EXACT SOLUTION OF CLAMPED THREE-DIMENSIONAL ELASTIC RECTANGULAR THICK PLATES

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.