Topological design for mechanical metamaterials using a multiphase level set method

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• 作者：Yu Wang ; Zhen Luo ; Nong Zhang ; Tao Wu
• 关键词：Thermoelastic metamaterials ; Microstructures ; Topological optimization ; Let set method
• 刊名：Structural and Multidisciplinary Optimization
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：54
• 期：4
• 页码：937-952
• 全文大小：5,652 KB
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Computer-Aided Engineering and Design
  Numerical and Computational Methods in Engineering
  Engineering Design
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1615-1488
• 卷排序：54

文摘

Metamaterials usually refer to artificially engineered composites with unusual properties that cannot be easily found in nature. This paper will develop a topological shape optimization method for design of mechanical metamaterials of thermoelastic micro-structured composites, which integrates numerical homogenization method with a multi-phase level set method (MPLSM). The homogenization method is applied to evaluate the effective macroscopic properties of a periodic microstructure, while the MPLSM will be utilized to implement shape and topology evolutions of the microstructure. A multi-phase level set representation model is established to describe the boundaries of the multi-material microstructure using a combination of all level set functions, without overlaps and empties. The Hamilton-Jacobi partial differential equation-based topological shape optimization problem will be transformed to a generalized size optimization problem. Typical numerical examples are used to demonstrate the effectiveness of the proposed method for designing metamaterials with expected and extreme thermal expansion coefficients.