSensor {} #Routing connects system components #and system starter ROUTE Starter.time TO Component1.someEventIn ROUTE Component1.someEventOut TO Component2.someEventIn ........... ROUTE ComponentN.someEventOut TO Component1.someEventIn } Fig. 7 VRML and JavaScript pseudo code for system model architecture To ensure the compatibility of inputs and outputs so that outputs of one instance of the PROTO could be connected to inputs of another instance of the same PROTO, the PROTO's inputs and outputs were chosen carefully to be of matching data types. For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. The Script inside the PROTO was mapped to its geometric properties in order to effect the visual representation of behaviour of individual instances. This created a generic component model suitable for interaction with other components. 3.1.3 System Model Architecture It was found that complex interactions between system components are best handled using a separate "container" PROTO(type) named Environment, capable of dealing with the influences between a large number of pairs of components (Fig. 6, Fig. 7). 3.2 Testing of emergent models of trusses In order to test the generality of the modelling method, a more complex structure was modelled using the same approach. Figure 8 shows an example of a two-dimensional truss, before (a), and after (b) application of load. a) before application of load b) after application of load Fig. 8 Bottom-up model of a two dimensional truss It was found that the system behaved realistically, and returned to the original state after being disturbed from the equilibrium. The co-ordinates on the side of the joints were changing as the system went from the initial state, to the maximum displacement state, and back to the equilibrium. The user was able to interact with this model in the real time, and examine its behaviour. 3.2 Emergent models of beams and portal frames Modelling of beams and portal frames that are made out of continuous material, required a different approach, in comparison with the approach used for modelling of trusses. Unlike the truss models, in which all of the individual components were manipulated by the environment, the beam models had to contain this capability within the component itself. Therefore, the model had to be completely redesigned, in order to satisfy this requirement. The very first exploratory model behaved as a lump of jelly, and was named "jelly-box". This model was subsequently scaled up and extended into a "jelly-beam" and "jelly-portal frame", all of which are described below. For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. for (j=0;j<NumberOfPoints;j++) { for (k=0;k<NumberOfPoints;k++) { if(j != k) force[j] +=displacement[j]*elasticity - velocity[j]*damping; acceleration[j] = force[j] / pointMass; velocity[j] = acceleration[j] * timestep; position[j] += velocity[j] * timestep; } } Fig. 9 Pseudo code of application of Newton's Laws to interaction of jelly-box corners. Jelly-box Jelly-box model 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 on the basis of Newton's laws, through elastic forces and friction/damping forces (Fig. 9). This gave rise to an emergent model of an elastic box, which enabled the user interaction in the real time (Fig 10). Fig. 10 "Jelly-box" before, during, and after the application of load Jelly-beam Scaling up of the jelly-box model, by adding multiple segments of the elementary component, created a jelly beam model. The code that runs the jelly-beam model is essentially the same as in Fig. 9, the only difference being the number of points that describe the shape of the beam. The operation of the model, with load applied interactively by clicking and dragging one of the corners is shown in Fig. 11. Fig. 11 User interaction with a Jelly-beam model For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. Jelly-portal frame Further scaling-up of the jelly-beam model, by adding more points and introducing corner components, created the jelly-portal frame model. The operation of this model, loaded with a constant prescribed force, is shown in Fig. 12. This model, like the previous two, was also capable of real time user interaction. Fig. 12 User interaction with a Jelly-portal frame model All of the three models described in this section: jelly-box, jelly-beam, and jelly-portal frame, were created using the same extendable code. Consequently, any new points added to create new shapes are automatically assigned physical properties. The resultant interaction between the points self-organises the model and gives rise to emergent model behaviour. 4. TESTING OF SPECIAL CASES The emergent models reported so far were based on a purposely developed code. This section examines applicability of the emergent modelling method to cases for which the code was not specifically developed, such as a shallow two-bar truss with snap-through behaviour. The snap-through behaviour is one of the most difficult problems to model in non-linear structural analysis, although it is possible to solve it using incremental iterative solution in combination with the Finite Element Method. This was the reason why the snap-through behaviour was chosen as one of the test cases for the bottom-up model. a) In static equilibrium position b) In alternative equilibrium position after applying load Fig. 13 Shallow two-bar truss with snap-through behaviour For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. Fig. 14 A bottom-up virtual reality model of a shallow two-bar truss with snap- through behaviour The system shown in Fig.13 is a shallow two-bar truss with two hinges. The system has three possible equilibrium states under the load, but only two of these are stable and they are shown in Fig. 13a) and Fig. 13b). After applying downward load, system shown in Fig. 13a) returns to the original equilibrium state or to the alternative stable equilibrium position shown in Fig. 13b). If the system under the load reaches a critical state, it will soon settle in an alternative stable equilibrium (Fig. 13b), after dynamic snap has occurred. There are always two dynamic snaps, from one equilibrium state to another. It is also possible to achieve the dynamic snap by applying upward load on the system shown in Fig. 13a, or by applying downward load on the system shown in Fig. 13b. This example is at the edge of chaos, and a slight change of initial conditions at some initial state may result in the system resting in an alternative equilibrium position. A virtual reality model of a shallow two-bar truss was developed (Jankovic et al., 2000) using the approach described earlier in the paper (Fig. 14). The model consisted of joints and bars as main components. The joints and bars were modelled as independent components, each being an "object" in terminology of object-oriented programming. The objects were connected through inputs and outputs only, in a similar way to which they are connected in reality. As originally hoped, the interaction between the model components did indeed give rise to emergent behaviour. The resultant model was not governed by any conventional solution method, except the basic Newton's laws, and neither the Finite Element Method or the incremental iterative solution were used. Effectively, an analogue model of the real structure was created in virtual reality and enabled the user to interact with it in the real time. 5. EVALUATION AND VALIDATION 5.1 Satisfaction of user needs The emergent models of structures reported in this paper appear to satisfy most of the user needs that the conventional methods did not. The visualisation and calculation have been combined together, and the consequent interactive behaviour of the models in the real time can enable the assessment of late design changes and dynamic review of the design in progress. The models also enable easy visualisation of results by clients, and a possibility to reduce a number of iterations of the design process. For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. 5.2 Validation of accuracy of the model However, an important question that needs to be answered before a real life application of emergent models of structures is how accurate are the models. The validation process is still in progress, and this section reports on the results of validation of the beam model to date. The validation was carried out with the objective to determine similarities and differences of results of operation of the emergent model, in comparison with established conventional methods and theory. Fig. 15 Reference case for comparison obtained from LUSAS The conventional method chosen for comparison was LUSAS, a software package running the standard Finite Element Method. The LUSAS model of the beam was created using 4 main horizontal segments, with overall dimensions of the beam of 10 m length by 1 m height (Fig. 15). This was compared with the jelly-beam model, which had the same dimensions, and a capability to operate in automatic mode in response to a fixed force, giving the resultant displacement (Fig. 16). The stiffness of material was calibrated to achieve the convergence of results. Fig. 16 Jelly-beam model responding to a fixed force and giving the resultant displacement The comparison of results of operation of jelly-beam model (EVROM - emergent virtual reality object model), LUSAS model of the beam, and a theoretical beam model is summarised in Table For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. 1. Although there appears to be a considerable similarity between the three models suggesting that the jelly-beam model is accurate, this is not quite the case with all points along the length of the beam. However, early indications from results of a modified jelly-beam model that applies different stiffness values between diagonal and non-diagonal points of box-components suggest that the fundamentals of the model are correct, and that internal model parameters need to be further calibrated in order to achieve absolute agreement with conventional methods that have been accepted by engineers. Table 1 Comparison of displacements in metres of three different beam models F = 10 N F = 50 N F = 100 N Beam theory 0.080 0.400 0.800 LUSAS 0.085 0.427 0.854 EVROM 0.083 0.411 0.822 5.3 What has been achieved It is believed that the work described in the paper has achieved the following: • Integration of physics and geometry - analogue models of structures • Usability - instantiation and measurement, instead of calculation • Accuracy - comparison with conventional methods reasonably consistent • Robustness - the models spontaneously self organise The latter point is particularly significant for modelling of structures that were not considered during the initial development of the method. For instance, the finding that the bottom-up model was capable of simulating the shallow two-bar truss with snap-through behaviour is believed to be significant. The conventional analysis of the same problem involves the Finite Element Method and the incremental iterative solution, and is a difficult problem to solve. The bottom-up model was able to solve this problem dynamically, allowing the user interaction in the real time, and without explicit programming. Another significant capability of the bottom-up model is believed to be the ability to simulate both static and dynamic behaviour of structures. 5.4 Problems and limitations One of the most significant problems of the emergent modelling method described here is the use of discrete time steps. As found by Jankovic and Dumpleton (2000), discrete time steps can cause a mismatch between the required time step and the frame rate that can be achieved on a particular computer. Consequently, extreme forces applied to the model can cause incorrect movement of the components, which can cause the computer code to crash. This can be prevented by reducing the time step, at the expense of speed of performance of the model, and also by careful choice of other model parameters. A limitation of this method is the need for calibration of model parameters to achieve convergence of results with conventional methods. For instance, the stiffness of material had to be varied in several steps until the jelly-beam exhibited similar displacements as LUSAS model and theoretical beam, in response to a pre-determined load. Furthermore, it was found that different stiffness values need to be applied to diagonal and non-diagonal interaction of points within an elementary box-component of the jelly-beam. However, this is hardly surprising, considering that initially the model parameters were chosen arbitrarily, and therefore the limitation of the method is the requirement for calibration. For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. 6. COMPARISON WITH OTHER METHODS This section gives an overview of a number of commonly used numerical methods, and makes a comparison between these and the emergent modelling method reported in this paper - Emergent Virtual Reality Object Method (EVROM). The methods compared are: • Implicit Finite Element Method (IFEM) • Boundary Element or Boundary Integral Method (BEM) • Explicit Finite Element Method (EFEM) • Discrete Element or Distinct Element Method (DEM) 6.1 Implicit Finite Element Method (IFEM) This is the most commonly available method. The key concept of the method is the subdivision of the structural domain into small individual members or elements. The element stiffness matrix, the element mass matrix (for dynamic analysis) and the element geometric matrix (for buckling analysis) are then formed by the weighted residual approach. Overall equilibrium is satisfied in an averaged sense. The stress-strain relationship is applied at the gauss points while the compatibility equation is satisfied all through the elements and may be violated across the element boundary. The elements are then assembled to form the global matrices and the Gauss elimination method is then commonly employed for the solution of the overall equations. For multiple load cases, the decomposed matrix can be stored and only resolution is required. Visualisation is normally separated from the computational phase. But modern finite element packages usually provide very comprehensive pre-processing and post-processing facilities. Some of the CAD packages may come with a FE program that includes basic features but minimum coverage. The accuracy of the method depends on the order of polynomial used for the elements and the mesh density used. For most structural problems, as the consistency condition is usually satisfied, stability and convergence is guaranteed because of the elliptical nature of the governing equation for linear analysis. In simple terms, consistency is the ability of the element to model the minimum behaviour which normally includes rigid body motion and constant strain conditions. However, in some element implementations especially for shell elements, reduced integration may be used. In these cases, stability and/or consistency may not be guaranteed and methods such as patch test should be used to establish the stability and consistency of the element. The coverage of the computer implementation can be very wide including all types of geometric and material non-linearity and these non-linearities are normally handled using iterative methods. However being a method based on the continuum assumption, it is not very efficient in the case of geometrical discontinuity. This can be handled by pre-determined contact planes and by the adoption of interaction rules similar to the DEM. Furthermore, as global assembly is needed, late design changes would require a complete re- analysis which may or may not require extensive user intervention depending the implementation. Many commercial codes are available such as SAFE (Ove Arup), LUSAS (FEA Ltd), ABAQUS, ANSYS, NASTRAN and COSMOS. In most cases, linear elastic analysis or simple elasto-plastic using classical material models are performed. It is estimated that linear elastic behaviour is used for 98% of cases in structural and mechanical analyses. For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. 6.2 Boundary Element Method (BEM) Not many commercial packages are available using this method for structural analysis though it is commonly used in some geotechnical and acoustic wave problems such as tunnelling and electromagnetic wave propagation when the domain extends to infinity and the material property remains constant. The key advantage of the method lies in its ability in reducing the dimensionality of the problem because only the boundary of the elements is discretised. The behaviour of the interior of the domain is satisfied a priori by a proper (sometimes this could be difficult to find) choice of fundamental (Green’s) function. As in the IFEM, element matrices are formed and assembled. But unlike IFEM, the matrix is normally densely populated but this is rarely a major problem due to the reduced number of degree-of-freedoms. The governing equations are satisfied in the whole interior of the element and the equilibrium equation is satisfied at nodes on the boundary and compatibility may be violated across the element boundary. The accuracy of the method is high as analytical solution is used as its bases. Again if the consistency and stability are satisfied which normally are, convergence is guaranteed. The main disadvantage of the method is its coverage. As fundamental solution to the governing equation is required, the method is usually limited to linear problems. Limited non-linear behaviour can be handled via the assumption of reversible plasticity and linear assumption within one analysing step. Iterative method can also be used within a non-linear step if required to achieve convergence. As with the IFEM, the BEM, being based on the continuum assumption, is also not very efficient in the case of geometric discontinuity. A global re-analysis is also required for late design change. 6.3 Explicit Finite Element Method (EFEM) The basic concepts of this method are the same as IFEM. The main difference lies with the solution method and this affects the range of applicability of the method. Global assemblage may or may not be performed but global connectivity is still registered. In most cases, a diagonal mass matrix is formed. The method is usually used in dynamic problems as no matrix decomposition or resolution is required. For static problems, dynamic relaxation type method can be used using real or artificial damping and mass matrix. As the method is explicit, a critical time step exists and the analysis has to progress using a time step less than or equal to it. As the method is in essence a step-by- step integration method, no iteration is required for non-linearity but eigenvalue type analyses such as free vibration and buckling analyses are not readily available. Unlike IFEM, as global assembly is not required, late design change could be incorporated in a relatively straightforward manner. The most commonly used commercially available EFEM code is DYNA3D from the Lawrence Livermore National Laboratory in USA and ABAQUS-Explicit. 6.4 Discrete Element or Distinct Element Method (DEM) This method has not been commonly applied to structural design. Some research applications have been used in concrete breakage and masonry problem. Instead of the subdivision of the domain using continuum assumption, the domain is divided into individual particles. Newton’s For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. laws and contact interaction laws are used to govern the individual and interaction behaviour of the particles. No global assembly nor a list of global connectivity is required. Visualisation can be made during each step of the method. The solution strategy is similar to that of EFEM. The accuracy of the method can sometimes be difficult to determine but if individual particles satisfy the consistency condition, convergence can usually be guaranteed. But as the behaviour is inherently non-linear and “emergent”, unique solution is not theoretical guaranteed and indeed not necessary. The coverage of the computer implementation can be very wide including all types of geometric and material non-linearity and again no iterative is required. Unlike the continuum methods, the method is very efficient in handling discontinuity and it is inherent discontinuous. Therefore late design change can be incorporated at ease. To the knowledge of the authors, only one commercial code is available which is UDEC and 3DEC from Ithaca Ltd and the method is commonly applied to geotechnical, chemical engineering and food processing problems. 6.5 Emergent Virtual Reality Object Method (EVROM) Unlike the DEM, the interaction between objects can be conducted via contact interaction or direct connection such as joints. Furthermore, there is no restriction on the choice of the basic objects. They can be objects with simple behaviour like the particles in DEM, but it can also be a bar element, a beam element, a plane stress element, a plate element or a shell element. Depending on whether the basic objects satisfy the stability and consistency condition or not, convergence can or cannot be guaranteed. The method is capable of tracing different paths if a bifurcation is to occur during an analysis. Depending on the choice of the basic objects used, the accuracy of the method can be made at least equal to the method used in the objects’ formulation. Dynamic relaxation can also be used for static problems. There is a complete integration of the analysis and visualisation therefore leading to more “intuitive” interaction between the user and the computer implementation. No commercial code is available to-date. However with the advance in computer hardware and virtual reality software technology, the incorporation of physical behaviour into these VR objects thus giving the global behaviour from these emergent behaviour seems to be the most efficient and cost-effective way forward for interactive structural design. 7. CONCLUSIONS The work described in this paper was inspired by the need of the structural design professionals for tools that would better satisfy the needs of engineers and clients. An ideal tool is expected to integrate the solution method and visualisation, to create a capability for dynamic review of the design in progress, and make an easy assessment of late design changes possible. Inspired by very efficient emergent models in the field of complexity, and in particular in the field of behavioural modelling of animal movement, where a considerable complexity of the system model is achieved using very simple component models, the authors conducted research into transferring these methods to structural analysis. For presentation at International Conference on Complexity and Complex Systems in Industry, University of Warwick, 19th - 20th September 2000. It was found that behavioural modelling principles are transferable to structures, and emergent models of trusses, beams, and portal frames were developed and tested. The models were developed using object oriented languages VRML and JavaScript that enabled integration of visualisation and the solution method in virtual reality. The models were capable of user interaction in the real time, and have effectively replaced structural calculations with instantiation of objects/components into an analogue virtual reality model, and measurement of forces and other parameters from the model. The validation of the new method was carried out by comparing the performance of an emergent model of a beam with an equivalent model in a standard Finite Element Method package, and with a theoretical model of the beam. A good convergence of results was found between the three methods, after the stiffness of material in the emergent model was calibrated. The work on a further calibration of the model, making a provision for several different stiffness values inside the material, showed that better agreement of displacements along the length of the beam would be achieved. More research, development and experimental validation is needed before this method becomes a viable alternative to the current structural analysis methods. However, it is possible to conclude that this method has a potential to satisfy the needs of engineers and clients like no other currently available method, because of its computational simplicity, integration of calculations and visualisation, and real time user interaction. This is believed to be best summarised in the words of one the project's industrial partners: "To set up a 3D model of a design, poke it, pull it, see what happens, change bits of it, would be a complete change in our method." It is believed that the main reason for advantages of this method is the application of principles of complexity, and in particular the application of behavioural modelling principles to structures. 8. REFERENCES 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. & J. Dumpleton (2000) Emergent modelling of complex systems in VRML. In Proceedings of Eurographics UK 2000, Swansea 4 -6 April 2000. Langton, C. G. (1992) Life at the edge of chaos. Proceedings of Artificial Life II. Addison- Wesley. Reynolds, C. W. (1987) Flocks, Herds, and Schools: A Distributed Behavioural Model. Computer Graphics. Vol. 21, No. 4. Tu, X and D. Terzopoulos (1994) "Artificial Fishes: Physics, Locomotion, Perception, Behavior", ACM Computer Graphics, Proceedings of SIGGRAPH'94. 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, R O'Rourke & Son Ltd, and InteSys Ltd.

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