基于On-the-Fly均匀化的梯度桁架结构拓扑优化
Topology Optimization of Graded Truss Lattices Based on On-the-Fly Homogenization
摘要：
我们介绍了一个计算框架的空间变化的架构，这是适用于功能梯度桁架网格下的准静态载荷的细胞结构的拓扑优化。我们利用一阶均匀化的方法，它取代了离散桁架的一个有效的连续描述处理的有限元在一个宏观的边值问题。通过定义局部桁架架构通过一组布拉维向量，我们制定的优化问题的空间变化的基向量，并证明其可行性和性能，通过一系列的基准问题在2D（虽然该方法是足够的一般也适用于3D，如所讨论的）。位移场和拓扑结构都是宏观尺度上连续变化的未知场，并且包含正则化以获得适定性。我们认为，以前的解决方案，从对齐桁架沿主应力方向被包括作为一个特殊情况。所概述的方法的结果在异构桁架架构与平滑变化的单元格，使易于制造与可调的长度尺度（后者避免了不适定性源于经典的非凸方法没有内在的长度尺度）。
英文摘要：
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).
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