论文标题
与弹性基础结合的壳以及膜情况最佳弹性和几何条件的存在
A Shell Bonded to an Elastic Foundation and the Existence of Optimal Elastic and Geometric Conditions for the Membrane Case
论文作者
论文摘要
在本文中，我们通过修改Koiter的线性壳方程来得出一个壳（即薄弹性体）的数学模型（即薄弹性体）。我们证明了解决方案的存在和唯一性，并明确地得出了管理方程式和一般情况的边界条件。最后，通过数值建模和渐近分析，我们表明，幼型模量，泊松比和壳的厚度（相对于弹性基础）以及接触区域的曲率半径，以使得平面溶液得出，以使得壳模型（即，象征效果均具有巨大的效果）的薄薄的薄薄片。通常在可拉伸和柔性电子的领域被认为是，当薄体（即壳或膜）相对更硬（即具有较高的年轻模量）而不是较厚的基础时，平面溶液大多是准确的。据我们所知，这是第一个分析表明，对于粘结到弹性基础的膜（或壳的平面溶液），仅较高的刚度（相对于弹性基础的刚度）不能保证更准确的解决方案。
In this article, we derive a mathematical model for a shell (i.e. a thin elastic body) bonded to an elastic foundation by modifying Koiter's linear shell equations. We prove the existence and the uniqueness of solutions, and we explicitly derive the governing equations and the boundary conditions for the general case. Finally, with numerical modelling and asymptotic analysis, we show that there exist optimal values for the Young's modulus, the Poisson's ratio and the thickness of the shell (relative to the elastic foundation), and the radius of curvature of the contact region such that the planar solution derived by the shell model (i.e. the membrane case, where stretching effects are dominant) results in a good approximation of the thin body. It is often regarded in the field of stretchable and flexible electronics that the planar solution is mostly accurate when the thin body (i.e. the shell or the membrane) is relatively stiffer (i.e. has a high Young's modulus) than the thicker foundation. As far as we are aware, this is the first analysis showing that for a membrane (or the planar solution of a shell) bonded to an elastic foundation, higher stiffness (relative to the elastic foundation's stiffness) alone would not guarantee a more accurate solution.
