轴向变刚度矩形截面梁的弹性及弹塑性弯曲  

Elastic and elasto-plastic bending of rectangular beams with variable stiffness along axial direction

作　　者：聂国隽[1] 徐敏[1] 仲政[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《中国科学：物理学、力学、天文学》2011年第1期86-93,共8页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(批准号:10872150;11072177);高等学校博士学科点专项科研基金(批准号:20070247029);广西大学工程防灾与结构安全省部共建教育部重点实验室开放课题资助项目

摘　　要：假定矩形截面梁的材料为非均匀的各向同性的理想弹塑性材料,其弹性模量、屈服强度以及梁的高度均是梁轴向坐标的函数,忽略剪切对变形及屈服的影响,在小变形前提下研究轴向变刚度梁的弹性及弹塑性弯曲问题.导出了截面高度及材料的弹性模量沿梁长度方向按照特殊函数变化时梁弹性及弹塑性变形的解析解.采用微分求积法实现了抗弯刚度任意变化时变刚度梁的弹性及弹塑性分析.通过数值算例分析了抗弯刚度的轴向变化对梁弹性及弹塑性性能的影响.Suppose that the beam with rectangular cross section is composed of an inhomogeneous, isotropic and ideally elasto-plastic material and the elastic modulus, yield limit of the material and the height of the beam, respectively, vary arbitrarily with the axial coordinate. The elastic and elasto-plastic bending of beams with variable stiffness is investigated under the framework of small deformation theory and regardless of the shear deformation. Exact solutions are presented for the elastic and elasto-plastic deformations of beams with bending stiffness having special variations along the axial direction. Differential quadrature method is employed to study the elastic and elasto-plastic bending of beams with arbitrarily variable stiffness. The influence of variable stiffness on the elastic and plastic performances of the beam is discussed through numerical examples.

关 键 词：变刚度梁 弹性 弹塑性 精确解 微分求积法 

分 类 号：O344.3[理学—固体力学]