This work delves into the study of stresses induced in a non-homogeneous pre-stressed nearly incompressible elastic substrate with irregularity as a result of a normal load moving on its rough surface. The irregularity on the free surface of the substrate is considered in the form of parabolic irregularity. The solution methodology features the applicability of perturbation method along with substitution method to obtain the displacement components. The expressions of the induced shear and normal stresses have been established in closed form, and their expressions for special cases of the considered problem have also been deduced, which concur well with the existing literature. The influences of affecting parameters viz., non-homogeneity, frictional coefficient, irregularity factor, irregularity depth, hydrostatic stress and depth of the substrate on shear and normal stresses have been depicted graphically by means of numerical computation. The computational results have been manifested for distinct cases of irregularity zone involving parabolic as well as rectangular irregularities present in the considered geometrical model. It has been figured out that the presence of non-homogeneity in the irregular substrate has significant impact on the developed stresses.

中文翻译：

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不规则超弹性基体在移动载荷作用下的动力学


这项工作深入研究了非均匀预应力、几乎不可压缩的弹性基材中产生的应力，由于法向载荷在其粗糙表面上移动而具有不规则性。基板自由表面上的不规则性以抛物线不规则性的形式考虑。求解方法的特点是微扰法和替代法可用于获得位移分量。诱导剪切应力和法向应力的表达式已经以封闭形式建立，并且还推导出了它们在所考虑问题的特殊情况下的表达式，这与现有文献非常吻合。影响参数，即非均匀性、摩擦系数、不规则系数、不规则深度、静水应力和基材深度对剪切应力和法向应力的影响已经通过数值计算以图形方式描述了。计算结果已经针对所考虑的几何模型中存在的涉及抛物线和矩形不规则的不规则区的不同情况进行了体现。已经发现，不规则基材中存在的非均匀性对产生的应力有重大影响。