![]() In PLSM, the level set function can be parameterized with several kinds of basis functions including globally supported radial basis functions (GSRBFs), compactly supported radial basis functions (CSRBFs), and so on. The conventional LSM is lack of ability for forming new holes in structures, thus some holes should be dug in the primary structures by initializing the level set functions, thus the results of such a method are greatly dependent on the initial designs of structures.įor improving the computational efficiency and stability as well as the ability for forming new holes in structures, reducing the calculation complexity and dependence on initial designs in the conventional LSM, the parameterized level set method (PLSM) was firstly proposed by Wang and his co-workers . ![]() Such a procedure, whose step length is limited by the Courant–Friedrichs–Lewy (CFL) condition, requires re-initialization for ensuring numerical stability . The evolution of boundaries of a solid domain in conventional LSM depends on solving an initial value Hamilton–Jacobi (H-J) partial differential equation (PDE). In comparison with density-based methods like SIMP method and ESO method, level set-based topology optimization methods are well-known for their capability for forming clearer boundaries of structures, which is brought by the updating scheme based on moving the boundaries of solid domains implicitly. The rapid development of additive manufacturing also contributes a lot to the development of topology optimization, for its ability to manufacture products from topology optimization, which often have irregular shapes . For this reason, topology optimization has gained more and more attention these days. Topology optimization can be used to improve some specific performances of structures and reduce the consumption of materials. Until now, various kinds of methods for realizing topology optimization have been proposed, including the homogenization based approach , the solid isotropic material with penalization (SIMP) method ,, , the level set method (LSM) ,, the evolutionary structural optimization (ESO) method ,, the moving morphable components (MMC) method ,, etc. Topology optimization is an effective technology for designing well-suited material distributions of structures in different proposes. ![]() Several computing tests are presented in this paper, which verify the stability, efficiency, scalability, and the potential to discover new structure styles of the framework. To realize the combination of distributed memory parallel computing technology and parameterized level set topology optimization using unstructured meshes, several means are taken: (1) the shape functions in finite element analysis are employed to parameterize the level set function (2) the data structure called directed acyclic graph is adopted to represent the unstructured mesh (3) the passive domain and boundary conditions are imposed directly on the geometry entities of the structures (4) a multiple averaging filter is introduced to reduce the tiny structural members in the optimized results for the requirement of manufacturability. A parallel parameterized level set topology optimization framework for large-scale structures with unstructured meshes is proposed in this work, in which the full-scale optimization is realized with distributed memory parallel computing technology while the arbitrary geometries and complex boundary conditions are conveniently handled with the usage of unstructured meshes. In addition to the requirements of full-scale optimization, the adaptability to structures with arbitrary geometries and complex boundary conditions is also important to topology optimization in practical engineering applications.
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