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Non‐stationary axially symmetric displacement of elastic half‐space in mixed boundary conditions
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-10-24 , DOI: 10.1002/zamm.202000062 Veniamin D. Kubenko 1 , Ihor V. Yanchevskyi 2
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-10-24 , DOI: 10.1002/zamm.202000062 Veniamin D. Kubenko 1 , Ihor V. Yanchevskyi 2
Affiliation
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The exact solution of the axially symmetric problem concerning the non‐stationary load action on the elastic half‐space surface in the condition of mixed boundary value problem with the given normal stress and tangent displacement on the boundary is obtained. The Laplace and Hankel integral transforms are used. Integral transforms inversion is carried out by means of tabular ratios and convolutions theorems for the wide range of non‐stationary loads. The vertical displacement expression is obtained in the explicit analytical form. The load applied to the bounded dimensions domain is particularly considered. The performed calculations indicate evolution of the elastic displacement in terms of time and space coordinates.
中文翻译：
混合边界条件下弹性半空间的非平稳轴向对称位移
在给定法向应力和边界切线位移为混合边界值问题的条件下，获得了关于弹性半空间表面上的非平稳载荷作用的轴对称问题的精确解。使用了Laplace和Hankel积分变换。积分变换反演是通过表格比率和卷积定理进行的，适用于各种非平稳载荷。垂直位移表达式以显式解析形式获得。特别要考虑施加到有界尺寸域上的载荷。进行的计算表明了弹性位移在时间和空间坐标方面的演变。
更新日期：2020-10-24
中文翻译：
混合边界条件下弹性半空间的非平稳轴向对称位移
在给定法向应力和边界切线位移为混合边界值问题的条件下，获得了关于弹性半空间表面上的非平稳载荷作用的轴对称问题的精确解。使用了Laplace和Hankel积分变换。积分变换反演是通过表格比率和卷积定理进行的，适用于各种非平稳载荷。垂直位移表达式以显式解析形式获得。特别要考虑施加到有界尺寸域上的载荷。进行的计算表明了弹性位移在时间和空间坐标方面的演变。
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