Optimization of clamped columns under distributed axial load and subject to stress constraints

Cagdas I. U., ADALI S.

ENGINEERING OPTIMIZATION, vol.39, no.4, pp.453-469, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 4
  • Publication Date: 2007
  • Doi Number: 10.1080/03052150701213013
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.453-469
  • Keywords: optimal columns, design optimization, clamped-clamped columns, distributed axial loads, stress constraints, BIMODAL OPTIMIZATION, LAGRANGE PROBLEM, OPTIMAL SHAPE, NONUNIFORM COLUMNS, STRONGEST COLUMN, OPTIMAL-DESIGN, FRAMES
  • Akdeniz University Affiliated: No


The optimum designs arc given for clamped-clamped columns under concentrated and distributed axial loads. The design objective is the maximization of the buckling load subject to volume and maximum stress constraints. The results for a minimum area constraint are also obtained for comparison. In the case of a stress constraint, the minimum thickness of an optimal column is not known a priori, since it depends on the maximum buckling load, which in turn depends on the minimum thickness necessitating an iterative solution. An iterative solution method is developed based on finite elements, and the results are obtained for n = 1, 2, 3 defined as I = a(n) A(n), with I being the moment of inertia, and A the cross-sectional area. The iterations start using the unimodal optimality condition and continue with the bimodal optimality condition if the second buckling load becomes less than or equal to the first one. Numerical results show that the optimal columns become larger in the direction of the distributed load due to the increase in the stress in this direction. Even though the optimal columns are symmetrical with respect to their mid-points when the compressive load is concentrated at the end-points, in the case of the columns subject to distributed axial loads the optimal shapes are unsymmetrical.