Optimal shapes of clamped–simply supported columns under distributed axial load and stress constraint

Abstract

The optimal cross-sectional shapes of clamped-simply supported columns are presented with the compressive load given by a combination of a non-uniform distributed load and a concentrated load. The buckling load is maximized subject to constraints on the volume of the column and on the maximum stress. The non-symmetry of the boundary conditions leads to optimal shapes which depend on the direction of the distributed load, with the optimal cross-section getting larger in the direction of the distributed load. This is a major difference in the optimal design of columns with symmetrical and asymmetrical boundary conditions when subjected to distributed axial loads. The minimum cross-sectional area is not known a priori in the case of a stress constraint since this depends on the buckling load, which in turn depends on the optimum shape. This aspect is the main difference between the optimal designs of area-constrained and stress-constrained columns. An iterative method is developed to compute the optimal shapes with the analysis performed using a finite element method. Results are given for various combinations of distributed and concentrated loads and constraints. Results for optimal columns with a minimum area constraint are also given for comparison purposes.

Unimodal Optimization of Axially Compressed Shear Deformable Columns

“…Also, this exclusion leads to thinner sections, which is important especially when optimizing statically indeterminate columns as the unimodal optimality condition leads to optimal designs where area vanishes at certain parts of the statically indeterminate columns. Also, stress has been used as a constraint in only a few papers [7][8][9], which becomes important when column length is short or material is weak.…”