AI 中文总结
该研究采用弹性动力学框架，通过拉普拉斯变换推导三维弹性空心球单轴压缩下的静态解，发现内表面存在局部应力集中，为相关领域提供了可靠分析方法。
AI 中文摘要
本文采用弹性动力学框架，重新研究受单轴压缩的三维弹性空心球的应力分析。通过应用拉普拉斯变换，对位移的标量势和矢量势进行展开，便于详细探究该系统的力学行为。在长时间极限下，推导得到位移和应力分布的静态解，这些解揭示了弹性空心球响应的关键信息。值得注意的是，在内表面上，某些物理量在压缩力与表面某点的夹角变为垂直的位置出现峰值，表明存在局部应力集中。这些发现为理解和预测受单轴载荷的弹性空心球的行为提供了可靠的分析方法，对材料科学和结构工程具有重要意义。
英文摘要
The stress analysis of a three-dimensional elastic hollow sphere subjected to uniaxial compression is revisited, employing an elastodynamic framework. Through the application of the Laplace transform, the scalar and vector potentials of displacement are expanded, facilitating a detailed exploration of the system's mechanical behavior. The static solutions for displacement and stress distributions are derived in the long-time limit, which reveal key insights into the response of the elastic hollow sphere. Notably, on the inner surface, certain quantities exhibit a peak at the point where the angle between the compressive force and the point on the surface becomes perpendicular, indicating localized stress concentration. These findings provide a robust analytical approach for understanding and predicting the behavior of elastic hollow spheres under uniaxial loading, with implications for material science and structural engineering.
Comments10 pages, 5 figures
