This paper proposes the topology optimization for steady-state heat conduction structures by incorporating the meshless-based generalized finite difference method (GFDM) and the solid isotropic microstructures with penalization interpolation model. In the meshless GFDM numerical scheme, the explicit formulae of the partial differential equation are expressed by the Taylor series expansions and the moving-least squares approximations to address the required partial derivatives of unknown nodal variables. With the relative density of meshless GFDM node as the design variable, the implementation of the topology optimization is formulated involving the minimization of heat potential capacity as the objective function under node number constraint. Moreover, sensitivity of the objective function is derived based on the adjoint method, and sensitivity filtering subsequently suppresses the checkerboard pattern. Next, the update of design variables at each iteration is solved by the optimality criteria method. At last, several numerical examples are illustrated to demonstrate the validity and feasibility of the proposed method.

通过结合基于无网格的广义有限差分法（GFDM）和带有补偿插值模型的固体各向同性微结构，提出了稳态导热结构的拓扑优化方法。在无网格GFDM数值方案中，偏微分方程的显式由泰勒级数展开和移动最小二乘近似表示，以解决未知节点变量所需的偏导数。以无网格GFDM节点的相对密度为设计变量，提出了拓扑优化的实现，其中以节点数约束下的热容量最小为目标函数。此外，目标函数的敏感性是基于伴随方法得出的，然后灵敏度过滤会抑制棋盘格图案。接下来，通过最优性准则方法解决每次迭代中设计变量的更新。最后，通过算例说明了该方法的有效性和可行性。