论文标题
具有初始应力的弹性板的Föppl-VonKármán方程
The Föppl-von Kármán equations of elastic plates with initial stress
论文作者
论文摘要
最初，压力的板被广泛用于现代制造技术，例如添加剂制造和紫外线光刻，用于通过应用外部刺激来调谐形态。在这项工作中，我们提出了一种具有初始应力的弹性板的Föppl-vonKármán方程的形式渐近衍生物，使用在不可压缩性和材料同时性的假设下具有初始应力的非线性弹性固体的组成型理论。与现有作品相比，我们的方法允许确定弹性板的形态过渡，而无需开具弹性体无压力状态的基本目标度量。我们在工程感兴趣的某些物理问题中明确解决了派生的FVK方程，讨论了初始应力分布如何驱动变形板中自发曲线的出现。所提出的数学框架可用于按需定制形状，在几个工程领域的应用程序范围从软机器人技术到4D打印。
Initially stressed plates are widely used in modern fabrication techniques, such as additive manufacturing and UV lithography, for their tunable morphology by application of external stimuli. In this work, we propose a formal asymptotic derivation of the Föppl-von Kármán equations for an elastic plate with initial stresses, using the constitutive theory of nonlinear elastic solids with initial stresses under the assumptions of incompressibility and material isotropy. Compared to existing works, our approach allows to determine the morphological transitions of the elastic plate without prescribing the underlying target metric of the unstressed state of the elastic body. We explicitly solve the derived FvK equations in some physical problems of engineering interest, discussing how the initial stress distribution drives the emergence of spontaneous curvatures within the deformed plate. The proposed mathematical framework can be used to tailor shape on demand, with applications in several engineering fields ranging from soft robotics to 4D printing.
