合肥工业大学学报（自然科学版）
閤肥工業大學學報（自然科學版）
합비공업대학학보（자연과학판）
JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY(NATURAL SCIENCE)
2014年
2期
220-224
,共5页
表面失稳%临界条件%弹性材料层%解析解
錶麵失穩%臨界條件%彈性材料層%解析解
표면실은%림계조건%탄성재료층%해석해
surface instability%critical condition%elastic material layer%analytic solution
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。
文章通過求解均質材料彈性層中增量位移錶示的平衡微分方程，分彆得齣瞭均質彈性層和材料參數不同的雙層結構彈性層錶麵失穩的解析解。結果錶明：均質材料彈性層錶麵失穩的臨界應變隻與材料的泊鬆比有關；而與彈性模量無關；對于雙層結構的彈性層，臨界應變和臨界波長與彈性層的錶層與裏層的厚度比和彈性模量比都相關，結果與相關文獻結論吻閤得很好。
문장통과구해균질재료탄성층중증량위이표시적평형미분방정，분별득출료균질탄성층화재료삼수불동적쌍층결구탄성층표면실은적해석해。결과표명：균질재료탄성층표면실은적림계응변지여재료적박송비유관；이여탄성모량무관；대우쌍층결구적탄성층，림계응변화림계파장여탄성층적표층여리층적후도비화탄성모량비도상관，결과여상관문헌결론문합득흔호。
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 .
