球面各向同性功能梯度压电球壳的三维热释电分析  

Three Dimensional Pyroelectric Analysis of Functionally Graded Piezoelectric Spherical Shell with Spherical Isotropy

作　　者：刘承斌[1] 边祖光[2] 

机构地区：[1]浙江大学土木系,杭州310058 [2]浙江大学宁波理工学院,宁波315100

出　　处：《力学季刊》2010年第4期562-569,共8页Chinese Quarterly of Mechanics

基　　金：国家杰出青年科学基金(10725210);浙江省自然科学基金(Y6100234)

摘　　要：采用层合近似技术,将压电球壳划分成厚度足够小的若干薄层,从而可将每一层内的材料参数近似为常数。在此基础上,利用状态空间列式和级数展开方法进行了解析求解。导出了稳态热传导问题内外边界温度场状态变量的整体传递关系,从而可以由边界处的温度条件决定球壳内任一点的温度场。给出了两类电弹性状态方程和相应的整体传递关系,其中第二类含有与温度场有关的非齐次项,从而可以确定由温度荷载引起的耦合电弹性场。最后给出了算例,讨论了材料梯度指标对非均匀球壳热释电响应的影响。An approximate laminate model was employed for the thermo-electro-elastic analysis of functionally graded pyroelectric spherical shell,which is divided into many sufficiently thin layers,within which all material parameters can be assumed constant.Based upon the state-space formulations,ananalytic solution was obtained by the series expansion technique.The global transfer relation between state variables of the thermal field was derived for steady thermal conduction,and the thermal field can be exactly determined once incorporating the prescribed surface temperatures into the relation.Two independent kinds of electro-elastic state equations were presented and the corresponding global transfer relations were also established.It notes that the second kind of state equation has an inhomogeneous item that is associated with the thermal effect.The coupled electro-elastic field induced by the temperature load then can be determined.Finally,the influence of material inhomogeneity on the pyroelectric response of the spherical shell were discussed numerically.

关 键 词：功能梯度压电球壳 热释电效应 层合模型 位移函数 应力函数 状态空间法 

分 类 号：O343.6[理学—固体力学] O343.8[理学—力学]