Topology Optimization In Three-dimensional Continuum Structures By BESO

Topology optimization theory is an important discipline which has enormous development space in many fields,but the development of bi-directional evolutionary structural topology optimization method is very limited which is aimed at theory research of two-dimensional structure,and the research and application of three-dimensional topology theory is less.However,the topology optimization problem of three-dimensional structure is very similar to the actual engineering structural problem,and the topological result can reflect the effectiveness of the solution intuitively,therefore,it has high research value and reference value.The main research content of this article is the stiffness optimization problem of three-dimensional structure.Firstly,basing on finite element analysis theory,this paper has expounded the evolutional optimization: the establishment of finite element model is analyzed,the principle of the method and the cause of the numerical instability phenomenon in the optimization process are analyzed and explained.Finally,the numerical examples given also demonstrate the correctness of the theory.Secondly,basing on the condition of fixed force,we have discussed the characteristics of dependent load,and completed the stiffness optimization analysis of common structure,and compared the results with the actual engineering structures.We can make a conclusion that the result of two kinds of load conditions is different in the structure,and the result of structure with dependent force is more reasonable,and it is necessary to consider the dependent force.Thirdly,basing on the condition of dependent force,we have discussed the relation of multi-materials and single material model,and completed the analysis of multi-materials theory.After comparing the two kinds of results of different models,we can conclude that the structure is consistent with the character of mechanical properties,and the structure we obtained is similar to the actual engineering structures,which demonstrates the correctness of the multi-materials theory.In the end,basing on the condition of multi-load and multi-materials,this paper has discussed the problem of stiffness optimization with additional displacement constraint,which consists of single node constraint and multiple nodes constraint.After comparing the results of volume constraint and additional displacement constraint problem,the effect can meet constraints requirement.What is more,in order to overcome the shortcomings of traditional methods which includes low efficiency and frequent oscillation,this paper has proposed a new method to solve the displacement constraint problem.The results are better than the original method and the process is more simple.Especially,when solving the multi-point displacement constraint problem,the advantage of new method is greater.