Exact solutions for rectangular anisotropic plates with four clamped edges

The plate problem has been investigated for centuries while exact solutions for anisotropic plates are still hard to obtain. In this paper, we aim to get exact solutions for rectangular anisotropic plates with four clamped edges through the state space method. A state space equation for the anisotropic elasticity is derived from the linear elasticity theory for the first time. The Fourier series in exponential form are adopted in the current work. This can transform the transfer matrix with differential operators in state space into a constant matrix. After superposition and differential treatments, the equations for the boundary conditions of four clamped edges are then combined with the state space equation for the anisotropic elasticity, forming a new compound state space which represents the 3D anisotropic plate problem to be solved. By use of the state space method, a solvable linear equation system under the compound state space is formed. Example solution cases for both orthotropic and monoclinic plates with different thicknesses are provided. For comparison purpose, numerical results from the finite element method are also given to indicate the reliability and accuracy of the current state space method.