Study On Bending Deformation Of Composite Thick Plates

This paper presents a new mathematic model and a set of close three-dimensional linear solutions, taking account all of the normal stresses and shear stresses, for axisymmetrically homogeneous isotropic circular plates, orthotropic elliptical plates and rectangular plates with all kinds of boundary conditions under uniform transverse load by using variable-separating method and analyzing weight of every-item in these solutions. Reasonability of the model and these three-dimensional linear solutions is demonstrated by comparing with FEM, the classical plate theory, some literature and some experimental results. The major work in the paper is as follows:Research on distribution of strains, stresses and displacements in axisymmetrically homogeneous isotropic circular plates, laminates and sandwich plates with clamped, simply supported edges conditions under uniform transverse load was performed by using displacement method. Three boundary conditions for displacement and three boundary conditions for stress were satisfered on these solutions。A new mathematical model, with less variable-item, taking account of the transverse strains and stresses, was gotten by the influence study of every-item of the three-dimensional solutions for axially symmetrical homogeneous isotropic circular plates.Based on the two-dimensional solutions, taking the solution functions as a set of finite series, three-dimensional solutions were presented for anisotropic elliptic plates, multilayered plates and sandwich plates with rigidly clamped boundary conditions under uniform transverse load, by getting the relationship of all items of the series from the three-dimensional equations of equilibrium.By investigating anisotropic elliptic plates with mid-plane clamped boundary conditions for influence of every-item of the three-dimensional solutions on the accuracy, a new simplified model was obtained, which with less variable-item took into account the transverse strains and stresses. And farther, the model was successfully applied to the anisotropic elliptic plates with simply supported edges boundary conditions.Using the three-dimensional analysis of the anisotropic elliptic plates with mid-plane clamped boundary conditions, with simply supported edges boundary conditions, and their simplified models for reference, some new models with less variable-item took into account the transverse strains and stresses were obtained for orthotropic rectangular plates with different boundary conditions, such as:four clamped edges, four simply supported edges, two opposite clamped and two opposite simplify supported edges, two opposite clamped and two opposite free edges, two opposite free and two opposite simplify supported edges under uniform transverse load.Taking the three-dimensional solutions as the foundation, a set of three-dimensional nonlinear solutions for axisymmetrically homogeneous isotropic circular plates was obtained by using the variable-separating method and turning the nonlinear three-dimensional equations into linear ones.Some experiments were conducted for axisymmetrically homogeneous isotropic circular plates and sandwich circular plates. The results were compared with FEM analysis, class plates and shell theory, three-dimensional exact theory and the paper's theory analysis.