Flat rod systems: optimization with overall stability control
An algorithm for discrete optimization of steel flat rod systems was developed on the basis of an evolutionary search. The task is to minimize the weight of the bars via taking into account constraints on stresses, displacements, and overall stability. The cross-sectional dimensions of the bars and the coordinates of their node connections were varied. Buckling is taken into account when stability is lost both in the object plane and out of the plane. Analysis of deformations of the considered structure variants was performed via the displacement-based finite element method. An iterative procedure for solving the task was formulated by using an auxiliary elite population, combined approaches to selection and mutation, and single-point crossover. The primary feature of the proposed computing scheme is simplified structure stability verification by determining stress-strain conditions with a tangent stiffness matrix and the additional self-balanced system of small fictitious forces. Assessment as to how constraint on stability was met was performed based on the results of the considered convergence of the internal iteration cycle used for analyzing load-carrying system behavior by taking into account the influence of longitudinal forces on the bars while bending. It was calculated that it is sufficient to perform only 3–5 iterations of this procedure to verify structure stability. Efficiency of the proposed algorithm is illustrated via the example of optimization of bar system with two supports and a frame with a girder truss.