Research On State Space Solution For Rectangular Thick Laminated Plates With Clamped/Free Edges

Both the classical theory of thin plates and all the theories of moderately-thick plates are based on some assumptions. If these theories are used to solve the thick laminated plates, the errors produced cannot be ignored. To obtain the three-dimensional exact sulotions of the rectangular thick laminated plates, some theories of thick plates based on the three-dimensional basic equations of elasticity are gradually proposed. As the most effective and popular solution in these theories, the state space method can deal with the continuity conditions on the interfaces between layers easily, and the form of the solution is simple and uniform. So it can be understond and applied easily. When the state space method is used to solve the rectangular thick laminated plates, the variables can be separatied skillfully by means of Double-Fourier series expansion, and the boundary conditions of fully simply supported rectangular plates can be satisfied strictly. However, it is still difficult to solve the rectangular thick laminated plates with non-simply-supported edges. The usual method is introducing undetermined boundary displacement functions on the non-simply-supported edges and solving them by means of dividing the layer into some sub-layers. The solutions presented do not satisfy strictly the boundary conditions on the non-simply-supported edges along the thickness direction.The present dissertation focuses on the rectangular thick laminated plates with clamped or free edges under static loads, and the state space method is adopted to obtain the three-dimensional exact solutions. In the solving process, to satisfy strictly the boundary conditions on the clamped or free edges, the boundary displacement functions are assumed on these edges, and they are treated as state variables and introduced into the state equations. Therefore, the homogeneous state equations are established for the rectangular laminated plates with different boundary conditions, and the three-dimensional exact solutions of the plates under the static loads are presented. The whole solving process is simple and distinct, and it is not necessary to deal with a large number of unknowns, so this method can be applied easily.In the third chapter to the seventh one, the homogeneous state equations are established for the rectangular thick single and laminated plates with different boundary conditions, and the three-dimensional exact solutions of the plates under the static loads are obtained. The calculated examples show that the solutions obtained in this dissertation are agreement with the finite element ones well; the solutions have high precision, good convergence, as well as wide range of application. Compared with the classical theory of thin plates and all the theories of moderately-thick plates, the present solutions satisfy all the three-dimensional basic equations of elasticity, and take all the elastic parameters into account. So they are the three-dimensional exact solutions in the true sense, can provide the precision distributions of the displacements and stresses along the thickness direction. Furthermore,this method is not affected by the thickness and material properties of plates,and can deal with the continuity conditions well. All of these reflect fully the superiority of the state space method to solve the thick laminated plates. Compared with the existing three-dimensional exact sulotions, an absolute analytic method is used to establish the homogeneous state equations of the rectangular laminated plates with different boundary conditions. The solutions can satisfy strictly the boundary conditions on the clamped or free edges, and the precise results of the displacements and stresses on these edges can be obtained. This indicates that the present method breaks the limitation of the existing three-dimensional exact sulotions to solve the rectangular laminated plates with non-simply-supported edges. In addition, the degrees of the polynomials associating with the boundary displacement functions on the clamped or free edges are compared and studied, the results show that the degrees of the polynomials have little effect on the accuracy and convergence of the present solutions.