功能梯度材料矩形板的三维静动态响应分析  

THREE-DIMENSIONAL ANALYSIS FOR STATIC BENDING AND FREE VIBRATION OF FUNCTIONALLY GRADED RECTANGULAR PLATE

作　　者：周凤玺[1,2] 李世荣[3] 

机构地区：[1]兰州理工大学土木工程学院,兰州730050 [2]西部土木工程防灾减灾教育部工程中心,兰州730050 [3]扬州大学建筑科学与工程学院,扬州225009

出　　处：《力学学报》2010年第2期325-331,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10872083);兰州理工大学博士基金(Z42001)资助项目~~

摘　　要：基于线弹性理论的基本方程,选用3个位移分量和3个应力分量作为状态变量,利用状态空间法建立了功能梯度矩形板的三维状态方程.考虑四边简支的边界条件,采用打靶法数值求解了材料常数沿板厚按幂率变化的弯曲问题和自由振动问题,为求解功能梯度材料三维弹性响应提供了一种方法.并且给出了功能梯度材料三维矩形板的静动态响应受组分材料分布以及板厚长比变化的影响规律.The state equation of functionally graded rectangular plate were established with the state variables of three displacement components and three stress components,based on the three-dimensional linear elastic theory by using of state space method.Considering simply supported boundary conditions,the static bending and free vibration problems of a three-dimensional functionally graded rectangular plate were numerically solved by shooting method with that the material properties through the thickness coordinate are assumed to obey the exponent law dependence.Effects of the volume fraction distributions of constituent materials,and thickness-to -side ratio of functionally graded rectangular plate on the dynamical and static responses were studied.The present algorithm can be used to research the three-dimensional elastic response of functionally graded materials.

关 键 词：功能梯度材料 三维分析 状态空间法 打靶法 静力弯曲 自由振动 

分 类 号：O343[理学—固体力学]