Stiff lattices with zero thermal expansion and enhanced stiffness via rib cross section optimization
Stiff lattices with zero thermal expansion and enhanced stiffness via rib cross section optimization
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DOI：
10.1007/s10999-012-9210-x
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发表时间：
2013-09-01
影响因子：
3.7
通讯作者：
Lakes, Roderic
中科院分区：
文献类型：
--
作者：
Lehman, Jeremy;Lakes, Roderic
对于受温度大波动影响的工程应用，尺寸稳定性是必不可少的，低甚至零热膨胀材料是理想的。除了提供最小的热膨胀外，还必须注意确保减轻机械刚度的降低。这可以通过设计由精心选择的晶格结构组成的结构分层材料来实现。本文对热膨胀系数为零的蜂窝进行了分析。所描述的二维晶格微结构设计是由正膨胀材料制成的。零膨胀是实现与使用弯曲，双材料肋元素，通过使用热诱导弯曲实现零整体热膨胀。这项工作建立在先前的结果之上，并为创建最佳肋骨横截面以增加机械刚度提供了进一步的分析。开展了三通和工字截面肋板的设计。导出了晶格整体力学刚度和整体热膨胀系数的解析方程。在模密度图中，将这些晶格的行为与具有非零热膨胀的三角形和正六边形蜂窝以及具有矩形肋截面的先前零膨胀晶格的行为进行了比较。与具有矩形截面肋的弯曲三角形零热膨胀晶格相比，晶格相对刚度提高了2.4倍。计算了材料界面处的热剪切应力，发现热剪切应力很小。
For engineering applications that are subject to large fluctuations in temperature, yet dimensional stability is essential, low or even zero thermal expansion materials are desirable. In addition to providing minimal thermal expansion care must be taken to ensure reductions in mechanical stiffness are mitigated. This can be achieved be designing structurally hierarchical materials composed of carefully chosen lattice structures. Within this manuscript honeycombs with thermal expansion coefficients equal to zero are developed analytically. The two dimensional lattice microstructure designs described are made of positive expansion materials. Zero expansion is attained with the use of curved, bi-material rib elements that by the use of thermally induced bending achieves zero overall thermal expansion. This work builds upon previous results, and provides further analysis into creating an optimal rib cross section to increase mechanical stiffness. The design of ribs with Tee shaped and I shaped cross sections is developed. Analytical equations are derived for the overall mechanical stiffness and overall thermal expansion coefficients of the lattices. The behavior of these lattices is compared with that of triangular and regular hexagonal honeycombs having non-zero thermal expansion as well as prior zero expansion lattices with rectangular rib cross sections in a modulus-density map. Lattice relative stiffness is improved by as much as a factor of 2.4 when compared with a curved, triangular, zero thermal expansion lattice with ribs of rectangular section. Thermal shear stress at the material interface is calculated and found to be small.