OPTIMAL DISCRETE SIZING OF TRUSS STRUCTURES SUBJECT TO BUCKLING CONSTRAINTS

The selective dynamic rounding (SDR) algorithm previously developed by the authors, and based on a dual step rounding approach, is used for the optimal sizing design of truss structures subject to linear buckli ng constraints. The algorithm begins with a continuous optimum followe d by a progressive freezing of individual variables while solving the remaining continuous problems. The allowable member stresses are predi cted by the linear regression of the tabular section properties, while the exact allowable compressive stresses are back-substituted for tho se variables fixed on discrete values in each intermediate mixed-discr ete nonlinear problem. It is shown that a continuous design based on t he regression analysis of section effectiveness vs. area is effective as a starting point for the dual step discrete optimization phase. A r ange of examples is used to illustrate that with ''conservative'' regr ession, discrete designs can be achieved which are significantly light er than those in which the variables have been rounded up.