Abstract

This paper examines the internal rectangular loading problems for an elastic halfspace where the shear modulus varies exponentially or linearly and the Poisson’s ratio keeps constant or varies linearly with depth. The numerical method is developed through applying the fundamental solution of layered elastic solids and integrating numerically it over the loading area. The adaptive integration of the displacement and traction integrals over the loading area is designed to calculate the nearly singular integral for the source point close to an element. The discretization approach is applied to deal with an arbitrarily depth-heterogeneous elastic solid. OpenMP directives are used to parallelize the internal loop, which controls element iterations so that a high computing speed can be obtained. For an axisymmetric internal loading problem, the displacements obtained with the present formulation are in a very good agreement with existing closed-form solutions. Finally, stresses and displacements in non-homogeneous halfspaces induced by horizontally and vertically uniform rectangular loadings are presented. Results illustrate the effect of non-homogeneous properties on the stress and displacement fields.

摘要

本文研究了弹性半空间的内部矩形加载问题，其中剪切模量呈指数或线性变化，泊松比保持恒定或随深度线性变化。数值方法是通过应用层状弹性固体的基本解并在加载区域上对其进行数值积分而发展起来的。加载区域上的位移和牵引积分的自适应积分旨在计算靠近单元的源点的近似奇异积分。离散化方法用于处理任意深度的非均匀弹性固体。OpenMP 指令用于并行化内部循环，该循环控制元素迭代，从而可以获得较高的计算速度。对于轴对称内部载荷问题，用当前公式获得的位移与现有的封闭形式解决方案非常吻合。最后，介绍了由水平和垂直均匀矩形载荷引起的非均匀半空间中的应力和位移。结果说明了非均匀特性对应力和位移场的影响。