Exact Analytic Solution for Laminated Plates With Free-Edges and Arbitrary Thickness

The problem of free-edges in three-dimensional elasticity is always a difficult one. The conditions that both normal stress and shear stress on the free edges equal zero are satisfied very difficultly. Based on the three-dimensional fundamental equations of elasticity and the state space method, the state equation for orthotropic plates was established through introduction boundary displacement function and consideration of all elastic constants of the orthotropic materials. Series expansion was carried out on the variables of the state equation. An exact solution was presented for laminated plates with arbitrary thickness by satisfaction of boundary conditions which can also satisfy the continuous conditions of stresses and displacements between plies of the laminates. The results of two examples show that the calculation process is simplified and the convergent solution can be achieved with less terms of series when the displacement function of free boundary is adopted. The numerical results with high accuracy can be obtained through comparison with the results of finite element. The results can be used as reference to numerical methods and semi-analytical methods.