粘接材料及结构在双轴受压和温度耦合作用下变形的尺度效应和非局部效应分析

doi:10.3969/j.issn.1007-2861.2014.02.007

上海大学学报(自然科学版) ›› 2015, Vol. 21 ›› Issue (4): 422-431.doi: 10.3969/j.issn.1007-2861.2014.02.007

粘接材料及结构在双轴受压和温度耦合作用下变形的尺度效应和非局部效应分析

刘亮, 彭香武, 王青占, 郭兴明

(上海大学上海市应用数学和力学研究所, 上海200072)

收稿日期:2014-03-04 出版日期:2015-08-31 发布日期:2015-08-31
通讯作者: 郭兴明(1964—), 男, 教授, 博士生导师, 研究方向为微纳米力学、材料的多尺度力学建模、连续介质力学. E-mail:xmguo@shu.edu.cn
基金资助:
国家自然科学基金资助项目(10972128, 11472163)

Scale effect on buckling of bonding materials under biaxial compression with temperature changes

LIU Liang, PENG Xiang-wu, WANG Qing-zhan, GUO Xing-ming

(Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China)

Received:2014-03-04 Online:2015-08-31 Published:2015-08-31

摘要/Abstract

摘要： 基于非局部理论, 分析了双层完好粘接板在双轴受压和温度场耦合作用下屈曲的尺度效应和非局部效应. 通过理论计算对经典弹性理论和非局部理论的计算结果进行了比较分析. 结果表明: 在非局部理论下, 由于系统内部结构之间的相互作用, 系统的屈曲临界力有所降低, 并且当屈曲波数越大时, 内部结构相互作用域进一步收缩, 使得有效弯曲刚度减小, 所以非局部参数对屈曲力的影响更为显著; 在外载荷和温度耦合作用下, 温度升高会导致屈曲临界力减小, 温度降低会导致屈曲临界力增大. 还对3 种不同温度场进行了讨论, 分析了在3 种温度场下温度变化对外载荷的影响, 以及与系统尺寸大小的关系.

关键词: 非局部理论, 屈曲, 双轴受压, 温度变化, 粘接材料

Abstract: The scale effect on buckling of bonding materials under biaxial compression coupled with temperature changes is studied. A developed nonlocal plate theory is applied to study the buckling behavior of the nonlocal multiple-plate model. The Navier’s approach is used to obtain exact solutions for buckling loads under simply supported boundary conditions. The effects of the scale coefficient, wave number, thickness ratio, elastic modular ratio and temperature changes on the buckling loads are investigated. It is shown that the critical buckling force may be overestimated with the classical continuum theory. The nonlocal effect is proved to be more prominent for higher buckling modes. In addition, three kinds of temperature changes are taken into account. The influence of temperature
changes on the buckling loads and the relationship with the system size are analyzed.

Key words: biaxial compression, bonding material, buckling, nonlocal elastic theory, temperature change

中图分类号:

O 34

刘亮, 彭香武, 王青占, 郭兴明. 粘接材料及结构在双轴受压和温度耦合作用下变形的尺度效应和非局部效应分析[J]. 上海大学学报(自然科学版), 2015, 21(4): 422-431.

LIU Liang, PENG Xiang-wu, WANG Qing-zhan, GUO Xing-ming. Scale effect on buckling of bonding materials under biaxial compression with temperature changes[J]. Journal of Shanghai University（Natural Science Edition）, 2015, 21(4): 422-431.

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粘接材料及结构在双轴受压和温度耦合作用下变形的尺度效应和非局部效应分析

Scale effect on buckling of bonding materials under biaxial compression with temperature changes

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