设计和优化多重加载条件下的功能分级三角晶格

IF 6.9 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
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引用次数: 0

摘要

使晶格填充物与加载物体的主应力方向保持一致对于提高刚度至关重要。然而,这一原理仅适用于单一加载条件,即二维应力场由两个正交主应力方向描述。在本文中,我们介绍了一种设计和优化三角晶格结构的新方法,以适应多重加载条件,即需要考虑多重应力场。我们的方法包括两个主要步骤:基于同质化的拓扑优化和基于几何的去同质化。为确保三角形网格的几何规则性,我们提出了一般秩 3 层压板的简化版本,并使用具有唯一边缘厚度的等边三角形对设计域进行参数化。在优化过程中,边缘厚度和方向会根据网格的同质化特性进行调整。我们的数值研究结果表明,与使用一般的秩 3 层板相比,这种简化只会导致刚度略微下降,降幅小于 5%,并能产生几何规则性极强的晶格结构。对于基于几何的去均匀化,我们采用场对齐三角测量法生成全局一致的三角形网格,其中每个三角形都根据优化的方向场定向。我们处理多重加载条件的方法类似于处理单一加载条件的去均匀化技术,可生成高度精细、优化和空间变化的晶格结构。这种方法的计算效率很高,因为模拟和优化是在设计域的低分辨率离散化条件下进行的。此外,由于我们的方法是基于几何的,因此获得的结构被编码成紧凑的几何格式,便于编辑和制造等下游操作。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Design and optimization of functionally-graded triangular lattices for multiple loading conditions

Design and optimization of functionally-graded triangular lattices for multiple loading conditions

Aligning lattice infills with the principal stress directions in loaded objects is crucial for improving stiffness. However, this principle only works for a single loading condition, where the stress field in 2D is described by two orthogonal principal stress directions. In this paper, we introduce a novel approach for designing and optimizing triangular lattice structures to accommodate multiple loading conditions, i.e., multiple stress fields need to be considered. Our method comprises two main steps: homogenization-based topology optimization and geometry-based de-homogenization. To ensure geometric regularity of the triangular lattices, we propose a simplified version of the general rank-3 laminate and parameterize the design domain using equilateral triangles with unique edge thickness. During optimization, edge thicknesses and orientations are adjusted based on the homogenized properties of the lattice. Our numerical findings demonstrate that this simplification introduces only a slight decrease in stiffness of less than 5% compared to using the general rank-3 laminate, and results in lattice structures with compelling geometric regularity. For geometry-based de-homogenization, we adopt a field-aligned triangulation approach to generate a globally consistent triangle mesh in which each triangle is oriented according to the optimized orientation field. Our approach for handling multiple loading conditions, akin to de-homogenization techniques for single loading conditions, yields highly detailed, optimized and spatially varying lattice structures. The method is computationally efficient, as simulations and optimizations are conducted at a low-resolution discretization of the design domain. Furthermore, since our approach is geometry-based, obtained structures are encoded into a compact geometric format that facilitates downstream operations such as editing and fabrication.

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来源期刊
CiteScore
12.70
自引率
15.30%
发文量
719
审稿时长
44 days
期刊介绍: Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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