Design and Applications of Triply Periodic Minimal Surfaces: A Survey
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摘要: 三周期极小曲面是一种隐函数表示的代数曲面,具有许多优良的性质.增材制造技术的快速发展极大地增强了复杂几何与拓扑结构的制造能力,三周期极小曲面作为几何建模工具越来越受到关注.首先,从数学表达、性质、应用以及几何设计方法等方面对三周期极小曲面的研究现状进行介绍;其次,对三周期极小曲面在力学、传热传质、组织工程和声学等方面的性能及相关应用进行总结,从几何建模方法的角度对三周期极小曲面进行分类梳理,将现有工作分为规则单元法、参数单元法、区域拼接法以及整体优化法4类,对各方法特点进行分析;最后,结合实际应用对该领域面临的挑战进行总结,并展望未来工作与发展趋势.Abstract: Triply Periodic Minimal Surface is a kind of algebraic surface expressed by implicit function. The rapid development of additive manufacturing technology has greatly enhanced the manufacturing capabilities of complex geometries and topological structures, Triply Periodic Minimal Surface, as a powerful geometric modeling tool, has received more and more attention. Firstly, this paper introduces the current research status of Triply Periodic Minimal Surface in terms of mathematical expression, properties, applications, and geometric design methods. Secondly, the mechanical property, heat and mass transfer, tissue engineering and acoustics performance are summarized. The existing works related to Triply Periodic Minimal Surface are classified and combed from the perspective of geometric modeling methods. They are grouped into four categories: regular unit method, parametric unit method, region splicing method and overall optimization method. The characteristics of each method are analyzed. Finally, in accordance with practical applications, we summarized challenges and prospected future works in this field.
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