Buckling of Continuous Circular Plates

The general theoretical development given in this paper considers the material to be orthotropic. Single Frobenius series solutions and double series solutions are obtained for orthotropic continuous plates. These solutions reduce to exact known solutions in the case of isotropic plates. For the purpose of numerical calculations, two cases of isotropic continuous plates—one over an intermediate rigid ring support and the other over an intermediate elastic ring support—are considered. For the case of a free plate over a rigid intermediate support, buckling loads increase as the support moves towards the center. In the case of an elastically supported fixed plate, the support elasticity considerably influences the buckling values, when the coefficient of support elasticity is more than 100. For lower modes a value of K₁ equal to 10,000 gives an almost fixed support. When the support is at distance of 0.355 times the radius of the plate the buckling resistance is found to be a maximum.