Skip to main content
SpringerLink
Log in

Industrial Applications

  • Chapter
  • First Online:
Book cover Michell Structures

  • 691 Accesses

Abstract

The theory of Michell structures teaches us how to optimally transmit the given load to the support, hence shows how to make structures ideally suited to the given load. The exact solutions to the Michell theory have been an inspiration for developing new numerical methods of Topology Optimization, which nowadays does contribute to essential changes in the design methods in many domains of engineering.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Aerodynamic water droplet with strong lightweight bone structure, Engineering Design Research Laboratory, Indiana University-Purdue University Indianapolis. http://www.engr.iupui.edu/~tovara/edrl/projects/Litecar.

  • Ario, I., Nakazawa, M., Tanaka, Y., Tanikura, I., & Ono, S. (2013). Development of a prototype deployable bridge based on origami skill. Automation in Construction, 32, 104–111.

    Article  Google Scholar 

  • Baker, W. F., Beghini, A., & Mazurek, A. (2011). Applications of structural optimization in architectural design, ASCE structures congress.

    Google Scholar 

  • Beghini, L. L. (2013). Building science through topology optimization. Doctoral dissertation, University of Illinois at Urbana-Champaign.

    Google Scholar 

  • Beghini, A., Beghini, L. L., & Baker, W. F. (2013). Applications of structural optimization in architectural design, ASCE structures congress.

    Google Scholar 

  • Bołbotowski, K., & Sokół, T. (2016). New method of generating Strut and Tie models using truss topology optimization. In M. Kleiber, T. Burczyński, K. Wilde, J. Górski, K. Winkelmann, & Ł. Smakosz (Eds.), Advances in mechanics: Theoretical, computational and interdisciplinary issues. London UK: CRC Press.

    Google Scholar 

  • Chikahiro, Y., Ario, I., Pawłowski, P., Graczykowski, C., Holnicki-Szulc, J. (2018). Optimization of the reinforcement layout in scissor type bridge by combination of FEM and Differential Evolution Algorithm (Submitted).

    Google Scholar 

  • Dewhurst, P. (2005). A general optimality criterion for combined strength and stiffness of dual-material-property structures. International Journal of Mechanical Sciences, 47, 293–302.

    Article  Google Scholar 

  • Flügge, W. (1973). Stresses in Shells (2nd ed.). Berlin: Springer.

    Book  Google Scholar 

  • Foxe, D. M. (2018). Reassessing Zalewski’s shells designs, and surfaces. In C. Mueller, S. Adriaenssens (Eds.), Creativity in Structural Design, Proceedings of the IASS Symposium 2018, July 16–20, 2018, MIT, Boston, USA.

    Google Scholar 

  • He, L., & Gilbert, M. (2015). Rationalization of trusses generated via layout optimization. Structural and Multidisciplinary Optimization, 52, 677–694.

    Article  MathSciNet  Google Scholar 

  • He, L., Gilbert, M., Johnson, T., Smith, C. (2018). Human-in-the-Loop Layout and Geometry. In A. Schumacher, T. Vietor, S. Fiebig, K. U. Bletzinger, K. Maute (Eds.), Advances in structural and multidisciplinary optimization. WCSMO 2017. Optimization of structures and components. Cham: Springer.

    Google Scholar 

  • Hemp, W. S. (1974). Michell framework for uniform load between fixed supports. Engineering Optimization, 1(1), 61–69.

    Article  Google Scholar 

  • Holnicki-Szulc, J., & Bielecki, T. (2000). Structures with highest ability of adaptation to overloading. In Proceedings of IUTAM Symposium on Smart Structures and Structronic Systems. 26–29 September 2000. Magdeburg, Germany.

    Google Scholar 

  • Holnicki-Szulc, J., & Knap, L. (2004). Adaptive crashworthiness concept. International Journal of Impact Engineering, 30(6), 639–663.

    Article  Google Scholar 

  • Holnicki-Szulc, J., Maćkiewicz, A., & Kołakowski, P. (1998). Design of adaptive structures for improved load capacity. AIAA Journal, 36(3), 471–476.

    Article  Google Scholar 

  • Holnicki-Szulc, J., Pawłowski, P., & Wikło, M. (2003). High-performance impact absorbing materials - The concept, design tools and applications. Smart Materials and Structures, 12, 461–467.

    Article  Google Scholar 

  • Kołakowski, P., Wikło, M., & Holnicki-Szulc, J. (2008). The virtual distortion method - A versatile reanalysis tool for structures and systems. Structural and Multidisciplinary Optimization, 36(3), 217–234.

    Article  Google Scholar 

  • Kuś, S., & Zalewski, W. (2000). Shaping structures. In Symposium, Conceptual Designing-Structural Shaping. Corrugated Iron Structures. Cable Structures (pp. 11–26) Rzeszów: Rzeszów University of Technology (in Polish).

    Google Scholar 

  • Lancaster, L. C. (2006). Materials and Construction of the Pantheon in Relation to the Developments in Vaulting in Antiquity. In G. Grasshof, M. Wäfler & M. Heinzelmann (Eds.), The Pantheon in Rome. Contributions to the Conference. Bern, November 9–12, 2006.

    Google Scholar 

  • Leonhardt, F., & Zellner, W. (1972). Vergleiche zwischen Hange - And Schragkabel brücken für Spann weiten über 600 m (Vol. 32, p. 1972). Zürich: der IVBH-Abhandlugen.

    Google Scholar 

  • Leonhardt, F. (1986). 1986. PCI Journal (September - October: Cable stayed bridges with prestressed concrete.

    Google Scholar 

  • Lewiński, T., Czarnecki, S., Czubacki, R., Łukasiak, T., & Wawruch, P. (2018). Constrained versions of the free material design methods and their applications in 3D printing. In A. Schumacher, Th. Vietor, S. Fiebig, K.-U. Bletzinger, K. Maute (Eds.), Advances in Structural and Multidisciplinary Optimization. Proceedings of the 12th World Congress of Structural and Multidisciplinary Optimization (WCSMO12) (pp. 1317–1332). Cham, Switzerland: Springer International Publishing.

    Google Scholar 

  • Marzec, Z., & Holnicki-Szulc, J. (1999) Adaptive barriers with maximal impact energy absorption. In Proceedings of 3rd World Congress on Structural and Multidisciplinary Optimization. 17–21 May 1999, Buffalo, NY.

    Google Scholar 

  • Maute, K., & Ramm, E. (1995a). Adaptive topology optimization. Structural Optimization, 10, 100–112.

    Article  Google Scholar 

  • Maute, K., & Ramm, E. (1995b). General shape optimization – an integrated model for topology and shape optimization. In Proceedings of the First World Congress of Structural and Mutidisciplinary Optimization, 28 May–2 June 1995, Goslar, Germany, Elsevier, Oxford, 1995 (pp. 299–306).

    Google Scholar 

  • Maute, K., Schwartz, S., & Ramm, E. (1998). Adaptive topology optimization of elasto-plastic structures. Structural and Multidisciplinary Optimization, 5, 81–89.

    Article  Google Scholar 

  • Mayer, R. R., Kikuchi, N., & Scott, R. A. (1996). Applications of topology optimization techniques to structural crashworthiness. International Journal for Numerical Methods in Engineering, 39, 1383–1403.

    Article  Google Scholar 

  • Mazurek, A. (2012). Geometrical aspects of optimum truss like structures for three-force problem. Structural and Multidisciplinary Optimization, 45, 21–32.

    Article  MathSciNet  Google Scholar 

  • Mazurek, A., Baker, W. F., & Tort, C. (2011). Geometrical aspects of optimum truss like structures. Structural and Multidisciplinary Optimization, 43, 231–242.

    Article  Google Scholar 

  • Moore, D. (1995). The Pantheon. www.romanconcrete.com.

  • Mrzygłód, M., & Kuczek, T. (2014). Structural and Multidisciplinary Optimization, 49(2), 327–336. https://doi.org/10.1007/s00158-013-0972-z.

    Article  Google Scholar 

  • Neves, M. M., Rodrigues, H., & Guedes, J. M. (1995). Generalized topology design of structures with a buckling load criterion. Structural and Multidisciplinary Optimization, 10, 71–78.

    Article  Google Scholar 

  • Novozhilov, V. V. (1964). Thin Shell Theory. Groningen, The Netherlands: Nordhoff.

    Book  Google Scholar 

  • Pawłowski, P., & Holnicki-Szulc, J. (2004). Adaptive structures under extreme loads – Impact detection, self-adaptation, self-repairing. In Proceedings of 3rd European Conference on Structural Control, 12–15 July 2004, Vienna, Austria.

    Google Scholar 

  • Pawłowski, P., & Wikło, M. (2004). Design of adaptive structures under random impact conditions. In J. Holnicki-Szulc & C. A. Mota-Soares (Eds.), Advances in smart technologies in structural engineering. Berlin: Springer.

    Google Scholar 

  • Pedersen, C. B. W. (2003a). Topology optimization design of crushed 2D-frames for desired energy absorption history. Structural and Multidisciplinary Optimization, 25, 368–382.

    Article  Google Scholar 

  • Pedersen, C. B. W. (2003b). Topology optimization for crashworthiness of frame structures. International Journal of Crashworthiness, 8, 29–39.

    Article  Google Scholar 

  • Pichugin, A. V., Tyas, A., & Gilbert, M. (2012). On the optimality of Hemp’s arch with vertical hangers. Structural and Multidisciplinary Optimization, 46, 17–25.

    Article  MathSciNet  Google Scholar 

  • Pichugin, A. V., Tyas, A., Gilbert, M., & He, L. (2015). Optimum structure for a uniform load over multiple spans. Structural and Multidisciplinary Optimization, 52, 1041–1050.

    Article  MathSciNet  Google Scholar 

  • Smith, Ch J, Gilbert, M., Todd, I., & Derguti, F. (2016). Application of layout optimization to the design of additively manufactured metallic components. Structural and Multidisciplinary Optimization, 54, 297–1313.

    Article  MathSciNet  Google Scholar 

  • Soto, C. A. (2001). Structural topology optimization: From minimizing compliance to maximizing energy absorption. International Journal of Vehicle Design, 25(1), 142–163.

    Article  MathSciNet  Google Scholar 

  • Soto, C. A. (2002). Application of structural topology optimization in the automotive industry: Past, present and future. In Proceedings of 5th World Congress of Computational Mechanics. 9–12 July 2002, Vienna, Austria.

    Google Scholar 

  • Stromberg, L. L., Beghini, A., Baker, W. F., & Paulino, G. H. (2011). Application of layout and topology optimization using pattern gradation for the conceptual design of buildings. Structural and Multidisciplinary Optimization, 43, 165–180.

    Article  Google Scholar 

  • Stromberg, L. L., Beghini, A., Baker, W. F., & Paulino, G. H. (2012). Topology optimization for braced frames: Combining continuum and beam/column elements. Engineering Structures, 37, 106–124.

    Article  Google Scholar 

  • Tyas, A., Pichugin, A. V., & Gilbert, M. (2011). Optimum structure to carry a uniform load between pinned supports: Exact analytical solution. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 467(2128), 1101–1120.

    Article  MathSciNet  Google Scholar 

  • Victoria, M., Querin, O. M., & Marte, P. (2011). Generation of strut-and-tie models by topology design using different material properties in tension and compression. Structural and Multidisciplinary Optimization, 44, 247–258.

    Article  Google Scholar 

  • Wikło, M., & Holnicki-Szulc, J. (2008a). Optimal design of adaptive structures: Part I. Remodeling for impact reception. Structural and Multidisciplinary Optimization, 37(3), 305–318.

    Article  Google Scholar 

  • Wikło, M., & Holnicki-Szulc, J. (2008b). Optimal design of adaptive structures: Part II. Adaptation to impact loads. Structural and Multidisciplinary Optimization, 37(4), 351–366.

    Article  Google Scholar 

  • Yamakawa, H., Tsutsui, Z., Takemae, K., Ujita, Y., & Suzuki, Y. (1999). Structural optimization for improvement of train crashworthiness in conceptual and preliminary design. In Proceedings of 3rd World Congress on Structural and Multidisciplinary Optimization, 17–21 May 1999, Buffalo, NY.

    Google Scholar 

  • Zabłocki, W. (2000). Optimization of structures and new forms of tall buildings. Architektura, 74(11), 96–98. (in Polish).

    Google Scholar 

  • Zalewski, W. (1962). Construction de la toiture du supermarket a Varsovie. In N. Esquillan & Y. Saillard (Eds.), Hanging roofs: Proceedings of the IASS Colloquium on Hanging Roofs, Continuous Metallic Shell Roofs and Superficial Lattice Roofs, Paris 9–11 July, 1962.

    Google Scholar 

  • Zalewski, W. (1963). Constance de la force comme critere de la forme ationelle d’une construction.

    Google Scholar 

  • Zalewski, W. (1964). Some new structural forms created in the period 1950–60 (in Polish).

    Google Scholar 

  • Zalewski, W., & Allen, E. (1998). Shaping Structures. Statics. New York: Wiley.

    Google Scholar 

  • Zalewski, W., & Zabłocki, W. (2002). Engineering inspirations in shaping tall buildings. In Lightweight Structures in Civil Engineering, Proceedings of the International Symposium, Warsaw, Poland, 24–28 June 2002 (pp. 109–118).

    Google Scholar 

  • Zalewski, W. (2000). Strength and lightness - The muses of a structural designer. Architektura, 74(11), 94–95. (in Polish).

    Google Scholar 

  • Zalewski, W. (2005). Shaping structures. Introduction and examples. In Proceedings of the 7th Symposium: New Achievements of Science in Civil Engineering. Shaping Structures, Cable Structures, Corrugated Iron Structures (pp. 49–72), Rzeszów (in Polish).

    Google Scholar 

  • Zegard, T. (2014). Structural optimization: From continuum and ground structures to additive manufacturing. Doctoral dissertation, University of Illinois at Urbana-Champaign.

    Google Scholar 

  • Zegard, T., & Paulino, G. H. (2016). Bridging topology optimization and additive manufacturing. Structural and Multidisciplinary Optimization, 53(1), 175–192.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Civil Engineering, Warsaw University of Technology, Warsaw, Poland

    Tomasz Lewiński & Tomasz Sokół

  2. Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

    Cezary Graczykowski

Authors
  1. Tomasz Lewiński
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tomasz Sokół
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cezary Graczykowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tomasz Lewiński .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lewiński, T., Sokół, T., Graczykowski, C. (2019). Industrial Applications. In: Michell Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-95180-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-95180-5_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95179-9

  • Online ISBN: 978-3-319-95180-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation