Skip to main content
SpringerLink
Log in
Book cover

Swift Analysis of Civil Engineering Structures Using Graph Theory Methods pp 123–180Cite as

Static Analysis of Nearly Regular Continuous Domains

  • Chapter
  • First Online:

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 290))

Abstract

Regarding the style and elegance of new designs as well as growing applications of prefabrication in structural and mechanical systems, many systems hold regular and near-regular geometrical patterns. Because of natural repetition of elements and nodes in numerical methods and regularity of meshes, regular and near regular patterns are also observed in many numerical solution resulting in decomposable stiffness matrices. In this chapter, finite element and mesh free solutions of regular and near-regular structural and mechanical systems are developed and discussed.

This is a preview of subscription content, 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   139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   179.99
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

Learn about institutional subscriptions

Notes

  1. 1.

    The modeled mesh includes more elements than the schematic Fig. 5.8.

  2. 2.

    The star point of a cloud is the node for which the function u (e.g., \(u_{h} \left( \varvec{x} \right)\)) is calculated. A cloud is known with its star point and the maximum value of the weight function in a cloud occurs in the star point.

References

  1. Shojaei, I., Rahami, H., Kaveh, A.: Efficient finite element solution of regular and near-regular systems using graph products. Acta Mech. 226(7), 2393–2405 (2015)

    Article  MathSciNet  Google Scholar 

  2. Logan, D.: A First Course in the Finite Element Method. Cengage Learning, Boston (2011)

    Google Scholar 

  3. Williams, V.V.: Breaking the Coppersmith-Winograd Barrier (2011)

    Google Scholar 

  4. Rahami, H., Kaveh, A., Shojaei, I., Gholipour, Y.: Analysis of irregular structures composed of regular and irregular parts using graph products. J. Comput. Civil Eng. 28(4) (2014)

    Article  Google Scholar 

  5. Nishida, N., Kanchiku, T., Kato, Y., Imajo, Y., Kawano, S., Taguchi, T.: Biomechanical analysis of the spinal cord in Brown-Séquard syndrome. Exp. Ther. Med. 6, 1184–1188 (2013)

    Article  Google Scholar 

  6. Shojaei, I., Kaveh, A., Rahami, H.: An efficient finite element solution using a large pre-solved regular element. Acta Mech. (2016). http://doi.org/10.1007/s00707-015-1552-7

    Article  MathSciNet  Google Scholar 

  7. Molano, R., Rodríguez, P.G., Caro, A., Durán, M.L.: Finding the largest area rectangle of arbitrary orientation in a closed contour. Appl. Math. Comput. 218, 9866–9874 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Johnson, C.: Numerical Solution of Partial Differential Equations by the Finite Element Method. Courier Corporation, USA (2012)

    Google Scholar 

  9. Kaveh, A.: Optimal Structural Analysis, 2nd edn. Wiley, UK (2014)

    MATH  Google Scholar 

  10. Kaveh, A., Rahami, H.: An efficient analysis of repetitive structures generated by graph products. Int. J. Numer. Methods Eng. 84, 108–126 (2010)

    Article  MathSciNet  Google Scholar 

  11. Kaveh, A., Shojaei, I., Rahami, H.: New developments in the optimal analysis of regular and near-regular structures: decomposition, graph products, force method. Acta Mech. 226, 665–681 (2015)

    Article  MathSciNet  Google Scholar 

  12. Kaveh, A., Rahami, H.: Factorization for efficient solution of eigenproblems of adjacency and Laplacian matrices for graph products. Int. J. Numer. Methods Eng. 75, 58–82 (2008)

    Article  MathSciNet  Google Scholar 

  13. Shojaei, I., Kaveh, A., Rahami, H.: Analysis of structures convertible to repeated structures using graph products. Comput. Struct. 125, 153–163 (2013)

    Article  Google Scholar 

  14. Unnikrishnan, G.U., Barest, G.D., Berry, D.B., Hussein, A.I., Morgan, E.F.: Effect of specimen-specific anisotropic material properties in quantitative computed tomography-based finite element analysis of the vertebra. J. Biomech. Eng. 135, 101007 (2013)

    Article  Google Scholar 

  15. Shojaei, I., Rahami, H., Kaveh, A.: A mesh free method using rectangular pre-solved domains using Kronecker products. Mech. Based Des. Struct. Mach. (2016). https://doi.org/10.1080/15397734.2016.1146147

    Article  MATH  Google Scholar 

  16. Onate, E., Idelsohn, S., Zienkiewicz, O., Taylor, R., Sacco, C.: A stabilized finite point method for analysis of fluid mechanics problems. Comput. Methods Appl. Mech. Eng. 139, 315–346 (1996)

    Article  MathSciNet  Google Scholar 

  17. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., Krysl, P.: Meshless methods: an overview and recent developments. Comput. Methods Appl. Mech. Eng. 139, 3–47 (1996)

    Article  Google Scholar 

  18. Szilard, R.: Theories and Applications of Plate Analysis: Classical Numerical and Engineering Methods. Wiley, Hoboken (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran

    Ali Kaveh

  2. School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran

    Hossein Rahami

  3. Align Technology Inc., San Jose, CA, USA

    Iman Shojaei

Authors
  1. Ali Kaveh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hossein Rahami
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Iman Shojaei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Kaveh .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kaveh, A., Rahami, H., Shojaei, I. (2020). Static Analysis of Nearly Regular Continuous Domains. In: Swift Analysis of Civil Engineering Structures Using Graph Theory Methods. Studies in Systems, Decision and Control, vol 290. Springer, Cham. https://doi.org/10.1007/978-3-030-45549-1_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-45549-1_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-45548-4

  • Online ISBN: 978-3-030-45549-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation