OPTIMIZATION OF BAR STRUCTURES WITH RANDOM IMPERFECTIONS WITH STABILITY CONSTRAINTS

Abstract

A method for the optimization of geometrically non-linear bar structures containing random global imperfections is presented. The initial imperfections are distributed randomly according to the normal law. Optimization is carried out with constraints on the unfailing operation probability of the structure for the overall loss of stability and constraints on the design variables. Criteria are formulated for the detection of asymmetric, symmetric special bifurcation points of the first or second type and the limit point. The probability density functions of buckling loads for the four types of critical points are derived. The optimization method is based on quadratic approximation of the objective function and linear approximation of the constraints on the probability that the structure does not lose stability. The method was verified on three test structures.

Keywords: optimization of geometrically non-linear rod structures, the global random imperfections, unfailing operation probability of the structure for the overall loss of stability, non-multiple singular bifurcation points, non-multiple limit points.