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总览 评价 田忠良 ， 梁海弋 * （ 中国科学技术大学近代力学系，合肥 230027； ） 摘要： 不均匀生长或温度膨胀等因素会导致板发生面外变形。在弹性板上有目的地设计这种面内生长应变分布可以获得预期的三维形状。面内不均匀膨胀导致的材料点与点之间的距离
田忠良， 梁海弋*
（
中国科学技术大学近代力学系，合肥 230027； ）
摘要：
不均匀生长或温度膨胀等因素会导致板发生面外变形。在弹性板上有目的地设计这种面内生长应变分布可以获得预期的三维形状。面内不均匀膨胀导致的材料点与点之间的距离变化，在数学上可以用度量张量描述。本文简略介绍了近些年发展起来的非欧几何弹性理论，其研究的核心内容为弹性体在目标度量张量作用下的空间变形。利用ABAQUS有限元软件模拟了预设目标度量张量的圆板变形，考察了面内膨胀函数与目标高斯曲率的关系。通过模拟分析了由板厚导致的高斯曲率和理论计算结果间的偏差，讨论了板厚对非欧几何板变形的影响。
关键词：
非欧几何板；目标度量张量；目标高斯曲率；稳定性
TIAN Zhongliang， LIANG Haiyi*
（
Department of modern mechanics，USTC，Hefei 230027； ）
Abstract：
The out-of-plane displacements of plates are influenced by factors such as nonuniform growth or thermal expansion. Expected three-dimensional shape of an elastic plate can be obtained by designing the distribution of in-plane growth strain in it. The distance between different points affected by in-plane nonuniform expansion can be described by metric of math. In this paper, the theory of non-Euclidean plates which has been developed in recently years is briefly introduced, whose core research is the 3D deformation of elastomer controlled by the target metric. The deformations of circular plates containing specified target metric are simulated by using the commercial ?nite-element software ABAQUS. The relationship between in-plane swelling functions and target Gaussian curvature is explored. The impact that the thickness of plates has on the deformation of non-Euclidean plates are studied through analyzing the deviation of Gaussian curvature induced by different thicknesses between simulation and theory.
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