利用复变格林函数法的Eshelby夹杂外场的一般显式解析解

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利用复变格林函数法的Eshelby夹杂外场的一般显式解析解

更新时间：2025-07-09

- 利用复变格林函数法的Eshelby夹杂外场的一般显式解析解
- Issue 7, Pages: 184-196(2022)
- 作者机构：
  
  1. 西安交通大学机械结构强度与振动国家重点实验室
  2. 长安大学地质工程与测绘学院
- 作者简介：
- 基金信息：
- DOI：
  CLC： O34
- Published：2022
- 稿件说明：
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[J]. 2022, (7): 184-196.
DOI：

[J]. 2022, (7): 184-196. DOI：

摘要

针对目前仍然没有文献给出椭圆异性夹杂外场的完全显式解析表达的情况，通过重新研究二维Eshelby椭圆异性夹杂问题，得到了具有均匀特征应变分布的Eshelby椭圆异性夹杂在远场载荷作用下内外场的一般显式解析解。此外，重新研究了经典的Inglis椭圆孔问题，得到了其在直角坐标系下的显式解析解。首先利用等效特征应变原理求解了具有均匀特征应变分布和远场载荷作用的椭圆异性夹杂内的应力分布，然后在平面弹性力学框架下，利用复变格林函数法描述了Eshelby椭圆异性夹杂模型，给出了远场载荷下具有均匀特征应变分布的Eshelby椭圆异性夹杂外部场的一般显式解析解，最后探讨了它在液体夹杂问题中的应用，结果表明：内部压力和远场载荷均会导致基体长轴两端端点附近应力高度集中；液体夹杂的存在会减小系统的剪切模量。本文得到的Eshelby椭圆异性夹杂问题的一般解析解更简便，而且其在液体夹杂问题中的研究结果能够解释土体液化的微观机理及液体夹杂对土体滑坡的影响。相比较曲线坐标系下的Inglis解，本文得到的直角坐标系下的Inglis解是一种通用形式，更简洁。

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