This paper presents a semi-analytical algorithm for the determination of the contact half width and surface pressure which results from both adhesive and non-adhesive contact problems involving functionally graded materials (FGM). The inhomogeneously elastic solid comprises a graded elastic coating whose shear modulus depends exponentially on the vertical coordinate and a homogeneously elastic substrate. The solid is assumed to be in a state of plane strain and thus a two-dimensional analysis is performed within this work.udUsing the work of Chidlow et al. (2011a) as a starting point, we derive a pair of integral equations which may be used to determine approximations to the contact pressure when either the surface deflection or the deflection gradient is known over the contact region. As these integral equations are non-singular, we use Galerkin's method to approximate the contact pressure and it is found that relatively small trial spaces allow accurate computation of the pressure. Information about the prescribed load is then used to formulate an iterative algorithm to determine the contact half width.udA selection of numerical results are presented using this method and it is found that the solutions computed here compare favourably with those of other authors. A further investigation is then conducted into the solution of adhesive contact problems using the assumptions of Maugis (1992) and Johnson and Greenwood (2008) to inform the nature of the adhesive stresses outside of the contact. It is found that both JKR-like and DMT-like behaviour can be observed in contact problems involving FGMs.
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机译:本文提出了一种用于确定接触半宽度和表面压力的半分析算法,该算法是由涉及功能梯度材料(FGM)的胶粘和非胶粘接触问题引起的。非均质弹性固体包括梯度弹性涂层和均质弹性基底,该梯度弹性涂层的剪切模量成指数地取决于垂直坐标。假设该固体处于平面应变状态,因此在这项工作中进行了二维分析。 d使用Chidlow等人的工作。 (2011a)作为出发点,我们推导出了一对积分方程,当已知在接触区域的表面挠度或挠度梯度时,可以用来确定接触压力的近似值。由于这些积分方程是非奇异的,因此我们使用Galerkin方法近似接触压力,并且发现相对较小的试验空间可以精确计算压力。然后,将有关规定载荷的信息用于制定一种确定接触半宽度的迭代算法。 ud使用此方法给出了数值结果的选择,并且发现这里计算出的解决方案与其他作者的解决方案相比具有优势。然后,使用Maugis(1992)和Johnson and Greenwood(2008)的假设对胶粘剂接触问题的解决方案进行进一步研究,以了解胶粘剂在接触之外的应力的性质。发现在涉及FGM的接触问题中可以观察到JKR类和DMT类行为。
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