具有尺度效应的双变量非线性梁的后屈曲分析  

Post-buckling Analysis of a Two-variable Nonlinear Beam with Scale Effects

作　　者：王鹏博 卿海 Wang Pengbo;Qing Hai(State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,江苏南京210016

出　　处：《甘肃科学学报》2021年第3期1-6,共6页Journal of Gansu Sciences

基　　金：国家自然科学基金面上项目(11672131)。

摘　　要：基于双变量变形理论,通过引入非线性项,建立了双变量变形梁的非线性后屈曲模型。在哈密尔顿原理的基础上,考虑偶应力理论和表面弹性理论及冯卡门非线性应变,推导了双变量梁后曲屈的非线性微分控制方程和边界条件。进而将归一化的控制方程及边界条件通过微分求积法及牛顿迭代法求解了不同边界条件下的后曲屈行为。对比了偶应力理论及弹性理论对微梁后屈曲行为的影响,研究了梁的厚度、长厚比及边界条件对双变量梁的后屈曲行为的影响。从而验证了偶应力和表面效应使得后屈曲路径变化。该模型得到了长厚比不同屈曲荷载变化的速率不同的结论。Based on the two-variable deformation theory,a nonlinear post-buckling model of a two-variable deformed beam is established by introducing a nonlinear term.Based on the Hamilton's principle,and taking into account the couple stress theory and surface elasticity theory as well as Von Karman nonlinear strain,the nonlinear differential governing equations and boundary conditions for post-buckling of a two-variable beam are derived.The governing equations and boundary conditions are normalized and then solved numerically by differential quadrature method and Newton's iteration method.The influence of the couple stress theory and the surface energy on the post-buckling of the microbeam is compared.The effects of beam thickness,length-to-thickness ratio and boundary conditions on the post-buckling behavior of bivariable beams are studied.It is verified that the change of the post-buckling path caused by the couple stress and the surface effect.The model obtained different conclusions about the rate of change of buckling load with different length-thickness ratio.

关 键 词：尺度效应 表面能 修正偶应力理论 微分求积法 后屈曲 

分 类 号：O342[理学—固体力学]