应力张量与电四极矩的联系以及应力分析的新方法  

The Relationship Between Stress Tensor and Electric Quadrupole Moment and a New Method for Stress Analysis

作　　者：李一杰[1] 张成园 石薇 许广智[1] LI Yi-jie;ZHANG Cheng-yuan;SHI Wei;XU Guang-zhi(School of Physics,Liaoning University,Shenyang 110036,China)

机构地区：[1]辽宁大学物理学院,辽宁沈阳110036

出　　处：《辽宁大学学报(自然科学版)》2024年第4期379-384,共6页Journal of Liaoning University:Natural Sciences Edition

基　　金：国家自然科学基金(11705078);辽宁大学本科教学改革研究项目(JG2022BYLW004,JG2023ZSWT14);辽宁大学研究生优质在线课程建设与教学模式综合改革研究项目(YJG202302096);2023年度辽宁省研究生教育教学改革研究项目(LNYJG2023001)。

摘　　要：本文通过对比应力与小尺度电荷分布,把应力张量与静电势多极展开中的电四极矩联系起来,指出二者分析方法可以通用.根据之前工作中得到的电四极矩与电四极子特征参数的对应关系,本文把应力张量的分量用两个等模矢量表示出来,通过求解方程组得到这两个矢量后,进而求出主应力、主方向等参数.新方法公式较简洁,主应力与其方向对应关系清晰,容易从三向应力问题过渡为二向应力问题.新方法为应力分析提供了新的思路.By comparing stress with the distribution of small-scale charges,the stress tensor is connected with the electric quadrupole moment in the multipole expansion of electrostatic potential in this paper and therefore analysis methods can be applied to both of them in common.Based on the corresponding relationship between the electric quadrupole moment and the characteristic parameters of the electric quadrupole obtained from previous work,the components of the stress tensor can be represented by two vectors with equal magnitude.After solving the equations system to obtain these two vectors,parameters such as the principal stress and principal direction can be obtained.The new method has a relatively concise formula.A clear correspondence is showed between the principal stress and its direction.Transition is comprehensible from a three-dimensional stress problem to a two-dimensional stress problem.This method provides a new idea for stress analysis.

关 键 词：应力分析 主应力 主方向 电四极矩 

分 类 号：O343.1[理学—固体力学] O343.2[理学—力学]