Buckling Of Inhomogeneous Polar Orthotropic Circular Plate

The studying of stability of structure is very important and it has been studied for a long time. Many theoretical results have come out. In recent years, composite material plates have been widely used and people begin to pay attention to the studying of orthotropic plate. But the theory of buckling of polar orthotropic plates is a challenge problem, and no perfect result has been worked out. In such circumstance, it is imperious to deduce an ideal solution but the complexity and special traits of composite material plate makes the analysis of the problem more difficult.Theoretically, there is a isotropic pole in the center of the polar orthotropic plate and linear orthotropic part near the periphery of the plate. So a transition area must exist between the pole and the periphery. This can result in the inhomogeneous property of the circular plate in fact. Because of the continuity of the material, the elasticity property must be continuous in the transition area. Here we name the transition area as transition core and assume the stiffness varying linearly with the radius. With the consideration of this area, the problem will be illuminated more accurately and the relation between transition core and buckling of plate will be found.In this thesis theoretical solution of inhomogeneous polar orthotropic plate was deduced and plate with clamped edges was taken as example. The displacement in radius direction, inner-force in radius direction, inner-force in annulus direction and buckling load with different core-radius ratio were worked out. The effect of core-radius ratio to the result was discussed in the conclusion. In reasoning and calculation, several circumstances were considered. At the center point the elasticity property was assumed as the property of matrix and fiber-material separately. Several illustrations were given to show the relation clearly.With the calculation result we can find that the inhomogeneous takes much less effects on the result with small core-radius ratio than that with great core-radius ratio and the small core-radius ratio's effect can be ignored, thus the calculation is same as homogeneous plate. The plate with great core-radius ratio should be calculated referenced the means given in this thesis.