Optimal Design Of Single-layer-bars Spatial Structures Based On Genetic Algorithm

Optimal design of single-layer-bars spatial structures with circular planarprojection is a hot spot in optimal design of discrete structures. Previous studies onthis issue which always take spherical radius of curvature, grid number in structuresand sections of bars as optimization variables are all based on one or several kindsof single-layer spherical reticulated shells. The optimal results obtained are still onekind of single-layer spherical reticulated shells which have specific manner of bar-connection. The optimization method established in this thesis overcomes thelimitations to a certain extent and makes a new exploration on the optimal designmethod of this kind structure.This thesis learns from the thought of ground structure method commonly usedin the topology optimization of trusses and constructs a new mesh based on whichthe initial bars-layout scheme forms. Bars and nodes were classified according tosymmetry. A set of possible vertical positions to each group of nodes and two typesof states (layout or no layout) to each group of bars were given, and a section tablewas created in which sections were arranged in ascending order according toproperties of sections. Based on Genetic Algorithm, shape, bars-layout, sections ofbars optimization methods were established. The interaction between the threeoptimization variables were tested and verified through examples.The bars-layout optimization method was established on the basis of dealingwith problems including the destruction of structural integrity, optimization gap andredistribution of load on invalid nodes. Destruction of structural integrity refers tothat isolated islands of bars or bars’ group may appear during optimal designprocess of bars-layout which will lead to a singular stiffness matrix of structure.Optimization gap refers to that a worse bars-arrangement occurred when a bad bars-arrangement transmitted to a better arrangement. Invalid node refers to node that nobar takes it as endpoint in the optimal layout process. Redistribution of loads oninvalid nodes refers to assign these loads to the adjacent nodes according to certainrules.On the basis of the work above, the layout-optimization method wasestablished in this paper which can optimize shape, bars-layout and sections of barsat the same time. The key is: three chromosomes were used to store information ofshapes, bars-layout and sections of bars of a structure respectively. These threechromosomes were defined as one group. According to the related rules formulated,genetic algorithm operations were carried out taking a set of chromosomes as a unit.Using layout-optimization method, the optimal design of structures with constraint-conditions of nodes or constraint-conditions of holes or neitherconstraint-conditions of nodes nor constraint-conditions of holes were studiedrespectively. Constraint-conditions of nodes or holes refer to some nodes or holes inthe structure must exist. Related optimal results show that: the locations andnumbers of restricting nodes, the presence or absence of restricting nodes and holeswill have impact on the results of optimal design.In addition, in order to improve the efficiency of optimization of single-layerspherical reticulated shell structures, the secondary optimization programs werewritten. Based on the structure-database, which composed of optimal resultsobtained in the section optimization of each structure scheme using GeneticAlgorithm from the first part of the program, the optimum structure scheme can beobtained, which was evaluated by mass under certain span and loading conditions.