无约束非欧板的弹性理论
Elastic theory of unconstrained non-Euclidean plates
摘要：
非欧几里德板是一类没有无应力构形的弹性体的子集。当从所有外部约束中释放时，这种物体表现出残余应力，并且即使在没有外力的情况下也可以呈现复杂的平衡形状。在这项工作中，我们提出了一个数学框架，这样的机构在线性弹性的协变理论，有效的大位移。我们提出了非欧几里德板的概念来近似许多自然形成的薄弹性结构。我们推导出一个薄板理论，这是现有的线性板理论的推广，适用于大位移，但小应变，和任意的内在几何形状。我们研究一个特殊的半球形板的例子。我们表明，发生了自发屈曲从拉伸为主的配置弯曲为主的配置，板厚度的变化。
英文摘要：
Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the absence of external forces. In this work we present a mathematical framework for such bodies in terms of a covariant theory of linear elasticity, valid for large displacements. We propose the concept of non-Euclidean plates to approximate many naturally formed thin elastic structures. We derive a thin plate theory, which is a generalization of existing linear plate theories, valid for large displacements but small strains, and arbitrary intrinsic geometry. We study a particular example of a hemispherical plate. We show the occurrence of a spontaneous buckling transition from a stretching dominated configuration to bending dominated configurations, under variation of the plate thickness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
