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论文类型：期刊论文

发表时间：2018-09-14

发表刊物：INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

收录刊物：SCIE

卷号：115

期号：11

页面范围：1315-1336

ISSN号：0029-5981

关键字：general design variable; level set; mathematical programming algorithm; multiple constraints; topology optimization; velocity field

摘要：In this paper, we propose a new implementation of the level set shape and topology optimization, the velocity field level set method. Therein, the normal velocity field is constructed with specified basis functions and velocity design variables defined on a given set of points that are independent of the finite element mesh. A general mathematical programming algorithm can be employed to find the optimal normal velocities on the basis of the sensitivity analysis. As compared with conventional level set methods, mapping the variational boundary shape optimization problem into a finite-dimensional design space and the use of a general optimizer makes it more efficient and straightforward to handle multiple constraints and additional design variables. Moreover, the level set function is updated by the Hamilton-Jacobi equation using the normal velocity field; thus, the inherent merits of the implicit representation is retained. Therefore, this method combines the merits of both the general mathematical programming and conventional level set methods. Integrated topology optimization of structures with embedded components of designable geometries is considered to show the capability of this method to deal with general design variables. Several numerical examples in 2D or 3D design domains illustrate the robustness and efficiency of the method using different basis functions.