This paper focuses on the utilization of local radial basis functions (LRBFs) based level set method (LSM) for topology optimization of two-dimensional thermal problems using both concentrated as well as uniformly distributed heat generation. The design domain is embedded implicitly into a higher-dimensional function, which is parametrized with the LRBFs through an explicit scheme. This novel combination of LRBFs and LSM has the capability of controlling the topological variations automatically, i.e., hole insertion, merging with each other and with the boundary. The governing equations of heat conduction system are solved with the finite element method to obtain the sensitivities at level set grid points as a velocity field for evolution of the structural geometry. The objective function is set to the heat transfer potential with the maximum material volume as the design constraint. Several experiments are conducted on benchmark test problems and the resulting optimal solutions reveals efficiency, convergence and good agreement with those reported in the literature.

本文侧重于利用基于局部径向基函数 (LRBF) 的水平集方法 (LSM) 对使用集中和均匀分布的热量生成的二维热问题进行拓扑优化。设计域隐式嵌入到高维函数中，该函数通过显式方案用 LRBF 进行参数化。LRBF 和 LSM 的这种新颖组合具有自动控制拓扑变化的能力，即孔插入、相互合并以及与边界合并。利用有限元法求解热传导系统的控制方程，得到水平集网格点的灵敏度，作为结构几何演化的速度场。目标函数设置为以最大材料体积为设计约束的传热势。对基准测试问题进行了多次实验，得到的最佳解决方案显示出效率、收敛性和与文献中报道的那些一致。