Winkler地基上矩形层合厚板三维解析解

钟阳, 田斌, 李锐

大连理工大学土木水利学院



摘要:

为求解Winkler地基上矩形简支层合厚板的三维解析解,采用有限积分变换和状态空间理论相结合的方法.在分析过程中舍弃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偏微分方程组化为两个彼此独立的四阶、二阶矩阵微分方程,根据结合面处状态向量的连续性求得沿板厚方向的状态向量传递方程,最后经过有限积分逆变换得到了层合板的三维解析解.通过计算实例验证了方法的正确性,预先将求解矩阵进行降阶处理,提高了求解效率.

关键词:  层合厚板  有限积分变换  Cayley-Hamilton定理  三维解析解

DOI：10.11918/j.issn.0367-6234.2011.04.022

分类号:TU311.4

基金项目:



Three-dimensional analytical solution of simply supported laminated thick rectangular plates on the winkler foundation

ZHONG Yang, TIAN Bin, LI Rui

School of Civil and Hydraulic Engineering,Dalian University of Technology,116024 Dalian, Liaoning,China

Abstract:

Three-dimensional analytical solution of simply supported laminated thick rectangular plates on the Winkler foundation was derived by the finite integral transform method and state space theory.During the analysis process,the preselection of various stress and displacement functions used commonly in thick plate model was abandoned,and based on the basic elasticity equations and variable substitution,a system of partial differential equations with respect to stress and displacement components was reduced to two matrix differential equations,one was second order and another was fourth order.The transfer equation of laminated plates was derived according to the continuity of state space vector of joint surface,the three-dimensional analytical solution of simply supported laminated thick rectangular plates on the Winkler foundation were obtained by the finite integral inverse transform method.Numerical results demonstrate the validity of the method in this paper,and compared with other methods,this method can greatly improve the solution efficiency because of the technique of reduced order.

Key words:  laminated thick rectangular plates  finite integral transform  Cayley-Hamilton theory  Three-dimensional analytical solution