Topology Optimization of Structures Made of Discrete Geometric Components With Different Materials
Topology Optimization of Structures Made of Discrete Geometric Components With Different Materials
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DOI：
10.1115/1.4040624
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发表时间：
2018-09
影响因子：
3.3
通讯作者：
Hesaneh Kazemi;A. Vaziri;Julián A. Norato
中科院分区：
文献类型：
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作者：
Hesaneh Kazemi;A. Vaziri;Julián A. Norato
我们提出了一种新的方法，同时拓扑优化和材料选择的离散几何部件，其中每个组件是由多种可用的材料之一的工会的结构。我们的方法是基于几何投影方法，从而一个分析描述的几何组件被顺利地映射到一个密度场上的一个固定的分析网格。除了规定组件的尺寸、位置和方向的参数之外，每个可用材料的尺寸变量被分配给每个组件。尺寸变量值为1表示零部件由相应的材料制成。此外，所有尺寸变量都可以为零，这意味着组件完全从设计中删除。我们通过在优化中的聚合约束惩罚大小变量的中间值。我们还引入了一个相互材料排斥的约束，以确保在最多一种材料有一个统一的大小变量在每个几何组件。除了这些限制，我们提出了一种新的聚合方案，执行工会的几何组件与不同的材料。这些成分有助于处理多材料情况。我们的配方可以很容易地扩展到任何数量的材料。我们证明了我们的方法与几个数值例子。
We present a new method for the simultaneous topology optimization and material selection of structures made by the union of discrete geometric components, where each component is made of one of multiple available materials. Our approach is based on the geometry projection method, whereby an analytical description of the geometric components is smoothly mapped onto a density field on a fixed analysis grid. In addition to the parameters that dictate the dimensions, position, and orientation of the component, a size variable per available material is ascribed to each component. A size variable value of unity indicates that the component is made of the corresponding material. Moreover, all size variables can be zero, signifying the component is entirely removed from the design. We penalize intermediate values of the size variables via an aggregate constraint in the optimization. We also introduce a mutual material exclusion constraint that ensures that at most one material has a unity size variable in each geometric component. In addition to these constraints, we propose a novel aggregation scheme to perform the union of geometric components with dissimilar materials. These ingredients facilitate treatment of the multi-material case. Our formulation can be readily extended to any number of materials. We demonstrate our method with several numerical examples.