弹性力学中主矢量及主矩正负号的统一表达  

UNIFIED EXPRESSION ON THE SIGNS OF PRINCIPAL VECTOR AND PRINCIPAL MOMENT IN ELASTIC MECHANICS

作　　者：刘章军 阮鑫鑫 LIU Zhangjun;RUAN Xinxin(School of Civil Engineering and Architecture,Wuhan Institute of Technology,Wuhan,Hubei 430074)

机构地区：[1]武汉工程大学土木工程与建筑学院,湖北武汉430074

出　　处：《物理与工程》2022年第5期34-39,共6页Physics and Engineering

基　　金：2020年湖北省高等学校省级教学研究项目(项目号:2020481);2020年国家级一流本科课程《弹性力学B》(证书号:2020131022);2020年度“湖北名师工作室”主持人人才资助项目。

摘　　要：在弹性力学中,由于未明确给出主矢量和主矩的正负号统一规定,在分析不同的问题时容易产生混淆。为此,首先考察材料力学中内力的正负号规定,并详细剖析在不同坐标系下材料力学中内力正负号规定所导致的差异性。同时,建议弹性力学中用应力分量来定义主矢量和主矩的正负号,从而实现材料力学与弹性力学问题解答的一致性。最后,通过对4个弹性力学典型应用实例的分析,进一步阐明所建议的主矢量和主矩正负号规定的统一性。实践表明,该统一表达可有效帮助学生理解力学概念,分析力学问题,教学效果显著。In elastic mechanics,since the signs of principal vector and principal moment are not clearly specified,it is easy to be confused when analyzing different problems.To this end,first of all,the signs of internal force in material mechanics are investigated carefully,and the differences brought by the signs of internal force in material mechanics under different coordinate systems are analyzed.Meanwhile,it is recommended to use stress components to define the signs of principal vectors and principal moments in elastic mechanics,so as to achieve consistency between material mechanics and elastic mechanics solutions.Finally,through the analysis of four typical examples in elastic mechanics,the unity of the signs associated with the proposed principal vector and principal moment is further clarified.Practice shows that the unified expression can effectively help students understand the concept of mechanics and analyze mechanics problems,and the teaching effect is remarkable.

关 键 词：弹性力学 材料力学 主矢量及主矩 正负号 统一表达 

分 类 号：TB301-4[一般工业技术—材料科学与工程] G642[文化科学—高等教育学]