Structural Topology Optimization Through Explicit Boundary Evolution

With the rapid development of computer technology and finite element method,topology optimization has received great deal of attentions by numerous researchers and achieved remarkable progress in the past three decades.Many approaches have been proposed for structural topology optimization and it now has become an indispensable tool in many application fields such as acoustics,electromagnetics and optics.However,with the deepening of research and the continuous improvement of design requirements,the inherent problems in traditional topology optimization methods(such as implicit topology description)have seriously restricted the further application of topology optimization.Traditional topology optimization is usually carried out with approaches where structural boundaries are represented in an implicit way.However,the approaches generally suffer certain drawbacks.So the aim of the present paper is to develop a topology optimization framework where both the shape and topology of a structure can be obtained simultaneously through an explicit boundary description and evolution.Firstly,B-spline is used to describe moving morphable voids(components)which are the basic building blocks of topology optimization,since it is the most popular mathematical tool in CAD/CAM due to its flexibility and precision for free-form shapes.In the optimization process,some numerical techniques are adopted to preserve the global smoothness of the structural boundary and avoid self-intersection.Secondly,based on the concept of moving morphable voids(components),two dual formulations are proposed to do topology optimization in an explicit and geometrical way.The topology change of a two-dimensional structure can be achieved by the deformation,intersection and merging of a set of closed parametric curves,which represent the boundary of the structure.The optimal structural topology can be obtained by determining the geometry characteristic parameters,such as the shape,length,thickness,and orientation as well as the layout of these components.Thirdly,in the present explicit boundary evolution-based approach,the computational effort associated with FEA can be reduced substantially by removing the unnecessary DOFs from the FE model at every step of numerical optimization.With use of the above treatment,the time for FEA can be reduced substantially especially when the allowable volume of solid material is small.This fact has been verified by the numerical examples provide in the next section.With some numerical examples,effectiveness and robustness of present method are demonstrated.The optimization results with rich geometric information can be obtained by the method in this paper.This optimization result can be directly used for manufacturing and further design analysis,which facilitates the further application of topology optimization in practical production.