从一道力学竞赛题解析扭曲变形效应对梁应力分布的影响  

ANALYSIS OF DISTORTION EFFECT ON BEAM STRESS DISTRIBUTION FROM A MECHANICS COMPETITION PROBLEM

作　　者：胡雅芬 赵增辉[1] 付靖宇 HU Yafen;ZHAO Zenghui;FU Jingyu(School of Energy and Mining Engineering,Shandong University of Science and Technology,Qingdao 266590,Shandong,China;School of Engineering Science,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]山东科技大学能源与矿业工程学院,山东青岛266590 [2]中国科学院大学工程科学学院,北京100049

出　　处：《力学与实践》2023年第1期200-205,共6页Mechanics in Engineering

基　　金：山东省本科教学改革研究面上项目(M2021229);山东科技大学优秀教学团队建设计划(JXTD20190501);山东科技大学教育教学研究“群星计划”(QX2021ZKT01);山东科技大学教学名师培育计划(MS20200501);山东省一流本科课程建设项目(材料力学)等资助。

摘　　要：针对第十届全国周培源大学生力学竞赛传送装置梁问题,考虑应力边界条件,运用弹性力学体系给出了相对精确的应力解答;考虑剪切扭曲效应对应力分量的影响,比较了本文解答和官方解答的异同,并进一步考虑横向和切向载荷的综合作用,完整推导出了扭曲应力修正项。分析结果表明,将梁的纵向位移表达为纵、横坐标函数的分离形式所推出的修正项完整函数与弹性力学解答是一致的,悬臂梁的跨高比对扭曲效应影响较显著,官方题解在细长梁范围内是完全合理的,本文拓展解答有助于深化对材料力学知识体系的理解。Aiming at the transmission device beam problem appeared in the 10th National Chou Peiyuan College Mechanics Competition, a relatively accurate stress solutions were given by using the elastic mechanical system based on the stress boundary conditions. Considering the influence of shear distortion effect on the stress component, the similarities and differences between the present solution and the official answer were compared,and the torsional stress correction term was derived by further considering the comprehensive effect of transverse and tangential loads. Results show that the complete function of the correction term derived by expressing the longitudinal displacement of the beam as the separated form of the longitudinal and abscissa functions is consistent with the elastic solution. The span-to-height ratio has a significant influence on the distortion effect. It is completely reasonable within the scope of slender beams according to the offical answer,and the expanded solutions in this paper will help deepen the understanding of the knowledge system of material mechanics.

关 键 词：周培源力学竞赛 悬臂梁 应力分析 扭曲效应 

分 类 号：O341[理学—固体力学]