平面问题中悬臂梁固支边界条件的简化方法  

A SIMPLIFIED METHOD FOR FIXED BOUNDARY CONDITIONS OF PLANAR CANTILEVER BEAMS

作　　者：杨振宇[1,2] 鲍强 卢子兴 YANG Zhenyu;BAO Qiang;LU Zixing(School of Aeronautic Science and Engineering,Beihang University,Beijing 100191,China;Ningbo Innovation Research Institute,Beihang University,Ningbo 315800,Zhejiang,China)

机构地区：[1]北京航空航天大学航空科学与工程学院,北京100191 [2]北京航空航天大学宁波创新研究院,浙江宁波315800

出　　处：《力学与实践》2022年第6期1404-1410,共7页Mechanics in Engineering

基　　金：国家自然科学基金资助项目(11972057)。

摘　　要：弹性力学在处理梁的固支边界条件时,基于应变分量积分得到的位移表达式通常比较复杂,无法精确满足固支边界条件,因而只能求得近似解。本文采用固支边界中点的位移约束,结合最小二乘法重新定义了固支边界条件,实现了对梁的位移的准确求解。比较不同边界条件提法的差异,将有助于学生灵活掌握边界条件的简化方法,为开展研究性教学提供素材。In the theory of elasticity,when dealing with the fixed boundary conditions of beams,the displacement expression based on the integration of strain component is usually complex,which is difficult to accurately meet the fixed boundary conditions,so only an approximate solution can be obtained.In this paper,the displacement constraint of the midpoint of the fixed boundary is adopted,and the fixed boundary condition is redefined combined with the least squares method,so as to realize the accurate solution of the displacement of the beam.By comparing the differences of four typical formulas of boundary conditions,it is helpful for students to flexibly grasp the simplification methods of the fixed boundary conditions and provide materials for research-based teaching.

关 键 词：平面问题 悬臂梁 固支边界条件 最小二乘法 

分 类 号：V343[航空宇航科学技术]