弹性材料层表面失稳的解析解  

Analytic solutions for surface instability of elastic layers

作　　者：孟吉祥 吴枝根[1] 

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2014年第2期220-224,共5页Journal of Hefei University of Technology：Natural Science

基　　金：合肥工业大学博士学位人员专项基金资助项目(4115103001)

摘　　要：文章通过求解均质材料弹性层中增量位移表示的平衡微分方程,分别得出了均质弹性层和材料参数不同的双层结构弹性层表面失稳的解析解。结果表明:均质材料弹性层表面失稳的临界应变只与材料的泊松比有关;而与弹性模量无关;对于双层结构的弹性层,临界应变和临界波长与弹性层的表层与里层的厚度比和弹性模量比都相关,结果与相关文献结论吻合得很好。By solving the differential equations of equilibrium expressed by incremental displacements for homogeneous elastic layer ,the analytical solutions for critical condition of surface instability of a homogeneous layer and a bilayer with different material properties are obtained respectively .The re-sults show that the critical strain of homogeneous elastic layers is related to Poisson ’s ratio and inde-pendent of the elastic modulus .For the elastic bilayer ,the critical strain and critical wavelength are related to both thickness ratio and elastic modulus ratio of surface and inner layers .The results ob-tained agree well with those in the related literature .

关 键 词：表面失稳 临界条件 弹性材料层 解析解 

分 类 号：O343.9[理学—固体力学]