梯度材料平板弯拉耦合力学的精确化支配方程  

Refined Equations for Functionally Graded Material Plates Under Bending-Tension Coupling

作　　者：胡超[1,2] 郑日恒[3] 孙旭峰[1] 周传平[2] 

机构地区：[1]扬州大学建筑科学与工程学院,江苏扬州225127 [2]同济大学航空航天与力学学院,上海200092 [3]中国航天科工集团公司三十一研究所,北京100074

出　　处：《应用数学和力学》2016年第7期756-765,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51378451,51276129);高超声速发动机技术国家重点实验室开放基金(20130103007)

摘　　要：基于非均匀材料弹性力学理论,采用算子谱分解和算子代数方法,对梯度材料平板结构弯曲与拉伸问题进行了研究.首次给出了指数梯度材料平板弯曲与拉伸的力学方程.研究结果表明:与各向同性平板结构弯曲和拉伸问题不同,在功能梯度平板中描述弯曲应力状态与描述拉伸应力状态的广义位移函数以及剪切函数都是耦合的.没有采用工程假设,推导得到的梯度材料平板结构力学方程是精确化的.通过分析可以认识和理解,分别对应于弯曲状态与拉伸状态的应力场耦合机理以及力学响应的构成等.给出的方程及其分析过程可望能够用于类平板形式热防护材料结构的应力分析与强度设计,推进热防护材料结构的轻型化.Based on the theory of elasticity for inhomogeneous media,the spectral compositions of operators and the Vieta＇s theorem of algebra were applied,and the bending-tension coupling problem of plates of functionally graded material（ FGM） was investigated. The refined equations for FGM plates under bendingtension coupling were given. It is shown that,unlike those for the isotropic plate under bending and tension,both the generalized displacement function and the shear function describing the bending stress state and the tension stress state for FGM plates are coupled. Since the derivation of the governing equations was conducted without prior assumptions,the proposed equations for FGM plates can be regarded as exact ones. The work also found out the coupling mechanism and the response structure. The proposed governing equations can be used to analyze the stress of the plate-like FGM structures for thermal protection,and to advance the lightweight design.

关 键 词：梯度板控制方程 算子谱分解 Vieta定理 弯曲与拉伸耦合 耦合机理与响应构成 

分 类 号：O302[理学—力学]