基于映射的梯度点阵结构设计方法

A graded lattice structure design method based on mapping process

点阵结构因具有高比强度、高比刚度的性能优势而在航空、航天等领域具有广阔的应用前景。梯度点阵结构相比于传统的均匀点阵结构具有更优的力学性能,因此,提出了一种基于密度与应力映射的梯度点阵结构设计方法。该方法对结构进行拓扑优化以获取结构的单元相对密度与应力分布信息,并建立单元相对密度、应力与胞元支柱截面尺寸之间的映射函数关系以确定其尺寸。采用反距离加权法对单元相对密度与应力进行过滤,将材料分布在结构的主要传力路径上,并提出了在结构质量不变条件下的胞元支柱尺寸控制方法。所提方法建立不同体积与胞元密度的点阵结构只需进行一次拓扑优化设计,并且该方法可应用于较复杂结构的点阵化设计,提升了点阵结构设计的效率。所提方法已通过数值算例验证了其可行性与有效性,可推广到相关结构的轻量化设计中。

A lattice structure has broad application prospects in aviation and aerospace due to its high specific strength and stiffness.A graded lattice structure may have better mechanical performance than uniform lattice structure.Therefore,a graded lattice structure design method based on density and stress mapping was proposed in this work.The topology optimization method was utilized to obtain the element relative density and stress values,which were used to determine the strut thickness based on an established mapping function between the values and the strut thickness.The inverse distance weighting method was used to filter the relative density and stress to distribute more material on the force path,and the strut minimum dimension control method was proposed under the condition that the structure mass remains unchanged.The design of lattice structure with different volumes are based on the only once topology optimization results,which can significantly improve the design efficiency.The proposed method can be used for structures with complex geometry because the unit cells are established based on the finite elements.The feasibility and effectiveness of the proposed method were verified by a case study,which proves that the proposed method can be extended to the lightweight design of related structures.