论文标题
卡普斯坦方程式的概括以及与柯库奇和奥登模型的比较库仑的静态摩擦定律
A Generalisation of the Capstan Equation and a Comparison Against Kikuchi and Oden's Model for Coulomb's Law of Static Friction
论文作者
论文摘要
在本文中，我们将Capstan方程扩展到非圆形几何形状。我们为具有零泊松比（或任意泊松比）的膜的封闭形式解决方案得出，该膜由刚性棱镜（在限制平衡情况下和稳态平衡的情况下）或刚性通用锥（仅在极限平衡情况下）支撑的刚性棱镜支撑。我们的模型表明，弹性体的应力轮廓取决于接触区域刚性障碍物的曲率变化。为了进行比较，我们扩展了Kikuchi和Oden的模型，以将库仑的静态摩擦定律扩展到曲面坐标，并进行数值实验，以检查库克基（Kikuchi）和奥登（Oden）模型在曲面坐标中所暗示的库仑静态摩擦定律的特性，并由我们的一般Capstaneequantization Capstaneequantation。我们的数值结果表明，对于固定的摩擦系数，摩擦力独立于弹性体的幼体模量，增加曲率，增加泊松比并降低弹性体的厚度增加了摩擦力。我们的分析还表明，对于给定的张力比，每种模型推断出的摩擦系数是不同的，表明隐含的摩擦程度取决于模型。
In this article, we extend the capstan equation to non-circular geometries. We derive a closed form solution for a membrane with a zero Poisson's ratio (or a string with an arbitrary Poisson's ratio) supported by a rigid prism (at limiting-equilibrium case and in steady-equilibrium case) or supported by a rigid general cone (at limiting-equilibrium case only). Our models indicate that the stress profile of the elastic body depends on the change in curvature of the rigid obstacle at the contact region. As a comparison, we extend Kikuchi and Oden's model for Coulomb's law of static friction to curvilinear coordinates, and conduct numerical experiments to examine the properties of Coulomb's law of static friction implied by Kikuchi and Oden's model in curvilinear coordinates and implied by our generalised capstan equation. Our numerical results indicate that for a fixed coefficient of friction, the frictional force is independent of the Young's modulus of the elastic body, and increasing the curvature, increasing the Poisson's ratio and decreasing the thickness of the elastic body increases the frictional force. Our analysis also shows that for given a tension ratio, the coefficient of friction inferred by each model is different, indicating that the implied-coefficient of friction is model dependent.
