Winkler地基上矩形层合厚板三维解析解

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...

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

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 plates model is abandoned; based on the 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 second order and another is 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 are obtained by the finite integral inverse transform method. Numerical results demonstrate the validity of the method in this paper. Compared with other methods, this paper method greatly improve the solution efficiency because of the technique of reduced order.