超弹性材料
方案(数学)
数学
微分方程
数学分析
差速器(机械装置)
截断(统计)
系列(地层学)
工作(物理)
常微分方程
应用数学
作者
Wang, Jiong,Li, Zhanfeng,Jin, Zili
标识
DOI:10.1177/10812865221089694
摘要
In this paper, a theoretical scheme is proposed for shape-programming of thin hyperelastic plates through differential growth. First, starting from the 3D governing system of a hyperelastic (neo-Hookean) plate, a consistent finite-strain plate equation system is formulated through a series expansion and truncation approach. Based on the plate equation system, the problem of shape-programming is studied under the stress-free assumption. By equating the stress components in the plate equations to be zero, the explicit relations between the growth functions and the geometrical quantities of target shape of the plate are derived. Then, a theoretical scheme of shape-programming is proposed, which can be used to identify the growth fields corresponding to arbitrary 3D shapes of the plate. To demonstrate the efficiency of the scheme, some typical examples are studied. The predicted growth functions in these examples are adopted in the numerical simulations, from which the target shapes of the plate can be recovered completely. The scheme of shape-programming proposed in the current work is applicable for manufacturing intelligent soft devices.
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