Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. The production of simulation friendly geometries is not a novel or relatively unresolved process in itself as. digital simulation using particle spring simulation frameworks is fairly well established especially following the. work of early architectural exponents such as Axel Killian Kilian and Ochsendorf 2005 However this. section describes the production of geometries that not only satisfy that criteria but also a number of others such. as fulfilling certain design intentions and the achieving of a desired structural performance. This early design workflow stresses an intuitive and qualitative knowledge aided by feedback generated. between early design methods and downstream validation processes such as structurally based topology. optimization and fabrication constraints This feedback loop is improved by the utilization of rapid iteration and. the evolution of the design geometry aided by the trial and error volume dependant nature of information. 2 1 2 Designing for a convergence solution, Generating these resultant geometries leads to the requirement of managing expected high resolution. simulation friendly meshes met by working primarily though a proposed low resolution designer friendly. Shepherd P and Richens P 1 and Bhooshan S and El Sayed M 2 Hierarchical Subdivision Surface HSS. This workflow generally begins with a designer s sketch solution to a spatial design problem typically. manifested as a pre dominantly quad faced low resolution mesh This mesh is constructed to accommodate. design features such as topological conditions and directionality holes and or boundary conditions touchdown. points clearances etc Given that these morphological developments rely both on the iterative nature of the. process and quick time span of each iteration ease intuition and speed of manipulation become crucial This. makes the low resolution nature of the design mesh quite important as it creates a freeform manipulation. friendly geometry used to explore design possibilities and limitations A low resolution mesh also facilitates the. intuitive tracking of important technical details such as the presence of singularity points and eventual pre. simulation details such as holes or fixed boundaries This is possible due to the ability to manipulate the. geometry s through adjusting a few vertices and or the addition subtraction of a few faces Fig 1. Figure 1 Multiple resolutions of design mesh showing relatively low number of faces 6 faces used to create. complex surface, Furthermore by taking advantage of the recursive refinement structure of subdivision surfaces the low. resolution mesh is easily converted into a high resolution mesh This higher resolution mesh has nice attributes. such as majority of its vertices of having equal valence relatively even spacing of vertices etc These features are. beneficial for downstream processes as conversion to NURBS surfaces even Finite Element Meshes etc. 2 1 3 Structural performance intuition, The manipulation friendly aspect of the workflow also allows for another major advantage namely that. of using a qualitative and intuitive understanding of structural principles of complex topologies to shape the base. geometries This is achieved primarily through two avenues the first being the ability to describe relatively. large curvature areas in the geometry s topology with a fairly small and easy to manage amount of geometric. information typically three to four mesh faces The second is the aforementioned ability to control and influence. Copyright 2014 by the author s, Published by the International Association for Shell and Spatial Structures IASS with permission. Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. the presence of singularity points Fig 2 in the overall tessellation of the inherited high resolution mesh These. are crucial as they usually describe points at which curvature inverts or drastically changes in the geometry Such. areas typically correlate with areas of weaker structural performance These points are easy to spot and predict in. the low resolution mesh as they tend to occur when the mesh valence varies from the predominant quad based. subdivision at a particular vertex, Figure 2 High resolution mesh with highlighted singularity points. 2 1 4 Downstream benefits, A HSS based workflow as described allows for the explorative evolution of multiple design resolutions through. rapid iterative processes This then develops both an intuition for structural performance and also resultant. geometries that are suited for downstream verification and analysis as described previously Additionally the. resultant geometries of the topology optimization processes described in next section needed to be rebuilt in a. similar low resolution manner This is mainly due to the fact that the Finite Element mesh is subdivided to a. resolution suited to the optimization process but neither conducive to other downstream processes nor design. manipulation The rebuilding process is aided by the discrete nature of describing a subdivision mesh through. vertex placement and edge connections which in this case was guided by the primary curvature lines of the. optimized mesh The benefits of the rebuilt mesh were most clearly observed in the structural analysis stage. where the mesh resolution and topology were easily edited to suit the process. Figure 3 Left to Right High resolution mesh FEM mesh 50000 vertices multi patch medium resolution. mesh 6200 vertices low resolution predominantly quad mesh 275 vertices. 2 2 Topology Optimization,Copyright 2014 by the author s. Published by the International Association for Shell and Spatial Structures IASS with permission. Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. The application of topological optimization TO as a constitutive design tool has obtained widespread adoption. within aeronautic automotive and naval industries Bends e M P and Sigmund O 3 While initial research. on the application of TO to architectural structures indicate the possibility for both significant performance gains. in terms of reduction of material consumptions and the infusion of particular design qualities specific to the. process DOMBERNOWSKY P and S NDERGAARD 4 DOMBERNOWSKY P and S NDERGAARD 5. STROMBERG L L et al 6 the topic in its relation to architectural construction remains widely unexplored. The prototype presented in this paper explores a bi directional generative modus of design application in which. the result of topological optimization not only serves to reduce the self weight of the concrete body through the. generation of structurally efficient rib patterns but also to significantly affect the appearance and effect of the. final architectural object, Figure 4 Shell design space FE model top left Shell design space FE model top right Material density. distribution after topology optimization bottom left displacements of post optimized concrete body bottom. This was achieved through the following optimization process the shell geometry designed following the steps. documented in the previous chapters was approximated in the FE solver HyperMesh 11 0 to a tetrahedric. Finite Element mesh of 100 x 100x 100 mm units Assuming a reinforced C35 concrete of 6 5e 9 elasticity. module a tensile strength of 3 MPa and a compressive strength of 34 MPa the mesh was subjected to a uniform. load of 2 92 kN m2 on the outer surface in the z direction representing the dead load and wind load of the. structure and fully supported along the bottom shell edge Using the optimization solver Optistruct 11 0 this. setup was topologically optimized for a minimization of compliance with a volume fraction of 25. Copyright 2014 by the author s, Published by the International Association for Shell and Spatial Structures IASS with permission. Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. Figure 5 Optimization results density studies, The resulting topology analysed in Hyperview 11 0 exhibited a 5 67 mm of displacement and maximum tensile. stress value of 0 08 kN cm2 well within the accepted properties of the material Applying a density filtering of. 0 29 the optimized mesh was re exported and remodelled in the Rhinoceros 5 0 CAD modeller The post. processed interpretation of the optimization result held a volume of 1 219 m3 by comparison to initiating starting. volume of the original shell of 1 85 m3 representing a 34 1 reduction of volume through optimization. Through this operation the self load of the concrete body was reduced hereby rendering visible the principal. load trajectory pattern of the structure as perforations of the input design space volume. Figure 6 Remodelled geometry in McNeel Rhinoceros,3 Structural design. The structural context of the design and the envisaged methods of construction required us to include various. considerations and make appropriate responses in the structural engineering of the proposed design This section. describes them,Copyright 2014 by the author s, Published by the International Association for Shell and Spatial Structures IASS with permission. Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. Figure 7 Deflection analysis,3 1 Governing lateral load Seismic or wind loads. Given that Mexico City is in a seismically active area we had to consider whether to use seismic loads or wind. loads as the governing lateral load Following are the key assumptions we made and subsequently decided to. use seismic loads of 300gal as the governing one,1 DL Self Load 24kN m3 x 0 08m 1 92 kN m2. 2a EX Seismic Load 300gal DL x 0 3 0 576 kN m2,2b EX Seismic Load 200gal DL x 0 2 0 384 kN m2. 3 WX Wind Load 0 44 kN m2 Based on the wind code tables. 3 2 Foundation design,3 2 1 Stiff beam versus counter weight approaches. The above assumptions had a substantial impact on the design of the foundation Given that we were attempting. to amount of concrete used via TO we were conscious not to lose those savings in the design of the foundation. of the structure This section describes the various considerations and the final choice of foundation design. made Figure 8,Figure 8 Foundation design as a stiff beam. Under self load the reaction uplift due to the geometry of the structure were 200Kg both sides in the front leg. and 60 Kg both sides at the rear These could have easily been countered with the weight of foundation. However the foundations had to consider the lateral loads mentioned above Under 300 gal lateral loads the shell. was found to be very sensitive against the side way Y axis forces We needed a foundation beam of about. 20cm x 30cm rectangular section at both front and rear touchdown areas Further these foundations required that. they have wider footings 40cm to 60cm width to spread the overall weight evenly to the supporting ground. Additionally the primary arcs of the touchdown areas of the geometry come very close toward the front leg. allowing rather limited stance between each touchdown point to act against bending action Thus even though. the overall weight was about 2 tonnes the concentration of compression and tension at each touchdown point. would have become about 5 5 ton It would have been rather uneconomical to try to cancel this heavy tonnage. Copyright 2014 by the author s, Published by the International Association for Shell and Spatial Structures IASS with permission. Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. with counterweight of concrete Instead we thought of designing a foundation beam with sufficient stiffness and. sectional area to act against the induced bending moment and shear. 3 2 2 Toppling, Another issue to be considered was that of toppling given the tall and narrow proportions of the design. However we found that the geometry was on the safe side given the following i Centre of Gravity upon which. the lateral force acts is 1 78m from the ground much lower than 3 0m ii Weight of the shell is 23 5 kN. including the steel and much lower than 30 0 kN Considering the factors above we decided to design the. foundation as a stiff beam of 20cm x 30cm box with 40cm x 10cm footing for the front legs The tail was. supplied with the foundation beam of the same profile as the geometry We then connected these two isolated. foundations together by a pair of concrete beams on either side Connecting beam was found not to require a. footing This foundation was estimated to weight about 0 5 ton significantly less than the counter weight. 3 3 Bending moments, Upon analysis it was found that the highly curved geometry of the shape induced considerable bending action in. the structure The compressive stress values used for analyses were reduced to the approximately 2 3rd the. design strength of the concrete as concrete could fail at lower than its compressive stress due to such bending. 3 4 Distance of apertures from boundary, The topological optimisation process produced long thin elements at the rear of the structure These however. had to be reduced due to the possibility of buckling given the very small distance from the edge to the. perforation A minimum distance of 120mm from the edges was established all around the piece and not any. concrete element was less than 120 x 120 mm in cross section. 3 5 Manual installation of steel bars, Free form nature of the geometry of the shell meant that the principal moment vector changed drastically across. the shell On the other hand considering the practicality of manual installation rebar placement would not be as. flexible as we would need it to be Therefore we needed to make somewhat redundant rebar placement on both. U and V directions of the shell so that each can cover both upward bending and downward bending by. themselves Additionally analyses performed after increasing safety factor to 5 to account for construction. errors and concrete creeping also indicated the prudence in this strategy Lastly 8mm diameter steel bars was. specified since at that thickness it could be manually bent to conform to the geometry. Figure 9 Principal moment vector field,Copyright 2014 by the author s. Published by the International Association for Shell and Spatial Structures IASS with permission. Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. Figure 10 Reinforcement distribution diagram,4 Fabrication. Following an iterative process of structural analysis and design refinement the optimization result was. remodelled in Rhinoceros for achieving a final topology optimized geometry that satisfied all the conditions of. the seismically active environment of Mexico City and with the adequate size to be built in 10 days using. manual labour Given the complex geometry of the shell and the existence of a CNC router on site a the Tec de. Monterrey we decided to contour the shape and cut it out of EPS Foam panels to be assembled on site and serve. as a guide for the workers to layout the rebar and pour the concrete An inverted negative of the shape was. remodelled on Rhino establishing all the edges at 90 degrees normal to the original surface to avoid the need of. perimeter tubes and be able to create a continuous curvature on the edges Figure 11 This model was divided in. 12 pieces that could fit the bed of the CNC machine and contoured at one inch segments a interval that. corresponds to the thickness of the low density polystyrene sheets that were locally available subsequently the. contours were nested to achieve the maximum material efficiency while reducing the cutting time As the model. is symmetrical in one axis it allows us to cut some pieces of foam together and then rotate them 180 degrees to. get their final position Figure 12 The contours were glued utilizing polystyrene solvent free industrial adhesive. on 12 blocks of contour to allow them to be transported on site utilizing a contour approach to the shape. generated another layer of texture to the geometry accentuating the curvature of the shell. 4 1 Construction on the building site, Once on site the construction of the formwork was organised in 12 blocks of contours of in all 160 polystyrene. sheets External scaffolding towers were deployed on site comprised of standard 2000 x 600 mm modules to. allow the workers to walk and move around the prototype Figure 13 The formwork was only going to be. utilised as guide work for the workers on site so it didn t need to be sanded to reduce the texture of the contours. or coated with any releasing agents The polystyrene blocks were assembled and reinforcement bars placed by. hand following the curvature of the surface A double sided wire mesh slip was created around all of the. perforations of the piece to ensure geometric fidelity as the rebar proved to be difficult to bend on this closed. angles accurately and using thinner wire would not strong enough to receive the concrete Figure 14 After. placing the reinforcement bars a double layer of wire metal mesh was applied on both sides of the rebar to. receive the concrete mixture The edges of the piece as well as the perimeter edge of each of the perforations had. to be covered with a double layer of wire mesh enclosed in a slip of plastic to ensure that the concrete mix. remains perpendicular to the surface all around the edges as doing a perpendicular edge in a traditional manner. would have been extremely complex given the curvature of the piece. A low water concrete mixture was cast into this double layer of metal mesh to avoid the need of vibration the. concrete was poured and compacted in 4 step sequence back bottom areas front bottom areas middle and top. the foam guide work had to be removed immediately after casting to be able to take it out without damaging the. surface and without having to destroy or further cut it. Copyright 2014 by the author s, Published by the International Association for Shell and Spatial Structures IASS with permission. Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. A layer of high water cement paste was applied to the piece after finishing the cast to even the surface and. prepare it to receive subsequent painting treatment The prototype is in a public park in the Santa Fe area of. Mexico City and was opened to the public on the 20th of September. The process from 3d modelling and preparation of formwork files to on site casting took 10 days and the. concrete was left to cure for 2 more weeks, Figure 21 Typical section of the formwork guide left and contoured negative model of the geometry right. Figure 12 CNC routing of contours left and contours ready to be glued and transported on site right. Copyright 2014 by the author s, Published by the International Association for Shell and Spatial Structures IASS with permission. Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. Figure 13 On site assembly of the formwork with scaffolding towers to the sides and placing of the. reinforcement bars, Figure 14 left to right Perimeter edges cover with reinforced wire plastic slip Piece after concrete was poured. and formwork removed,Copyright 2014 by the author s. Published by the International Association for Shell and Spatial Structures IASS with permission. Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. Figure 15 Topology optimized shell prototype 4 x 5 x 2m 8 cm thick. 5 CONCLUSIONS, We presented the specifics of a time bound design collaboration including computational geometry and design. tools and their use in multi stage collaborative design phase incorporation of structural design in early design. strategies to describe complex geometry form work and steel layout onsite in a labour intensive economy. 5 1 Computational geometry and design technologies. 5 1 1 Subdivision surfaces, Growth in the role of simulation in conceptual design and evaluation of building performance is coupled with. need for architects to manage the dichotomy between high resolution geometries used in simulation and lower. resolution free form manipulation friendly CAD geometries We argued for the benefits of Hierarchical. Subdivision surfaces in this process concentrating specifically on its uses in. i Design and collaboration workflow enabling multiple resolutions of design and analysis rapid. iteration and evolution of design geometry, ii Developing an intuition for structural performance of geometries due to the nature of the smooth. curvature flows produced by subdivision geometries and the correlation of the curvature with. structural performance,5 1 2 Topology optimisation and shell structures. Incorporation of structural analysis within the rapid iterative and free form nature of early design is quite a. challenge The methods and software are neither easily accessible to architects nor easily incorporated within. methods and software they use Further they are time consuming and defy easy integration of architectural. constraints In this context recent developments with regard to development and availability software to. Copyright 2014 by the author s, Published by the International Association for Shell and Spatial Structures IASS with permission. Proceedings of the IASS SLTE 2014 Symposium, Shells Membranes and Spatial Structures Footprints. optimise material layout within a given design space is a welcome development We specially argued for the. benefits of such topology optimisation in, i Reduction in material quantities and thus reduction of economic and environmental costs. ii Reduction in the design iteration time,5 2 Structural design. We also discussed the difficulties in developing details of structural design in the context of free form. geometry seismically active physical environment and labour intensive economic environment in which the. prototype was built focussing specifically on, i Development of reinforcement fibre layout in the geometries developed by the processes above. ii Design of foundation for such unusual geometries with the explicitly design intention to minimise the. size and complexity of the same,5 3 Fabrication, Further we presented our strategies to enable a straight forward translation of the design to physical reality. i Description of geometry complex geometry on site given the constraints of time and labour intensive. ii Development of guide work Form work for concrete negotiating requirements of. pouring compaction with the complexities of the geometries produced by topology optimisation. In conclusion we hope to have made a case for a more holistic design practise from collaborative design to. fabrication and a thus a more holistic reduction of costs design time and resource material savings via. topology optimisation and the need to include fabrication costs in such evaluations. ACKNOWLEDGEMENTS, We would like to thank the director of Zaha Hadid Architects Mr Patrik Schumacher for his guidance and. support of this research prototype We would like to thank Tom Newby of Expedition Engineers London for his. professional timely and invaluable advice regarding the structural performance of the proposed design. REFERENCES, 1 Shepherd P Richens P Subdivision Surface Modelling for Architecture in IASS 2009 Proceedings of the. International Association for Shell and Spatial Structures Symposium Valencia 2009. 2 Bhooshan S and El Sayed M Use of Sub division Surfaces Architectural Form Finding and Procedural. Modelling Proceedings of the international conference on simulation in Architecture and urbanism simAUD. 2011 Boston USA, 3 Bends e M P and Sigmund O 2003 Topology Optimization theory methods and applications Springer. 4 DOMBERNOWSKY P and S NDERGAARD A 2011 Unikabeton prototype In FABRICATE Making Digital. Architecture Riverside Architectural Press, 5 DOMBERNOWSKY P and S NDERGAARD A 2012 Design analysis and realization of topology optimized. concrete structures International Association for Shell and Spatial Structures 53 209 216. 6 STROMBERG L L BEGHINI A BAKER W F and PAULINO G H 2012 Topology optimization for. braced frames combining continuum and beam column elements Engineering Structures 37 106 124. Copyright 2014 by the author s, Published by the International Association for Shell and Spatial Structures IASS with permission.
Piramida adalah... Mastaba Piramida a. Makam para bangsawan Mesir Tempat mumi Firaun Mesir dimakamkan b. Makam para Firaun Mesir Tempat penyimpanan harta karun Raja Mesir c. memiliki beberapa persamaan. Dari Kuil pemujaan Dewa Ra Makam para ulama dan bangsawan Mesir d. Tempat pemujaan bangsa Sumeria Tempat pemakaman bangsawan Mesir e.
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