热载荷下粘弹性功能梯度材料薄板的准静态响应  

QUASI-STATIC RESPONSE OF FUNCTIONALLY GRADED VISCO-ELASTIC PLATES UNDER THERMAL LOADS

作　　者：王明禄[1] 张能辉[2] 

机构地区：[1]上海市应用数学和力学研究所,上海200072 [2]上海大学力学系,上海200436

出　　处：《固体力学学报》2004年第4期479-482,共4页Chinese Journal of Solid Mechanics

基　　金：上海市教委青年基金(01QN70);国家自然科学基金(10172056);上海市重点学科资助.

摘　　要：由热粘弹性功能梯度材料的本构方程出发,利用Ｌａｐｌａｃｅ变换,通过引进薄板的“结构函数”和“热函数”,建立了各向同性薄板的数学模型.采用卷积双线性形式,给出了薄板准静态问题的简化Ｇｕｒｔｉｎ型泛函.在空域上和时域上分别采用Ｒｉｔｚ法和Ｌｅｇｅｎｄｒｅ插值法考察了温度变化和功能梯度对于薄板响应的影响.According to the constitutive relation of linear thermovisoelasticity, a mathematical model of viscoelastic FGM thin plates under thermal loads is set up with the help of Laplace transformation method and the introduction of “structure function” and “thermal function”. The corresponding simplified Gurtin type variational principle of FGM thin plates is presented by means of convolution bilinear forms. The influence of temperature variation and functional gradient of materials is investigated by combining the Ritz method in the spatial domain and the Legendre interpolation method in the temporal domain.

关 键 词：双线性形式 泛函 结构函数 准静态 功能梯度 卷积 LAPLACE变换 性功能 梯度材料 影响 

分 类 号：O345[理学—固体力学]