点阵优化(OptiStruct)

Lattice Structure Optimization

0、Introduction

Lattice Structure Optimization is a novel solution to create blended Solid and Lattice structures from concept to detailed final design. This technology is developed in particular to assist design innovation for additive layer manufacturing (3D printing). The solution is achieved through two optimization phases. Phase I carries out classic Topology Optimization, albeit(虽然，即使)reduced penalty options are provided to allow more porous（多气孔的）material with intermediate density to exist. Phase II transforms porous zones from Phase I into explicit（显示的，明确的）lattice structure. Then lattice member dimensions are optimized in the second phase, typically with detailed constraints on stress, displacements, etc. The final result is a structure blended with solid parts and lattice zones of varying material volume. For this release（发布，版本）two types of lattice cell layout are offered: tetrahedron and pyramid/diamond cells derived from tetrahedral and hexahedral meshes, respectively. For this release the lattice cell size is directly related to the mesh size in the model.

点阵结构优化是一种新颖的解决方案，可从概念到详细的最终设计，创建了混合的固体和晶格结构。该技术尤其用于辅助添加剂层制造（3D打印）的设计创新。该解决方案通过两个优化阶段实现。第一阶段进行经典的拓扑优化，尽管提供了减少的惩罚选项，以允许存在具有中等密度的更多孔材料。阶段II将多相区域从阶段I转换为显式晶格结构。然后，在第二阶段优化晶格构件尺寸，通常具有对应力，位移等的详细约束。最终结果是与实心部件和不同材料体积的晶格区域混合的结构。对于该版本，提供了两种类型的晶格单元布局：分别来自四面体和六面体网格的四面体和金字塔/金刚石单元。对于此版本，晶格单元大小与模型中的网格大小直接相关。

Motivation（动机）

Lattice Structure Optimization is initially similar to topology optimization; however, design domains can now include elements with intermediate densities. Theoretically, from a physical point of view, such structures can be more efficient compared to those in which design elements are penalized to densities of 0 or 1.

格结构优化最初类似于拓扑优化; 但是，设计域现在可以包含具有中间密度的元素。从理论上讲，从物理角度来看，与设计元素受到0或1密度惩罚的结构相比，这种结构可以更有效。

Figure 1: Difference between Lattice Optimization (Phase 1) and Topology Optimization.

A possible major application of Lattice Structure Optimization is Additive Layer Manufacturing which can take advantage of the intricate（复杂的）lattice representation of the intermediate densities. This can lead to more efficient structures as compared to blocky structures, which require more material to sustain similar loading.

点阵结构优化的一个主要应用是增材制造，其可以利用中间密度的复杂晶格表示。与块状结构相比，这可以导致更有效的结构，块状结构需要更多的材料来维持类似的负载。

It should be noted that typically porous material represented by periodic lattice structures exhibits lower stiffness per volume unit compared to fully dense material. For tetrahedron and diamond lattice cells, the homogenized Young's modulus to density relationship is approximately given as

, where E0 specifies Young's modulus of the dense material.

应当注意，与完全致密的材料相比，通常由周期性晶格结构表示的多孔材料表现出每单位体积更低的刚度。对于四面体和金刚石晶格单元，均匀化的杨氏模量与密度的关系近似给出，其中E0指定致密材料的杨氏模量。

Varying levels of lattice/porous domains in topology results are controlled by the parameter POROSITY. With POROSITY defined as LOW, the natural penalty of 1.8 is applied, which would typically lead to a final design with mostly fully dense materials distribution (or voids) if a simple 'stiffest structure' formulation (compliance minimization for a given target volume) is applied.

拓扑结果中不同层次的格子/多孔域是由参数孔隙度控制的。由于孔隙度被定义为低，应用了1.8的自然惩罚，这通常会导致最终的设计，如果一个简单的“最硬结构”的公式（给定目标量的遵从最小化）被应用，那么它的最终设计将会是完全密集的材料分布（或空洞）。