浅梁弯曲挠度经典计算公式的精度分析  

Precision Analysis of Classical Bending Deflection Formulae of Simply-Supported Beams

作　　者：杨怡[1] 刘济科[2] 

机构地区：[1]华南理工大学土木与交通学院,广东广州510640 [2]中山大学力学系,广东广州510275

出　　处：《华南理工大学学报（自然科学版）》2008年第6期30-34,共5页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10772202;10672060);中国博士后科学基金资助项目(20060400757)

摘　　要：提出一种新的简支梁变形模式,其横截面内除了挠度和转角,还考虑了面内变形.运用U变换法和四结点矩形单元,分析了简支梁的平面弯曲问题,求解出二维有限元格式下受集中荷载作用梁的上下自由表面位移的解析解,并将所得的解析解与材料力学中关于浅梁弯曲挠度的计算结果进行比较,讨论经典简支浅梁弯曲挠度计算公式的适用范围,并对其误差进行了定量讨论.A new deformation mode of the simply-supported beam is presented, which considers not only the deflection and slope but also the plane transmutation in the cross section. Then, the plane bending of the simply-supported beam is analyzed by means of the U-transformation and the four-node rectangular element, and the analytical displacements on the upper and lower surfaces under a concentrated load of magnitude in a two-dimension finite element mode are obtained. The displacements are compared with the deflection calculated on the basis of the material mechanics. Moreover, the applicable field of the classical bending deflection formulae of the simply-supported beam is discussed, and the corresponding precision is quantitatively analyzed.

关 键 词：U变换 简支梁 平面弯曲 挠度 精度 解析解 

分 类 号：O341[理学—固体力学]