Skip to main content

Optimal Force Method: Analysis of Skeletal Structures

  • Chapter
  • First Online:
  • 4243 Accesses

Abstract

This chapter starts with presenting simple and general methods for calculating the degree of static indeterminacy of different types of skeletal structures, such as rigid-jointed planar and space frames, pin-jointed planar trusses and ball-jointed space trusses. Then the progress made in the force method of structural analysis in recent years is presented. Efficient methods are developed for the formation of highly sparse flexibility matrices for different types of skeletal structures.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
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

References

  1. Henderson JC de C, Bickley WG (1955) Statical indeterminacy of a structure. Aircr Eng 27:400–402

    Google Scholar 

  2. Maunder EWA (1971) Topological and linear analysis of skeletal structures. Ph.D. thesis, London University, IC

    Google Scholar 

  3. Kaveh A (1992) Recent developments in the force method of structural analysis. Appl Mech Rev 45:401–418

    Article  Google Scholar 

  4. Langefors B (1961) Algebraic topology and elastic networks, SAAB TN49. Linköping

    Google Scholar 

  5. Denke PH (1962) A general digital computer analysis of statically indeterminate structures, NASA-TD-D-1666

    Google Scholar 

  6. Robinson J (1973) Integrated theory of finite element methods. Wiley, New York

    MATH  Google Scholar 

  7. Topçu A (1979) A contribution to the systematic analysis of finite element structures using the force method (in German). Doctoral dissertation, Essen University

    Google Scholar 

  8. Kaneko I, Lawo M, Thierauf G (1982) On computational procedures for the force methods. Int J Numer Method Eng 18:1469–1495

    Article  MathSciNet  MATH  Google Scholar 

  9. Gilbert JR, Heath MT (1987) Computing a sparse basis for the null space. SIAM J Algebra Discr Method 8:446–459

    Article  MathSciNet  MATH  Google Scholar 

  10. Coleman TF, Pothen A (1987) The null space problem II; algorithms. SIAM J Algebra Discr Method 8:544–561

    Article  MathSciNet  Google Scholar 

  11. Patnaik SN (1986) Integrated force method versus the standard force method. Comput Struct 22:151–164

    Article  MATH  Google Scholar 

  12. Kaveh A, Jahanshahi M (2006) An efficient program for cycle basis selection and bandwidth optimization. Asian J Civil Eng 7(1):95–109

    Google Scholar 

  13. Kaveh A, Daei M (2010) Suboptimal cycle bases of graphs using an ant colony system algorithm. Eng Comput 27(4):485–494

    Article  MATH  Google Scholar 

  14. Timoshenko S, Young DH (1945) Theory of structures. McGraw-Hill, New York

    Google Scholar 

  15. Kaveh A (1974) Application of topology and matroid theory to the analysis of structures. Ph.D. thesis, London University, IC

    Google Scholar 

  16. Kaveh A (1988) Topological properties of skeletal structures. Comput Struct 29:403–411

    Article  MathSciNet  MATH  Google Scholar 

  17. Mauch SP, Fenves SJ (1967) Release and constraints in structural networks. J Struct Div ASCE 93:401–417

    Google Scholar 

  18. Müller-Breslau H (1912) Die graphische Statik der Baukonstruktionen. Alfred Kröner Verlag, 1907, und Leipzig

    Google Scholar 

  19. Kaveh A (2004) Structural mechanics: graph and matrix methods, 3rd edn. Research Studies Press, Baldock

    Google Scholar 

  20. Henderson JC de C, Maunder EWA (1969) A problem in applied topology. J Inst Math Appl 5:254–269

    Google Scholar 

  21. Kaveh A (1976) Improved cycle bases for the flexibility analysis of structures. Comput Method Appl Mech Eng 9:267–272

    Article  MathSciNet  MATH  Google Scholar 

  22. Kaveh A (1988) Suboptimal cycle bases of graphs for the flexibility analysis of skeletal structures. Comput Method Appl Mech Eng 71:259–271

    Article  MathSciNet  MATH  Google Scholar 

  23. Stepanec GF (1964) Basis systems of vector cycles with extremal properties in graphs. Uspekhi Mat Nauk 19:171–175 (in Russian)

    MathSciNet  MATH  Google Scholar 

  24. Zykov AA (1969) Theory of finite graphs. Nuaka, Novosibirsk (in Russian)

    MATH  Google Scholar 

  25. Hubicka E, Syslø MM (1975) Minimal bases of cycles of a graph. In: Fiedler M (ed) Recent advances in graph theory. Academia Praha, Prague, pp 283–293

    Google Scholar 

  26. Kaveh A, Roosta GR (1994) Revised Greedy algorithm for the formation of minimal cycle basis of a graph. Commun Numer Method Eng 10:523–530

    Article  MathSciNet  MATH  Google Scholar 

  27. Horton JD (1987) A polynomial time algorithm to find the shortest cycle basis of a graph. SIAM J Comput 16:358–366

    Article  MathSciNet  MATH  Google Scholar 

  28. Lawler EL (1976) Combinatorial optimization; networks and matroids. Holt, Rinehart and Winston, New York

    MATH  Google Scholar 

  29. Kolasinska E (1980) On a minimum cycle basis of a graph. Zastos Math 16:631–639

    MathSciNet  MATH  Google Scholar 

  30. Kaveh A, Mokhtar-zadeh A (1993) A comparative study of the combinatorial and algebraic force methods. In: Proceedings of the Civil-Comp93, Edinburgh, pp 21–30

    Google Scholar 

  31. Brusa L, Riccio F (1989) A frontal technique for vector computers. Int J Numer Method Eng 28:1635–1644

    Article  Google Scholar 

  32. Prezemieniecki JS (1968) Theory of matrix structural analysis. McGraw-Hill, New York

    Google Scholar 

  33. Pestel EC, Leckie FA (1963) Matrix methods in elastomechanics. McGraw-Hill, New York

    Google Scholar 

  34. Kaveh A (1993) Matroids applied to the force method of structural analysis. Z Angew Math Mech 73:T355–T357

    MATH  Google Scholar 

  35. Heath MT, Plemmons RJ, Ward RC (1984) Sparse orthogonal schemes for structural optimization using the force method. SIAM J Sci Stat Comput 5:514–532

    Article  MathSciNet  MATH  Google Scholar 

  36. Cassell AC (1976) An alternative method for finite element analysis; a combinatorial approach to the flexibility method. Proc R Soc Lond A352:73–89

    Article  MathSciNet  Google Scholar 

  37. Kaveh A (1979) A combinatorial optimization problem; optimal generalized cycle bases. Comput Method Appl Mech Eng 20:39–52

    Article  MATH  Google Scholar 

  38. Coleman TF, Pothen A (1986) The null space problem I; complexity. SIAM J Algebra Disc Method 7:527–537

    Article  MathSciNet  MATH  Google Scholar 

  39. Plemmons RJ, White RE (1990) Substructuring methods for computing the null space of equilibrium matrices. SIAM J Matrix Anal Appl 11:1–22

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Kaveh, A. (2014). Optimal Force Method: Analysis of Skeletal Structures. In: Computational Structural Analysis and Finite Element Methods. Springer, Cham. https://doi.org/10.1007/978-3-319-02964-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-02964-1_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02963-4

  • Online ISBN: 978-3-319-02964-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics