15 Generative Art Conference GA2012,AN ALTERNATIVE APPROACH TO STRUCTURAL. OPTIMISATION IN GENERATIVE DESIGN,Yekta Ipek BArch Hons BEng Hons. Architectural Design Computing Graduate Programme Istanbul Technical. University Istanbul Turkey,www laborthographic org. www mimarliktabilisim itu edu tr,e mail yektaipek gmail com. Dr Guzden Varinlioglu BArch MFA PhD, Architectural Design Computing Graduate Programme Istanbul Technical. University Istanbul Turkey,zg n Balaban BSc AA Msc. Architectural Design Computing Graduate Programme Istanbul Technical. University Istanbul Turkey,Prof Gulen Cagdas BArch MArch PhD. Architectural Design Computing Graduate Programme Istanbul Technical. University Istanbul Turkey, The paper presents a structural optimisation model that proposes alternative. methods using generative approaches Current methods of optimisation are defined. by three operations modularity repetition and differentiation As an appropriate. example of these methods voronoi structure is explored for its potentials for. optimisation form finding and structural performance A voronoi is modular but not. repetitive with potential for a great variety of complex geometries Using voronoi. diagrams the pattern in architectural design can be formed according to structural. performance, In this paper a generative algorithm is proposed at initial design phases while. designing a structure for a given surface The structural performance data is. converted into geometrical data on the double curved surface to represent the. structural values as an architectural pattern At initial stages the surface on which. the pattern is formed is analysed using the finite element methods FEM to obtain. values on the surface Later according to the data obtained the surface pattern is. generated using a generative algorithm which is developed in Rhinoceros software. and Grasshopper plug in With the help of this algorithm it is possible to create. multiple solutions the structural performance requirements besides one concrete. optimised result Thus the proposed work also evokes alternative methods for the. design decisions made at the preliminary design phase by means of generative. 15 Generative Art Conference GA2012,1 Introduction. In the field of engineering optimisation plays an important role to find the optimum. solution Generally it refers to maximum or minimum boundaries of solutions to the. problems that the designer faces during the problem solving activity Similarly the. optimisation methods are mainly based on mathematical interpretations and relations. related to the defined problem There are two types of problem solving activity well. and ill defined problems In well defined problems steps to the outcome are clearly. defined whereas in ill defined problems the specifications are clearly set As stated. by Eastman the major distinction between well and ill defined problems is the. assumed availability of a specification process for defining the problem space. Eastman 1969 669 1 Thus optimisation methods are deeply linked with well. defined problems instead of ill defined problems, Optimisation is one of the techniques used by engineers to define the solution range. set for the problem However in the field of architecture designers deal mostly with. ill defined problems They predominantly focus on the methods to enrich both the. design processes and the outcomes In that sense generative methods facilitate the. design process by helping the designer to find the optimal solution Generative. methods in which the output is generated by set of rules or an algorithm and. normally by a computer program named also as tools are generator for the designer. during the design process Shea 2005 254 2 Using the implicit capabilities of. generative methods the number of solution sets is increased. 1 1 Deterministic vs Stochastic Approaches, Deterministic approaches and stochastic approaches are two design methods used. during the problem solving process in the ill defined problems Similarly deterministic. algorithms are used as exploratory algorithm when there is a clear inside into the. nature of variables Stochastic algorithms are used in problems when there are. uncertainties in the elements the search space or the path for solutions Barros et. al 2012 3 Thus the deterministic approach commonly used while stochastic. approach has limited use in the architectural design Deterministic approaches in. architectural design leads the designer to arrive to concrete solutions and to produce. one exact solution based on the data driven from the parameters If no change. occurs in the parameters the solution does not change Thus randomness has no. place in finding the final solution, As opposed to deterministic approach the stochastic approach includes. randomness After processing each loop during the generative process of the design. stochastic approach creates diverse outcomes This probabilistic result is the. outcome of the randomness Thus stochastic approach helps the designer to use. generative methods during the design process for augmenting various solutions. To better clarify the distinction between deterministic and stochastic approaches. example of a hollow cube is displayed to be filled with intended design geometry. Fig 1 The design of infilling of the cube is based on geometrical rules In the first. 15 Generative Art Conference GA2012, approach defined as the deterministic approach the designer draws previously. constructed and defined product in its mind Imagining the final product the designer. codes the process in terms of geometrical and mathematical rules The designer. processes and implements the rules of form generation into a computer based. algorithmic model In the second approach defined as stochastic approach the. designer does not have to construct the final product in its mind and to code the. design product in terms of mathematical and geometrical rules for the whole design. process The designer needs to construct only the behaviours or intelligences of the. elements creating the geometry inside the box In this approach design system. simulates and processes the elements to create the geometry inside the hollow cube. While comparing the two approaches we concluded that the deterministic approach. brings one solution as opposed to stochastic approach bringing different design. outcomes during each execution of the generative system Thus the stochastic. approach gives the designer divergent design outcome and can be considered much. more generative then the approach, Figure 1 Strategies for the design of an infilling geometry of a cube. 1 2 Paradox between optimisation and generative methods. Optimisation techniques are used to find the optimum single solution to a defined. problem Generative methods are used to create more enriched solution sets during. the design process Optimisation follows the deterministic approaches whereas. generative techniques tend to follow stochastic approaches Thus the contradiction. between these two concepts optimisation and generative methods should be further. examined by defining the optimisation,2 Optimisation. Optimisation is the search for optimum solutions During the optimisation process. engineers pick the best solution for the problem regarding the constraints 4. Optimisation methods help to define the solution domain boundaries by scaling down. the solution set range Moreover optimisation is a decision support system for the. problem solving process to find proper solution in the solution set domain. Consequently optimisation methods help to reduce the exploration time within the. solution set containing numerous different solutions for specific type of problems. 15 Generative Art Conference GA2012,2 1 Optimisation methods in engineering. Optimisation methods are highly associated with the field of engineering Engineering. deals with well defined problems with specifically defined inputs goals and steps to. reach the goal Facilitating the problem solving process by narrowing down the. solution set for specific problem the methods have become useful and popular in the. field of engineering in time Moreover the ease of interpretation of optimisation. algorithms used for well defined engineering problems makes the optimisation. methods additionally powerful and useful,2 2 Optimisation methods in architecture. In the contrast to the straightforward interpretation of optimisation algorithms in the. field of engineering the implementations of the optimisation methods in the field of. design are complex in nature The problems faced in architecture are mostly ill. defined therefore it is hard to interpret as an algorithm and to search for the solution. of problems Furthermore the goals and steps for the problem can not be generally. interpreted in a mathematical way due to the nature of the problem Optimisation. methods delineate the design problems by making the solution set narrow down. thus the optimisation methods might be considered as decision support system. within the design process 5, 3 Alternative Approaches to the Structural Optimisation in. Generative Design, As the structural performance has to be optimised the engineering requirements. offer more than one single solution for the problem At the initial stage of the design. process we proposed an algorithm in order to clarify the dilemma between. generative and optimisation methods in structural performance The proposed. algorithm forms patterns along the surface of a structure and gives the designer an. optimised relevant solution This algorithm is based on voronoi polygons as its. cellular formation deforms the surface pattern by optimising the structural. performance of the design product,3 1 Operations, The pattern on the surface formed by the algorithm is defined by three operations. modularisation repetition and differentiation These operations representing the. geometric abilities of the pattern are frameworks of the pattern formed for the. structure Using these operations pattern can be modified and optimised according. to the structural performance, The first operation modularisation is widely used for creating cellular formations. Considered as one of the main operations modularisation is widely associated with. grids to explore further geometries In that sense grids help to deform geometries of. 15 Generative Art Conference GA2012, the modular systems creating more complex and deformed patterns The second. operation repetition refers to the growth of the system In a holistic perspective. repetition and growth algorithms lead the system to diverse structural and. geometrical solutions Likewise repetition overlaps with modularisation and growth. of the system Because of its close relation to the grid system the growth algorithms. have the ability to affect the grid system which implies the ability to change the. whole pattern Finally the third operation differentiation makes cells deform based to. their locality and place in the system By the help of the differentiation of intelligence. system meets the performance requirements within a predefined range This. operation helps the pattern to meet the performance requirements and to maximize. the performance of the system Therefore this operation reduces complexity of the. systems in terms of performance requirements and increases the efficiency of the. design performance To conclude with these operations are the keys elements to. reach modified and optimised solutions,3 2 Technology. In this paper we chose a pattern type the voronoi to optimise a design problem A. voronoi pattern is produced on a double curved surface as a structural element. Voronoi pattern gives the designer a chance of optimisation within the critical. boundaries of structural performance As displayed below voronoi pattern is formed. and tested for several diverse grid types The formation of point sets defines end. product characteristics of the voronoi pattern The ability for creating complex. patterns of the voronoi pattern is highly associated with the grid formation. Voronoi pattern behave differently on different grid layouts For example on a square. grid layout the pattern forms itself as a square After the deformation the voronoi. generates itself as a deformed pattern The square cells remain as non deformed. grid while the voronoi patterns are created at deformed areas Fig 2 Similar result is. achieved while the general layout is in a polar or hexagonal form Fig 3. Figure 2 Deformation of the square grid,15 Generative Art Conference GA2012. Figure 3 Deformation of the polar and hexagonal form. The model presented in this paper is created using Rhinoceros 3D modelling. software Grasshopper plug in finite element method software Elmer The algorithm. is implemented in Grasshopper 8 0 14 a generative modelling environment plug in. for Rhinoceros 3D modelling software First the doubly curved surface which is the. base for the structure is modelled in Rhinoceros Second the surface is analysed. under given load conditions in terms of structural stress by using finite element. method software Elmer The generated stress map defines the local behaviours of. the voronoi pattern Using the stress map a grid is generated to form the pattern. using modularisation and repetition operations,15 Generative Art Conference GA2012. 1 Mark de Berg Otfried Cheong Marc van Kreveld and Mark Overmars Computational Geometry Springer Verlag 1997 2 Heino Engel Tragsysteme Structure Systems Hatje Cantz Verlag 2006 3 www laborthographic org Abstract The paper presents a structural optimisation model that proposes alternative methods using generative approaches

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