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Design of Meta-Materials Outside the Homogenization Limit Using Multiscale Analysis and Topology Optimization.

机译：使用多尺度分析和拓扑优化设计均质化界限之外的元材料。

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摘要

The field of meta-materials engineering has largely expanded mechanical design possibilities over the last two decades; some notable design advances include the systematic engineering of negative Poisson's ratio materials and functionally graded materials, materials designed for optimal electronic and thermo-mechanical performances, and the design of materials under uncertainty. With these innovations, the systematic engineering of materials for design-specific uses is becoming more common in industrial and military uses. The motivation for this body of research is the design of the shear beam for a non-pneumatic wheel. Previously, a design optimization of a finite element model of the non-pneumatic wheel was completed, where a linear elastic material was simulated in the shear beam to reduce hysteretic energy losses. As part of the optimization, a set of optimal orthotropic material properties and other geometric properties were identified for the shear beam. Given that no such natural linear elastic material exists, a meta-material can be engineered that meets these properties using the aforementioned tools. However, manufacturing constraints prevent the use of standard homogenization analysis and optimization tools in the engineering of the shear beam due to limitations in the accuracy of the homogenization process for thin materials.;In this research, the more general volume averaging analysis is shown to be an accurate tool for meta-material analysis for engineering thin-layered materials. Given an accurate analysis method, several optimization formulations are proposed, and optimality conditions are derived to determine the most mathematically feasible and numerically reliable formulation for topology optimization of a material design problem using a continuous material interpolation over the design domain. This formulation is implemented to engineer meta-materials for problems using the volume averaging analysis, which includes the use of variable linking and the derivation of first-order design sensitivities to increase computational efficiency. Inspired by honeycomb materials, a new method of discretizing the material design domain into unit cells with non-simple connectivity is proposed as a way of increasing the solution space of the topology optimization problem. Finally, these methods are used in the meta-material design process to identify several candidate meta-material geometries from a polycarbonate base material for the shear layer of the non-pneumatic wheel; notable geometries include an 'x'-like geometry, a bent column-like geometry identified previously as a bristle, and, remarkably, an auxetic honeycomb geometry. This is the first reported result demonstrating the auxetic honeycomb geometry to be a minimum weight structure in shear loading where a general topology optimization method was used.
机译：在过去的二十年中，超材料工程领域极大地扩展了机械设计的可能性。一些显着的设计进展包括负泊松比材料和功能渐变材料的系统工程，为实现最佳电子和热机械性能而设计的材料以及不确定性下的材料设计。通过这些创新，用于特定设计用途的材料的系统工程在工业和军事用途中变得越来越普遍。该研究的动机是为非充气车轮设计剪切梁。以前，完成了非充气车轮有限元模型的设计优化，其中在剪切梁中模拟了线性弹性材料以减少滞后能量损失。作为优化的一部分，确定了剪切梁的一组最佳正交异性材料特性和其他几何特性。如果不存在这种天然的线性弹性材料，则可以使用上述工具设计满足这些特性的超常材料。但是，由于薄材料的均质化过程的精度受到限制，因此制造方面的限制使得在剪切梁的工程设计中无法使用标准的均质化分析和优化工具。用于工程薄层材料的超材料分析的准确工具。给定一种精确的分析方法，提出了几种优化公式，并推导了最佳条件，以确定在设计域上使用连续材料插值法对材料设计问题进行拓扑优化的最数学上可行且数值可靠的公式。通过使用体积平均分析，可以实现此公式来设计超材料，以解决问题，其中包括使用变量链接和推导一阶设计敏感度以提高计算效率。在蜂窝材料的启发下，提出了一种将材料设计域离散为具有非简单连通性的单元的新方法，作为增加拓扑优化问题的求解空间的一种方法。最后，这些方法用于超材料设计过程中，以从聚碳酸酯基础材料中确定非气动轮的剪切层的几种候选超材料几何形状。显着的几何形状包括“ x”形几何形状，以前被识别为刚毛的弯曲的圆柱状几何形状，以及引人注目的蜂窝状几何形状。这是第一个报告的结果，表明在使用常规拓扑优化方法的情况下，膨胀蜂窝的几何形状是剪切载荷中的最小重量结构。

著录项

  • 作者

    Czech, Christopher.;

  • 作者单位

    Clemson University.;

  • 授予单位 Clemson University.;
  • 学科 Engineering Mechanical.;Engineering Materials Science.
  • 学位 Ph.D.
  • 年度 2012
  • 页码 215 p.
  • 总页数 215
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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