Study On Structural Topology Optimization Based On Parameterized Level Set Method And Numerical Manifold Element

As a structural design method,the topology optimization enables the structure to find the optimal shape of the structure satisfying the optimal performance in a given design domain under certain constraint conditions.Compared with other topology optimization methods,the parameterized level set method can generate clear and smooth structural boundaries.The traditional parameterized level set method is limited by the low continuity and high mesh requirements of the finite element method,and it is greatly limited in the calculation accuracy and the accurate representation of complex boundary.The numerical manifold method uses two cover systems to discrete the model,which can effectively and accurately represent the complex boundary of the design domain.combining the above two points,a new 3D numerical manifold element and a new topology optimization method that couples PLSM and the NMM has been proposed in this thesis.Firstly,a new 3D numerical manifold element has been proposed in this thesis.The derivation process of this element and the formulations of this element in 2D cases are given.To improve the calculation accuracy of the elements around the complex boundary,this thesis proposed a new mesh generation technology and a simplex integral method based on the multilevel subdivision technology.Secondly,a parameterized level set method based on numerical manifold method is proposed in this thesis.This method uses the compactly supported radial basis function(CSRBF)to realize the interpolation of the level set function,and the method of moving asymptotes(MMA)to update the design variables.The sensitivity analysis,the interpolation scheme,the calculation of stiffness and volume fraction,and the simple procedure of this new method are given.Finally,this thesis uses a 2D cantilever beam example to verify the effectiveness of the new method,and analyzes the influence of mesh size and initial design.Several examples with complex boundaries are used to study the application of the new method under complex boundaries conditions,and a 3D cantilever beam example is used to verify the effectiveness of this method in 3D conditions.The results show that the new method can reflect the advantages of numerical manifold element and parametrized level set method,and has a good application prospect.