表面效应对多孔纳米梁后屈曲行为的影响分析  

INFLUENCE OF SURFACE EFFECT ON POST-BUCKLING BEHAVIOR OF POROUS NANOBEAMS

作　　者：李清禄[1] 张海坤 王思瑶 张靖华[1] LI Qinglu;ZHANG Haikun;WANG Siyao;ZHANG Jinghua(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《力学与实践》2023年第1期83-89,共7页Mechanics in Engineering

基　　金：国家自然科学基金(12062010);兰州理工大学一流本科课程项目资助。

摘　　要：为分析表面效应对多孔梁在轴向压力下的屈曲和后屈曲行为的影响,使用Gurtin-Murdoch表面弹性理论,建立了轴向可伸长梁的非线性后屈曲控制微分方程。其中假设梁的孔隙分布在其厚度上具有对称和非对称的两种非均匀模式。采用打靶法数值求解,给出了不同孔隙率系数下多孔纳米梁发生屈曲的临界载荷和后屈曲平衡路径曲线,讨论了表面材料特性对后屈曲行为的影响。结果表明:纳米梁具有十分显著的表面效应,表面效应对多孔纳米梁的屈曲和后屈曲行为有重要影响。In order to analyze the influence of surface effect on the buckling and post-buckling behavior of porous beams under axial pressure, the nonlinear post-buckling governing differential equation of axially extensible beams was established by using Gurtin-Murdoch surface elasticity theory. It was assumed that the pore distribution of the beam has two non-uniform modes, one symmetry and the other asymmetry along its thickness direction. The critical load and post-buckling equilibrium path curve of porous nanobeams under different porosity coefficients were given by the shooting method. The influences of surface material properties on post-buckling behavior were discussed. The results show that nanobeams have very significant surface effects, and the surface effect has an important influence on the buckling and post-buckling behavior of porous nanobeams.

关 键 词：纳米梁 几何非线性 表面应力 后屈曲 数值解 

分 类 号：O321[理学—一般力学与力学基础] TB330.1[理学—力学]