Study On Structure Shape Optimization Using Element-free Galerkin Method And Genetic Optimal Algorithm

In recent thirty years, shape optimization has become a main aspect among structural optimizations, that find the optimal shape of a continuum medium to maximize or minimize a given criterion (often called an objective function), such as minimize the weight of the body and remove the stress concentrations, subjected to the stress or displacement constraint conditions. A novel approach to continuum shape optimization problem, combining Element Free Galerkin (EFG) with Genetic Algorithm (GA), is presented in this thesis, and the intensive study of the method is implemented.Firstly, the development of structural optimization is briefly reviewed. Structural optimization problems are concluded into three levels, one of which is shape optimization. The main study of shape optimization is reviewed. After analyze the character of traditional continuum mechanics methods and normal shape optimization methods and take full advantage of the features of meshfree method and the merits of GA, the aim and content of the thesis is brought forward.Secondly, main procedures of meshfree methods are reviewed. Moving Least Square approximation (MLS) of EFG and weight functions are described. The disposing of discontinued problem and imposition of essential boundary conditions are studied. The discrete equation from weak form equation and the numerical implement are given. Through examples, the merits and drawbacks of regular quadrature background mesh and element background mesh are analyzed in detail, and mixed background mesh is proposed. The validity is verified by numerical example.Thirdly, the basic concepts of GA are reviewed from the point of view of application. The origin, development and application in engineering design are reviewed. The execution steps of GA are introduced in detail. The characters of different encoding methods are analyzed. The choice of fitness function, relative parameters and convergence criterion are studied.Fourthly, making full use of Matlab GA toolbox, a mature and stable program design plat, and taking the toolbox's drawback which can't directly deal with implicit expression constraint condition into account, the toolbox is developed and the original function file is improved. The whole program design of the shape optimization design method using EFGM and GA is completed. The rationality and performance of the proposed approach are demonstrated via two 2-D numerical examples.Last, the representation method of changeable geometry and design variable are discussed. On the basis of the optimization of cantilever beam and fillet, which have received much attention in the shape optimization literature, compare different changeable geometry's representation method and encoding methods under different design variables. The representation method of changeable geometry, design variable and encoding method, which are suitable for shape optimization design using EFGM and GA, are concluded.