Lauren L. Beghini¹, Alessandro Beghini², William F. Baker², Neil Katz², Glaucio H. Paulino¹ ¹Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, U.S.A. ²Skidmore, Owings & Merrill, LLP, Chicago, IL, U.S.A. Research Objecves Conclusions References To apply topology opmizaon to the field of structural engineering through high-rise building design Ulize manufacturing and layout constraints to make results more meaningful Address the importance of achieving a balance between engineering and architecture for efficient, sustainable design Historical examples of structures by architects with strong and innovave engineering concepts L.L . Beghini, A. Beghini, W. F. Baker, N. Katz, and G. H. Paulino. "Connecng architecture and engineering through structural topology opmizaon" Engineering Structures. Under revision. L.L . Stromberg, A. Beghini, W. F. Baker, and G. H. Paulino. "Topology opmizaon for braced frames: Combining connuum and beam/column elements." Engi- neering Structures. Vol 37, pp. 106-124, 2012. L.L . Stromberg, A. Beghini, W. F. Baker, and G. H. Paulino. "Applicaon of layout and topology opmizaon using paern gradaon for the conceptual design of buildings." Structural and Muldisciplinary Opmizaon. Vol 43, No. 2, pp. 165-180, 2011. Goal: overcome dichotomy between architectural aesthecs and engineering efficiency using topology opmizaon Introducon: Engineering and Architecture [1-3] Mulple websites Antonio Gaudi¹ Buckminster Fuller² Felix Candela³ Acknowledgements Naonal Science Foundaon Graduate Research Fellowship (GRFP) Skidmore, Owings, & Merrill, LLP Topology opmizaon using barycentric-elements can be a valuable tool to bridge the gap between engineering and architecture in the design industry. Moreover, re- sulng designs will be more efficient and sustainable, by opmizing the material consumpon. Opmal design problem: Example: Minimum Compliance Basic Topology Opmizaon Framework Other Criteria: Eigenmodes Deflecon (P-Δ) Buckling load Natural frequency min (, ) .. (, ) , , d du du f st g i k i = = … 0 1 for min (, ) (, ) () .. d du pu du Kdu p d d f g g V V st T = = ( ) - = ( ) - 1 2 Polygonal elements in nature: Bio-Inspired Design: Zendai Compeon (China) Picture of physical model using topology opmizaon results (courtesy of SOM) and resemblance to spider webs Clockwise: Giant’s Causeway (Ireland), honeycomb, giraffe’s skin, dragonfly wings [Mulple websites] Polygonal Finite Elements Applicaon of Barycentric Elements: Polygonal Meshes for Design 3D Voronoi mesh (CVT): Aſter Lloyd’s Algorithm Inial Voronoi Mesh Laplace shape funcons using natural neighbors: Polygonal shape funcon C. Talischi, G. H. Paulino, A. Pereira, and I. F. M. Menezes. “Polygonal finite elements for topology opmiza- on: A unifying paradigm.” IJNME. Vol 82, No. 6, pp. 671-698, 2010. φ i i j j w w ( ( ) () ) x x x = ∑ ∈ J w s h i i i () () () x x x =