Three-Parameter Optimization of an Axially Loaded Beam on a Foundation

A beam of circular cross-section, made of viscoelastic material of Kelvin–Voigt type, is
considered. The beam is symmetric with respect to its center, the length and volume of the
beam are fixed and its ends are simply supported. The radius of the cross-section is a cubic
function of co-ordinate. The beam interacts with a foundation of Winkler, Pasternak or Hetényi
type and is axially loaded by a non-conservative force P(t) = P0 + P1 cos #t. Only the first
instability region is taken into account. The shape of the beam is optimal if the critical value
of P1 is maximal. A few numerical examples are presented on graphs.