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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >'Color' level sets: a multi-phase method for structural topology optimization with multiple materials
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'Color' level sets: a multi-phase method for structural topology optimization with multiple materials

机译：“颜色”级集：使用多种材料进行结构拓扑优化的多阶段方法

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摘要

In this paper we address the problem of structural shape and topology optimization in a multi-material domain. A level-set method is employed as an alternative approach to the popular homogenization-based methods of rule of mixtures for multi-material modeling. A multi-phase level-set model is adapted for material and topology representation. This model eliminates the need for a material interpolation or phase mixing scheme. It only requires m level-set functions to represent a structure of n = 2~m different material phases, in a principle similar to combining colors from the three primary colors. Therefore, this multi-phase model may be referred to as a "color" level-set representation which has its unique benefits: it is flexible to handle complex topologies; it substantially reduces the number of model functions when n > 3; it automatically avoids the problem of overlap between material phases of a conventional partitioning approach. We describe numerical techniques for efficient and robust implementation of the method, by embedding a rectilinear grid in a fixed finite element mesh defined on a reference design domain. This would separate the issues of accuracy in numerical calculations of the physical equation and in the level-set model propagation. A gradient projection method is described for incorporating multiple constraints in the problem. Finally, the benefits and the advantages of the developed method are illustrated with several 2D examples of mean compliance minimization of multi-material structures.
机译：在本文中，我们解决了多材料领域中结构形状和拓扑优化的问题。水平设置方法用作流行的基于均质化的多材料建模混合物规则的替代方法。多相水平集模型适用于材料和拓扑表示。该模型消除了对材料插值或相位混合方案的需要。它只需要m个水平设定函数即可表示n = 2〜m个不同材料相的结构，其原理类似于组合三种原色的颜色。因此，这种多阶段模型可以称为“颜色”水平集表示形式，它具有其独特的优势：灵活地处理复杂的拓扑；当n> 3时，它将大大减少模型函数的数量；它自动避免了传统分区方法的材料相之间重叠的问题。通过将直线网格嵌入参考设计域中定义的固定有限元网格中，我们描述了用于高效，稳健实现该方法的数值技术。这将把物理方程的数值计算和水平集模型传播中的精度问题分开。描述了一种用于在问题中包含多个约束的梯度投影方法。最后，用几个二维示例说明了所开发方法的优点和优点，这些示例均显示了最小化多材料结构的平均柔度。

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