Discrete sizing optimization of stepped cylindrical silo using PSO method and implicit dynamic FE analysis

Considering the size discreteness of commercially available metal plates and the intrinsic buckling strength vulnerability of slender silo, this paper proposed a methodology, which integrated the nonlinear implicit dynamic Finite Element Method (FEM), Particle Swarm Optimization (PSO) algorithm and MATLAB programming, to optimize the wall-thickness layout for stepped thin-walled cylindrical silo, with the objective of minimizing silo mass while ensuring its structural stability. Taking into account both practicality and reliability, silo discharge loads were amplified 1.6 times to try to reflect the comprehensive effectiveness of negative and positive factors on slender silo buckling strength. When evaluating the fitness of PSO method, nonlinear implicit dynamic FEM results, such as kinetic energy history data plots, total energy history data plots, etc., were used to intuitively determine whether silo buckled or not. In essence, the optimal wall-thickness layout problem of a stepped silo is an NP-hard combinational optimization problem. The discrete thicknesses of rolled metal plates set an unavoidable constraint on stepped silo size optimization, which implies that there are only a few specific thickness values could be selected. In addition, the data of plate width are also discrete and one width value might correspond to several thickness data. For reasons for saving the potential cutting costs, the heights of most silo segments should be an integral multiple of the corresponding plate width value as far as possible, while the overall height of the silo should be kept still. To realize this goal, numerical processing techniques, such as generating a random number from a uniformly distributed set of discrete positive integers, linear normalization and linear interpolation, etc., were applied in this study.