Optimum design of cantilevered columns under the combined action of conservative and nonconservative loads: Part I: The undamped case

Abstract

This paper considers stability optimization of undamped cantilevered columns subjected to the simultaneous action of a conservative (‘dead’) load and a nonconservative (‘follower’) load at their free ends. The load combination is characterized by a ‘nonconservativeness parameter’ η, where η=0 corresponds to a purely conservative load (an Euler column) and η=1 to a pure follower load (Beck’s column). The optimization problem is considered in the form of volume minimization by constant critical load and is solved numerically by using finite elements and sequential linear optimization. It is shown that the minimum volume design for constant critical load is equivalent to the maximum critical load design for constant volume; for any design and any load combination, critical load/(volume of column) 2 = constant. Optimum designs are determined for η=0.0, 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. For the uniform column, stability is lost by divergence for η<0.5 and by flutter for η>0.5. For the optimal columns, divergence occurs only in the case η=0.0; for the other η-values considered, stability is lost by flutter. The largest benefit of optimization is obtained in the case η=0.4; here the critical load for the optimal column is more than ten times larger than for the uniform column. The stability of the optimal columns for other types of loads than the design-load is thoroughly investigated and illustrated by diagrams.