Studies On Problems Of Structure Topology Optimization Algorithm

Topology Optimization(the optimization of the structure layout)is an optimization method to find the structural material optimal arrangements based on constrains, loads and optimal objectives, which can greatly improve the performance of the structure or save the materials and can bring lots of economic return. As a new branch of structure mechanics, it can not only solve difficult problems in optimization, but also have significant practical value. Topology optimization can be stated as finding the optimal arrangement of structural material by gradually removing or redistributing the material in a given design domain which is an unshaped model just with outer boundary rather then initial ordered structure. So, research in topology optimal design method is essential in both theoretical study and practical application.This paper presented the resent advances in optimization; gave out the groundwork of topology optimization, included the model sorts such as mechanical model, mathematical model and their solution; and then compared the advantage and disadvantage of the two kinds of mechanical model (truss-like structure and continuum structure).In this paper two optimization methods were presented: 1) optimal criteria method based on SIMP(Simplified Isotropic Material with Penalization); 2) boundary element method based on ESO (Evolutionary Structural Optimization).Optimal criteria (OC) method is to set up the criteria of optimal design from a certain assumption and interactive formula, and then solve interactively. This method is characterized of rapid convergence, less iterations and the number of reanalysis independent on the structural variables and its complications, which is benefit for the large-scaled structures, especially for the structure constrained with structural properties and necessary to calculate the derivatives by FEM. However, it needs different optimal criteria for different kinds of optimal problems. Otherwise, the constraints acting or not should be distinguished. Therefore, OC is always used to solve the single-constraint problems with less constraint condition. For the model with OC based on SIMP, the expression and description of the topology is the base ground of topology optimization. The author systematically studied the homogenization theory and SIMP material interpolation method, set up the topology optimal model of continuum structure with SIMP.Boundary element method (BEM) based on ESO combine the evolutionary optimization concept with BEM analysis to describe the trend of boundary line by NURBS curve. Choose and confirm control points as the design variables, insert holes in low stress region to achieve the optimization. The holes'boundary described by NURBS curve has the similar properties with the outer boundary. This method has the advantages of both ESO and BEM. Besides, the inner boundary provides large flexibility in design. And the borders remain stable in each iteration step except customizing stress concentration.Finally, the developments of topology optimization are given.