论文标题
两个不同幂律分级弹性物体的二维接触
Two-dimensional contact of two different power-law graded elastic bodies
论文作者
论文摘要
先前对级别材料接触的研究涉及刚体（PUNCH）与弹性不均匀基础的接触，其不均匀性的特征是年轻的模量随着功能的深度变化。本文模拟了两个具有不同指数的弹性不均匀的幂律分级物体的赫兹和粘合剂接触。该问题受两个不同幂核的积分方程的控制。提出了Gegenbauer正交多项式解决方案的非标准方法。它导致特殊结构的线性代数方程的无限系统。评估了系统系数的积分表示，并研究了系统的属性。结果表明，如果指数重合一个无限系统，则可以采用一个简单的精确解决方案，该解决方案与年轻模量不同但指数相同的情况相对应。接触区的长度，压力分布和接触体的表面正常位移的公式以方便的计算形式获得。研究了不匹配在年轻模量指数中的影响。对赫兹和粘合剂接触模型的比较分析阐明了表面能密度对接触压力，接触区大小以及接触区域以外的接触物体的剖面的影响。
Previous study of contact of power-law graded materials concerned the contact of a rigid body (punch) with an elastic inhomogeneous foundation whose inhomogeneity is characterized by the Young modulus varying with depth as a power function. This paper models Hertzian and adhesive contact of two elastic inhomogeneous power-law graded bodies with different exponents. The problem is governed by an integral equation with two different power kernels. A nonstandard method of Gegenbauer orthogonal polynomials for its solution is proposed. It leads to infinite system of linear algebraic equations of a special structure. The integral representations of the system coefficients are evaluated, and the properties of the system are studied. It is shown that if the exponents coincide, the infinite system admits a simple exact solution that corresponds to the case when the Young moduli are different but the exponents are the same. Formulas for the length of the contact zone, the pressure distribution, and the surface normal displacements of the contacting bodies are obtain in the form convenient for computations. Effects of the mismatch in the Young moduli exponents are studied. A comparative analysis of the Hertzian and adhesive contact models clarifies the effects of the surface energy density on the contact pressure, the contact zone size, and the profile of the contacting bodies outside the contact area.
