梯度空心多孔结构优化设计方法

Optimization Design Method for Graded Hollow Cellular Structures

针对空心多孔结构参数化建模困难、承载性能不足的问题,提出了一种梯度空心多孔结构优化设计方法。将不同水平参数的I-WP(I-wrapped package)型三周期极小曲面进行布尔运算实现了空心多孔结构单胞的隐式建模,并基于数值均匀化法对该结构的等效弹性属性进行了评估。通过引入凸优化理论的仿射概念,构造混合水平集函数,实现了梯度空心多孔结构的参数化建模;以刚度最大化为目标函数,建立了基于混合水平集方法的梯度空心多孔结构拓扑优化模型,通过优化准则算法进行求解,得到了具有良好连续性的梯度多孔结构。对优化结构进行了有限元分析,并采用选择性激光烧结技术制造了模型样件,开展了力学实验。数值案例和实验结果表明,该方法可有效实现空心多孔结构的参数化设计,显著提高了多孔结构的承载性能。

To realize the parametric modeling and improve load-bearing capacity of hollow cellular structures,an optimization design method for graded hollow cellular structures was proposed.The implicit modeling of hollow cellular unit cell was realized by the Boolean operation of I-Wrapped Package(I-WP)triply periodic minimal surfaces(TPMS)with different level parameters.The numerical homogenization method was applied to evaluate the effective elastic properties of hollow cellular structures.By introducing the affine concept of convex optimization theory,the hybrid level set function(LSF)was constructed to realize the parametric modeling of the graded hollow cellular structures.A graded hollow cellular structures topology optimization model was established with the maximum stiffness based on the HLSM.The optimality criteria(OC)was used to solve the model to obtain a cellular structure with superior continuity.The finite element method was performed to analyze the mechanical performance of the optimized structures.Then selective laser sintering(SLS)technology was used to manufacture specimens and the mechanics experiments were carried out.Numerical examples and experimental results show that this method may effectively realize the parametric design of hollow cellular structures,and significantly improve the load-bearing performance of the structures.