梯度点阵结构参数化设计与优化方法

Parametric Design and Optimization of Graded Lattice Structures

针对在不同边界条件下均匀点阵结构不能充分发挥其力学性能,而梯度点阵结构建模困难的问题,提出一种梯度点阵结构的参数化设计与优化方法.首先基于STL格式表示点阵结构模型,通过建立点阵结构设计参数与相对密度的映射关系实现梯度点阵结构的参数化建模;然后采用均匀化方法获得点阵结构相对密度与等效力学性能之间的关系;最后以最小化柔顺度为目标,以边界条件和相对密度为约束条件,建立梯度点阵结构密度优化模型和求解方法.以三点弯曲梁模型为案例的实验结果表明,优化后的模型弯曲刚度提高147.2%,最大承载能力提高82.31%,验证了所提方法是可行和有效的.

In order to solve the problems that the mechanical properties of uniform lattice structure cannot be fully achieved under different boundary conditions,as well as the difficulty of modeling the graded lattice structure,a parametric design and optimization method of graded lattice structures is proposed.Firstly,the model of lattice structures is represented by STL format,and the relationship between design parameters and relative density of lattice structures is developed to realize the parametric design of graded lattice structures.Then,the relationship between relative density and equivalent mechanical properties of lattice structures is obtained using the homogenization method.Finally,the density optimization model of graded lattice struc-ture with the minimum compliance of structure under boundary conditions and relative density constraints is established and solved.The experimental results of a three-point bending beam model show that the bending stiffness of the optimized model is increased by 147.2%and the maximum load-bearing capacity is increased by 82.31%,which verifies that the proposed method is feasible and effective.