论文标题
基于在线均质化的拓扑优化分级桁架晶格
Topology Optimization of Graded Truss Lattices Based on On-the-Fly Homogenization
论文作者
论文摘要
我们引入了一个计算框架，用于具有空间变化的架构的蜂窝结构的拓扑优化，该结构适用于在准持续负载下功能分级的桁架晶格。我们利用了一阶均质化方法，该方法将离散的桁架替换为有效的连续性描述，该描述在宏观边界价值问题中被有限元素处理。通过通过一组Bravais矢量来定义局部桁架体系结构，我们就空间变化的基础向量提出了优化问题，并通过2D中的一系列基准问题证明了其可行性和性能（尽管该方法足够通用，可以在3D中适用于3D）。位移场和拓扑都在宏观上不连续变化，并且包括适当的定期化。我们认为，从沿原理压力方向对齐桁架获得的先前解决方案被作为特殊情况。概述的方法导致具有平稳变化的单元电池的异质桁架体系结构，从而可以轻松地制造出可调长度的尺度（后者避免了由经典的非convex方法构成的不属性，而没有内在长度尺度）。
We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order homogenization approach, which replaces the discrete truss by an effective continuum description to be treated by finite elements in a macroscale boundary value problem. By defining the local truss architecture through a set of Bravais vectors, we formulate the optimization problem with regards to the spatially varying basis vectors and demonstrate its feasibility and performance through a series of benchmark problems in 2D (though the method is sufficiently general to also apply in 3D, as discussed). Both the displacement field and the topology are continuously varying unknown fields on the macroscale, and a regularization is included for well-posedness. We argue that prior solutions obtained from aligning trusses along the directions of principal stresses are included as a special case. The outlined approach results in heterogeneous truss architectures with a smoothly varying unit cell, enabling easy fabrication with a tunable length scale (the latter avoiding the ill-posedness stemming from classical nonconvex methods without an intrinsic length scale).
