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Published in: Structural and Multidisciplinary Optimization 2/2020

19-02-2020 | Industrial Application Paper

Advancing building engineering through structural and topology optimization

Authors: Tomás Zegard, Christian Hartz, Arek Mazurek, William F. Baker

Published in: Structural and Multidisciplinary Optimization | Issue 2/2020

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Abstract

Traditional building design is often done in a (pseudo-) sequential manner: the architect defines the form, the structural engineer defines the material and member dimensions, and the mechanical engineer defines the openings, clearances, and additional spaces that ensure proper operation of the building. The design process should ideally be linear, where each discipline receives a complete design from the previous. In reality, however, upstream revisions are usually substantive: significant work in the schematic design and design development phases are due to resolving upstream issues. That said, within the conceptual design and initial phase, the process is mostly linear. This work presents a set of tools that move towards an integrated design optimization, where the building’s form and structure are optimized together and not as separate stages in the design. This approach often results in a higher impact/gain in efficiency, safety, cost-savings, and ultimately results in innovative designs. This industrial application manuscript provides specific details on the implementation and experience gained from the development of various topology optimization tools for use in building engineering. These are all accompanied by examples of their use in applied building projects or more general structural engineering problems. Part of the success of this effort is attributed to the environment in which these tools are implemented, which is friendly to architects. In contrast, commercial tools for this purpose tend to cater to engineers instead.

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Footnotes
1
As structures become more extreme (taller, long cantilevers, long spans, etc), the architect is more open to contributions or comments from the structural engineer regarding the building geometry.
 
2
Skidmore, Owings and Merrill LLP (SOM) is an architecture+engineering firm with worldwide presence specializing in the design of super-tall buildings and large complexes, among others. It has a long-standing tradition of innovative and cutting edge designs, and has introduced significant changes to the practice of building engineering throughout its 80 years (at the time of this writing).
 
3
Less common approaches assign density variables to the nodes (Matsui and Terada 2004), or to a finer discretization that is nested within the analysis one (Nguyen et al. 2009)
 
4
There if ongoing work to obtain analytical clean geometrical descriptions out of density-based topology optimization results. This is often referred to as obtaining a CAD file.
 
5
The marching cubes algorithm works with any hexahedra. Hence, a more appropriate name could be marching hexahedra.
 
6
The marching squares algorithm works with any quadrangle. Hence, a more appropriate name would be marching quadrangles.
 
7
Operations such as and, or, and subtract.
 
8
Refer to https://​web.​ornl.​gov/​sci/​eere/​amie/​ and https://​www.​som.​com/​projects/​amie for additional information on the project and all of the involved parties.
 
Literature
go back to reference Allaire G, Francfort G (1993) A numerical algorithm for topology and shape optimization. In: Bendsøe M, Mota Soares C (eds) Topology design of structures. Springer, Netherlands, pp 239–248 Allaire G, Francfort G (1993) A numerical algorithm for topology and shape optimization. In: Bendsøe M, Mota Soares C (eds) Topology design of structures. Springer, Netherlands, pp 239–248
go back to reference Allaire G, Kohn R (1993) Topology optimization and optimal shape design using homogenization. In: Bendsøe M, Mota Soares C (eds) Topology design of structures. Springer, Netherlands, pp 207–218 Allaire G, Kohn R (1993) Topology optimization and optimal shape design using homogenization. In: Bendsøe M, Mota Soares C (eds) Topology design of structures. Springer, Netherlands, pp 207–218
go back to reference Arora J (2011) Introduction to optimum design, 3rd edn. Academic Press, Waltham Arora J (2011) Introduction to optimum design, 3rd edn. Academic Press, Waltham
go back to reference Ben-Tal A, Bendsøe M (1993) A new method for optimal truss topology design. SIAM J Optim 3(2):322–358MathSciNetMATH Ben-Tal A, Bendsøe M (1993) A new method for optimal truss topology design. SIAM J Optim 3(2):322–358MathSciNetMATH
go back to reference Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Engineering online library, 2nd edn. Springer, Berlin Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Engineering online library, 2nd edn. Springer, Berlin
go back to reference Besserud K, Katz N, Beghini A (2013) Structural emergence: architectural and structural design collaboration at SOM. Arch Des 83(2):48–55 Besserud K, Katz N, Beghini A (2013) Structural emergence: architectural and structural design collaboration at SOM. Arch Des 83(2):48–55
go back to reference Bow RH (1873) Economics of construction in relation to framed structures. ICE Publishing, London Bow RH (1873) Economics of construction in relation to framed structures. ICE Publishing, London
go back to reference Christensen P, Klarbring A (2009) An introduction to structural optimization, 1st edn. Springer, BerlinMATH Christensen P, Klarbring A (2009) An introduction to structural optimization, 1st edn. Springer, BerlinMATH
go back to reference Cremona L (1872) Le figure reciproche nella statica grafica. Tipografia Giuseppe Bernardoni, Milan, ItalyMATH Cremona L (1872) Le figure reciproche nella statica grafica. Tipografia Giuseppe Bernardoni, Milan, ItalyMATH
go back to reference Díaz A, Sigmund O (1995) Checkerboard patterns in layout optimization. Struct Optim 10(1):40–45 Díaz A, Sigmund O (1995) Checkerboard patterns in layout optimization. Struct Optim 10(1):40–45
go back to reference Doi A, Koide A (1991) An efficient method of triangulating equi-valued surfaces by using tetrahedral cells. IEICE Trans Inform Syst E74-D(1):214–224 Doi A, Koide A (1991) An efficient method of triangulating equi-valued surfaces by using tetrahedral cells. IEICE Trans Inform Syst E74-D(1):214–224
go back to reference Dombernowsky P, Sondergaard A (2009) Three-dimensional topology optimisation in architectural and structural design of concrete structures. In: Domingo A, Lazaro C (eds) International association for shell and spatial structures (IASS) symposium, Valencia, pp 1066–1077 Dombernowsky P, Sondergaard A (2009) Three-dimensional topology optimisation in architectural and structural design of concrete structures. In: Domingo A, Lazaro C (eds) International association for shell and spatial structures (IASS) symposium, Valencia, pp 1066–1077
go back to reference Dorn WS, Gomory RE, Greenberg HJ (1964) Automatic design of optimal structures. J de Mecanique 3(1):25–52 Dorn WS, Gomory RE, Greenberg HJ (1964) Automatic design of optimal structures. J de Mecanique 3(1):25–52
go back to reference Eastman C, Teicholz P, Sacks R, Liston K (2011) BIM handbook: a guide to building information modeling for owners, managers, designers, engineers and contractors, 2nd edn. Wiley, Hoboken Eastman C, Teicholz P, Sacks R, Liston K (2011) BIM handbook: a guide to building information modeling for owners, managers, designers, engineers and contractors, 2nd edn. Wiley, Hoboken
go back to reference Golub GH, Van Loan CF (2013) Matrix computations, 4th edn. The Johns Hopkins University Press, BaltimoreMATH Golub GH, Van Loan CF (2013) Matrix computations, 4th edn. The Johns Hopkins University Press, BaltimoreMATH
go back to reference Graczykowski C, Lewiński T (2005) The lightest plane structures of a bounded stress level transmitting a point load to a circular support. Control Cybern 34(1):227–253MathSciNetMATH Graczykowski C, Lewiński T (2005) The lightest plane structures of a bounded stress level transmitting a point load to a circular support. Control Cybern 34(1):227–253MathSciNetMATH
go back to reference Haber RB, Jog CS, Bendsøe MP (1996) A new approach to variable-topology shape design using a constraint on perimeter. Struct Optim 11(1–2):1–12 Haber RB, Jog CS, Bendsøe MP (1996) A new approach to variable-topology shape design using a constraint on perimeter. Struct Optim 11(1–2):1–12
go back to reference Hartz C, Mazurek A, Miki M, Zegard T, Mitchell T, Baker WF (2018) The application of 2D and 3D graphic statics in design. J Int Assoc Shell Spatial Struct 59(4):235–242 Hartz C, Mazurek A, Miki M, Zegard T, Mitchell T, Baker WF (2018) The application of 2D and 3D graphic statics in design. J Int Assoc Shell Spatial Struct 59(4):235–242
go back to reference Heath MT (2002) Scientific computing: an introductory survey, 2nd edn. McGraw Hill, New YorkMATH Heath MT (2002) Scientific computing: an introductory survey, 2nd edn. McGraw Hill, New YorkMATH
go back to reference Hemp WS (1973) Optimum structures, 1st edn. Oxford University Press, Oxford Hemp WS (1973) Optimum structures, 1st edn. Oxford University Press, Oxford
go back to reference Karmarkar N (1984) A new polynomial-time algorithm for linear programming. Combinatorica 4(4):373–395MathSciNetMATH Karmarkar N (1984) A new polynomial-time algorithm for linear programming. Combinatorica 4(4):373–395MathSciNetMATH
go back to reference Kirsch F, Döllner J (2005) OpenCSG: a library for image-based CSG rendering. In: USENIX annual technical conference, FREENIX track Kirsch F, Döllner J (2005) OpenCSG: a library for image-based CSG rendering. In: USENIX annual technical conference, FREENIX track
go back to reference Lewiński T, Zhou M, Rozvany GIN (1994b) Extended exact solutions for least-weight truss layouts—part I: cantilever with a horizontal axis of symmetry. Int J Mech Sci 36(5):375–398MATH Lewiński T, Zhou M, Rozvany GIN (1994b) Extended exact solutions for least-weight truss layouts—part I: cantilever with a horizontal axis of symmetry. Int J Mech Sci 36(5):375–398MATH
go back to reference Lewiński T, Sokół T, Graczykowski C (2019) Michell structures. Springer, Cham Lewiński T, Sokół T, Graczykowski C (2019) Michell structures. Springer, Cham
go back to reference Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. In: Proceedings of the 14th annual conference on computer graphics and interactive techniques SIGGRAPH ’87. ACM, New York, pp 163–169, DOI https://doi.org/10.1145/37401.37422, (to appear in print) Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. In: Proceedings of the 14th annual conference on computer graphics and interactive techniques SIGGRAPH ’87. ACM, New York, pp 163–169, DOI https://​doi.​org/​10.​1145/​37401.​37422, (to appear in print)
go back to reference Maxwell JC (1864) On reciprocal figures and diagrams of forces. Philos Mag Series 4 27(182):250–261 Maxwell JC (1864) On reciprocal figures and diagrams of forces. Philos Mag Series 4 27(182):250–261
go back to reference Mazurek A (2012) Optimum distribution of material in structures with multiple optimization criteria. In: Structural engineers association of Illinois, Chicago Mazurek A (2012) Optimum distribution of material in structures with multiple optimization criteria. In: Structural engineers association of Illinois, Chicago
go back to reference Ohsaki M (2010) Optimization of finite dimensional structures, 1st edn. CRC Press, Boca RatonMATH Ohsaki M (2010) Optimization of finite dimensional structures, 1st edn. CRC Press, Boca RatonMATH
go back to reference Prager W (1958) On a problem of optimal design. In: Olszak W (ed) IUTAM Symposium on non-homogeneity in elasticity and plasticity. Pergamon Press, Warsaw Prager W (1958) On a problem of optimal design. In: Olszak W (ed) IUTAM Symposium on non-homogeneity in elasticity and plasticity. Pergamon Press, Warsaw
go back to reference Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes 3rd edition: the art of scientific computing, 3rd edn. Cambridge University Press, New YorkMATH Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes 3rd edition: the art of scientific computing, 3rd edn. Cambridge University Press, New YorkMATH
go back to reference Rozvany GIN (1998) Exact analytical solutions for some popular benchmark problems in topology optimization. Struct Optim 15(1):42–48MATH Rozvany GIN (1998) Exact analytical solutions for some popular benchmark problems in topology optimization. Struct Optim 15(1):42–48MATH
go back to reference Rozvany G, Gollub W (1990) Michell layouts for various combinations of line supports—I. Int J Mech Sci 32(12):1021–1043MATH Rozvany G, Gollub W (1990) Michell layouts for various combinations of line supports—I. Int J Mech Sci 32(12):1021–1043MATH
go back to reference Rozvany G, Gollub W, Zhou M (1997) Exact Michell layouts for various combinations of line supports—part II. Struct Optim 14(2-3):138–149 Rozvany G, Gollub W, Zhou M (1997) Exact Michell layouts for various combinations of line supports—part II. Struct Optim 14(2-3):138–149
go back to reference Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21 (2):120–127 Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21 (2):120–127
go back to reference Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16(1):68–75 Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16(1):68–75
go back to reference Topping BHV (1983) Shape optimization of skeletal structures: a review. J Struct Eng 109(8):1933–1951 Topping BHV (1983) Shape optimization of skeletal structures: a review. J Struct Eng 109(8):1933–1951
go back to reference Trudeau RJ (1994) Introduction to graph theory. Dover books on mathematics, 2nd edn. Dover Publications, New York Trudeau RJ (1994) Introduction to graph theory. Dover books on mathematics, 2nd edn. Dover Publications, New York
go back to reference Vanderplaats GN (2005) Numerical optimization techniques for engineering design, 4th edn. Vanderplaats R&D, Inc, Colorado SpringsMATH Vanderplaats GN (2005) Numerical optimization techniques for engineering design, 4th edn. Vanderplaats R&D, Inc, Colorado SpringsMATH
go back to reference Wang F, Lazarov BS, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767–784MATH Wang F, Lazarov BS, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767–784MATH
go back to reference Wenger R (2013) Isosurfaces: geometry, topology, and algorithms. CRC Press, Boca RatonMATH Wenger R (2013) Isosurfaces: geometry, topology, and algorithms. CRC Press, Boca RatonMATH
go back to reference Zalewski W, Allen E (1997) Shaping structures: statics. Wiley, New York, USA Zalewski W, Allen E (1997) Shaping structures: statics. Wiley, New York, USA
go back to reference Zegard T, Paulino GH (2015) GRAND3 – ground structure based topology optimization on arbitrary 3D domains using MATLAB. Struct Multidiscip Optim 52(6):1161–1184 Zegard T, Paulino GH (2015) GRAND3 – ground structure based topology optimization on arbitrary 3D domains using MATLAB. Struct Multidiscip Optim 52(6):1161–1184
go back to reference Zegard T, Paulino GH (2016) Bridging topology optimization and additive manufacturing. Struct Multidiscip Optim 53(1):175–192 Zegard T, Paulino GH (2016) Bridging topology optimization and additive manufacturing. Struct Multidiscip Optim 53(1):175–192
go back to reference Zhang XS, Paulino GH, Ramos AS Jr (2018) Multi-material topology optimization with multiple volume constraints: combining the ZPR update with a ground-structure algorithm to select a single material per overlapping set. Int J Numer Methods Eng 114(10):1053–1073. https://doi.org/10.1002/nme.5736 CrossRef Zhang XS, Paulino GH, Ramos AS Jr (2018) Multi-material topology optimization with multiple volume constraints: combining the ZPR update with a ground-structure algorithm to select a single material per overlapping set. Int J Numer Methods Eng 114(10):1053–1073. https://​doi.​org/​10.​1002/​nme.​5736 CrossRef
Metadata
Title
Advancing building engineering through structural and topology optimization
Authors
Tomás Zegard
Christian Hartz
Arek Mazurek
William F. Baker
Publication date
19-02-2020
Publisher
Springer Berlin Heidelberg
Published in
Structural and Multidisciplinary Optimization / Issue 2/2020
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-020-02506-6

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