Skip to main content
Log in

Design of an optimum column with elastic clamping

  • Brief Notes
  • Published:
Structural optimization Aims and scope Submit manuscript

Abstract

The paper deals with the problem of finding the optimum shapes of columns with elastic clamping. It has previously been solved numerically for the particular case of columns with similar cross-sections. The present paper gives solutions to the problem of columns with various types of cross-sections and the optimal shapes are found in analytical form.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • Adali, S. 1979: Optimal shape and nonhomogenuity of nonuniformly compressed column.Int. J. Solids. & Struct. 15, 935–949

    Google Scholar 

  • Albul, A.V.; Banichuk, N.V.; Barsuk, A.A. 1980: Optimization of stability for elastic columns with thermal loads.MTT (Mechanics of Solids) 3, 127–133

    Google Scholar 

  • Banichuk, N.V. 1974: Optimization of stability for a column with an elastic clamping.MTT (Mechanics of Solids) 9, 150–154

    Google Scholar 

  • Banichuk, N.V.; Barsuk, A.A. 1982: Optimization of stability of elastic columns against simultaneons compression and torsion.Applied Problems of Strength and Plasticity, 122-126

  • Banichuk, N.V.; Karihaloo, B.L. 1977: On the solution of optimization problems with singularities.Int. J. Solids. & Struct. 13, 725–733

    Google Scholar 

  • Banichuk, N.V. Larichev, A.D. 1981: Optimization problem for reinforced composite beams subjected to compression and bending.Stroit. Mechanika i Rashchet Sooruzhenii 6, 9912

    Google Scholar 

  • Chentsov, N.G. 1936: Column of least weight.Research Articles, TsA GI 265, 1–48

    Google Scholar 

  • Clausen, T. 1851: About the shape of architectural columns.Bull. Phys. Math. Acad. St. Peterbourg 9, 279–294

    Google Scholar 

  • Karihaloo, B.L. 1979: Optimal design of multi-purpose tie-column of solid construction.Int. J. Solids & Struct. 15, 103–109

    Google Scholar 

  • Karihaloo, B.L.; Parbery R.D. 1979: The optimal design of beamcolumns.Int. J. Solids & Struct. 15, 855–859

    Google Scholar 

  • Karihaloo, B.L.; Parbery, R.D. 1980: Optimum design of beamcolumns subjected to concentrated moments.Eng. Optimiz. 5, 59–66

    Google Scholar 

  • Keller, J.B. 1960: The shape of the strongest column.Arch. Rational Mech. & Anal. 5, 275–285

    Google Scholar 

  • Keller, J.B.; Niordson, F.I. 1966: The tallest column.J. Math. Mech. 16, 433–446

    Google Scholar 

  • Lagrange, J.L. 1770–1773: Sur la figure des colonnes.Miscellanea Taurinensia V, 123

    Google Scholar 

  • Luré, A.I. 1965: Application of the maximum principle to some simplest problems of mechanics.Research Works of Leningrad Polytechnical Institute 252, 34–46

    Google Scholar 

  • Masur, E.F. 1975: Optimal placement of available sections in structural eigenvalue problems.J. Optimiz. Theory Appl. 15, 69–84

    Google Scholar 

  • Mróz, Z.; Rozvany, G.I.N. 1975: Optimal design of structures with variable support conditions.J. Optimiz. Theory Appl. 15, 85–101

    Google Scholar 

  • Mróz, Z.; Rozvany, G.I.N. 1977: Column design: optimization of support conditions and segmentation.J. Struct. Mech. 5, 279–290

    Google Scholar 

  • Nikolai, E.L. 1907: Lagrange's problem on the best shape column.Notes of the St. Petersburg Polytechnical Institute 8

  • Olhoff, N. 1981: Optimization of columns against buckling. In: Haug, E.J.; Cea, J. (eds.)Optimization of distributed parameter structures, pp. 152–176. Alphen aan den Rijn: Sijthoff and Noordhoff

    Google Scholar 

  • Olhoff, N.; Niordson, F.I. 1979: Some problems concerning singularities of optimal beams and columns.Z. Angew. Math. Mech. 59, T16-T26

    Google Scholar 

  • Olhoff, N.; Rasmussen, S.H. 1977: On single and bimodal optimum buckling loads of clamped columns.Int. J. Solids & Struct. 13, 605–614

    Google Scholar 

  • Olhoff, N.; Taylor, J.E. 1978: Designing continuous columns for minimum total cost of material and interior supports.J. Struct. Mech. 6, 367–382

    Google Scholar 

  • Tadjbakhsh, I.; Keller, J.B. 1962: Strongest columns and isoperimetric inequalities for eigenvalues.J. Appl. Mech. 9, 159–164

    Google Scholar 

  • Taylor, J.E. 1967: The strongest column; an energy approach.J. Appl. Mechanics, Trans. ASME 34, 486–487

    Google Scholar 

  • Taylor, J.E.; Lui, C.Y. 1968: Optimal design of columns.AIAA J. 6, 1496–1502

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Banichuk, N.V., Barsuk, A.A. Design of an optimum column with elastic clamping. Structural Optimization 9, 254–257 (1995). https://doi.org/10.1007/BF01743979

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01743979

Keywords

Navigation