弹性基底粘接薄板起皱的非局部分析  

Nonlocal analysis of wrinkling in thin plate bonded on elastic substrate

作　　者：彭香武 赵建中[1] 郭兴明[1] PENG Xiangwu;ZHAO Jianzhong;GUO Xingming(Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, Chin)

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072

出　　处：《上海大学学报（自然科学版）》2017年第6期927-936,共10页Journal of Shanghai University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11472163)

摘　　要：基于非局部理论,研究了粘接在弹性基底上的薄板的条纹形起皱问题.通过比较经典弹性理论和非局部理论的数值计算结果,讨论了弹性基底的下表面条件和泊松比、弹性基底与薄板的厚度比以及模量比对起皱行为的尺度效应和非局部效应.数值算例表明:粘接在不可压缩、薄硬的弹性基底上的薄板起皱的非局部效应显著;而对于厚软的弹性基底,粘接薄板非局部效应可忽略.Based on the nonlocal elastic theory, the paper studies stripe wrinkle of a thin plate bonded on an elastic substrate. The classic elastic results and nonlocal results are compared based on numerical calculation. The nonlocal scale effects of lower surface condition and Poisson ratio of the elastic substrate, thickness ratio, and modulus ratio are investigated. Numerical examples show that the nonlocal effect is significant when the substrate is incompressible, thin and stiff, and can be ignored when the substrate is thick and soft.

关 键 词：非局部理论 波浪形起皱 Winkler弹性系数 

分 类 号：O34[理学—固体力学]