正六角形单胞周期性蜂窝板等效刚度研究  

Study of effective stiffnesses of periodic honeycomb plate with regular hexagonal unit cell

作　　者：蔡园武[1] 徐亮[1] 程耿东[1] 

机构地区：[1]大连理工大学工程力学系,辽宁大连116024

出　　处：《大连理工大学学报》2014年第4期377-383,共7页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(91216201;11372062);"九七三"国家重点基础研究发展计划资助项目(2014CB049000)

摘　　要：利用已提出的一种周期性板等效刚度求解新方法,研究了六角形蜂窝板在壁厚和单胞高度等在相当大的范围内变化时的等效刚度,给出了计算蜂窝板等效刚度的一系列解析近似公式,并对其进行了验证.这种新方法能够精确实现理论上严格的渐近均匀化方法,并具有代表体元法的直观简洁,可以根据单胞的不同尺寸采用不同的单元类型,大大提高了求解效率.最后讨论了文献中已有的近似解析解的精度、经典层合板理论成立的条件及泊松比的影响等.Using a new method of calculating effective stiffnesses of periodic plate structures,the effective stiffnesses of hexagonal honeycomb plate are studied with various wall thicknesses and cell heights varying in large extent.A series of explicit approximate formulas are given to estimate the effective stiffnesses,and the results are verified.The new method can exactly realize asymptotic homogenization method which is strict in theory,and is easy to implement as the representive volume element （RVE）method.It is able to use different element types to model the honeycomb unit cell according to its specific sizes and improve efficiency.At last,the accuracy of the explicit approximate formulas,valid condition of the classical laminate theory and the influence of the Poisson＇s ratio are discussed.

关 键 词：等效刚度 蜂窝板 渐近均匀化 有限元法 层合板理论 

分 类 号：O341[理学—固体力学]