Structural Skeleton Based Feature Size Control Method In Structural Topology Optimization

Recent decades have witnessed tremendous development and applications of structural topology optimization in a wide range of industrial fields. However, with the increasing complexity and extensiveness of the concerning problems, structural topology optimization is facing more and more challenging issues. The present dissertation aims to address one of the long-standing and challenging problems in structural topology optimization:structural feature size control of the optimal topology.Structural feature size refers to the geometry parameter that can represent the structural feature such as length of the component, width of the section or radius of the fillet, In engineering design, the width of beam’s section is often required to be smaller than a threshold value with the consideration of manufacture ability. Sometimes, from stability point of view, the width of beam’s section is required to be greater than a prescribed value. In embed components system, the distance between some special components should be greater/smaller than a critical value in order to guarantee the safety and stability. In order to overcome the existing challenges, the present dissertation conducts various researches on structural feature size control problem based on structural skeleton which is a key concept in computational geometry field.Firstly, the definition of structural size and structural feature size is given for the first time through the introduction of structural skeleton. The structural feature size control method introduced in this dissertation is local and explicit. The method is proved theoretically through two propositions.Secondly, skeleton based structural feature size control method is a pure geometry constraint. It doesn’t depend on specific physical problem or topology optimization framework. In the present dissertation, the identification of structural skeleton, structural feature size constraint, problem formulation and shape sensitivity analysis are given under SIMP and Level set framework, respectively. Some numerical examples are also illustrated to demonstrate the effectiveness of the proposed approach.Lastly, the structural skeleton based feature size control approach can not only control the feature size of the solid material, but also it can be applied to the holes in the structure. An explicit layout control method is introduced based on feature size control method proposed in the present dissertation. Compared with traditional non-overlap constraint, explicit layout control problem is more complex and potential in application.In the present dissertation, both numerical practice and theoretical analysis are considered. It provides an innovative idea for feature size control in structural topology by the introduction of structural skeleton which can contain all the geometry information of the structure. The present research can give a novel reference for the application of structural topology optimization in complex structure and important equipment innovative design.