固支三维弹性矩形厚板的精确解  

EXACT SOLUTION OF CLAMPED THREE-DIMENSIONAL ELASTIC RECTANGULAR THICK PLATES

作　　者：田斌[1] 李锐[2] 陈凯[1] 

机构地区：[1]中国路桥工程有限责任公司科技部,北京100011 [2]大连理工大学建设工程学部,大连116024

出　　处：《工程力学》2012年第9期209-214,共6页Engineering Mechanics

摘　　要：采用有限积分变换和状态空间理论相结合的方法推导出了固支三维弹性矩形厚板的精确解。在分析过程中摒弃以往薄板和中厚板理论中有关应力和位移函数的各种人为假定,完全从三维弹性力学基本方程出发,经过变量代换将关于应力和位移分量的六阶偏微分方程组化为2个彼此独立的四阶、二阶矩阵微分方程,再利用有限积分变换的方法得到空间状态方程,并由Cayley-Hamilton定理求得应力和位移分量沿板厚度z方向的传递矩阵,最后利用边界条件定解出待定常数,经过有限积分逆变换解得了固支三维厚板的精确解。通过计算实例验证了该文方法的正确性。The exact solution of clamped three-dimensional rectangular thick plates is derived by the finite integral transform method and state space theory in this paper. The preselection of various stress and displacement functions, commonly used in thick plate models, is abandoned. Based on basic elasticity equations and variable substitution, a system of partial differential equations with respect to stress and displacement components are reduced to two matrix differential equations, one is of second order and another is of fourth order. Then the matrix equations are transferred into the state space equations in the domain of finite integral transform and the transfer matrix in the z direction is presented by Cayley-Hamilton theorem. In the end, the unknown constants are determined via the boundary conditions and the exact solution of clamped three-dimensional rectangular thick plates is obtained. Numerical results demonstrate the validity of the method developed in this paper.

关 键 词：固支三维矩形厚板 有限积分变换 状态向量 CAYLEY-HAMILTON定理 精确解 

分 类 号：O343.2[理学—固体力学]