A physical driven method for constructing functionally graded lattice structure is proposed by extending the conventional Solid Isotropic Material with Penalization (SIMP) method with linear buckling load factors and total volume constraints rather than introducing local volume constraints. It can efficiently and effectively construct functionally graded lattice structure by using the SIMP material model for topology optimization with different buckling load factors according to the linearized buckling criteria and the same volume fraction, which greatly improved both the stability and stiffness of the optimal structure. Furthermore, the optimized structures of the illustrative cases are manufactured by means of the fused deposition modeling. Both the numerical analysis and mechanics experiments are further conducted to illustrate the effectiveness of the proposed method compared with the structural topology optimization with SIMP method and the infill structure. To the best of our knowledge, it is the first time to validate the topology optimization of functionally graded lattice structure via both numerical analysis and mechanics experiments.

通过使用线性屈曲载荷因子和总体积约束而不是引入局部体积约束来扩展传统的带有惩罚的固体各向同性材料 (SIMP) 方法，提出了一种用于构造功能梯度晶格结构的物理驱动方法。根据线性化屈曲准则和相同体积分数，利用SIMP材料模型在不同屈曲载荷因子下进行拓扑优化，可以高效、有效地构建功能梯度晶格结构，极大地提高了优化结构的稳定性和刚度。此外，示例性案例的优化结构是通过熔融沉积建模制造的。进一步进行了数值分析和力学实验，以说明与SIMP方法和填充结构的结构拓扑优化相比，该方法的有效性。据我们所知，这是第一次通过数值分析和力学实验验证功能梯度晶格结构的拓扑优化。