Secondary buckling of a heated circular plate

Upon heating, a circular plate with immovable edge exhibits buckling, which results in axisymmetric postcritical bending. Progressive axisymmetric bending due to increasing thermal load in the postbuckling range leads to substantial redistribution of the stresses in the plate and occurrence of high compressive circumferential stresses in a narrow zone adjacent to the plate edge. In this case, secondary buckling can occur resulting in unsymmetric stress-strain state. The aim of the present work is to study stability behavior of the postbuckling axisymmetric equilibrium configurations of a circular plate subjected to uniform temperature rise. The plate edge is assumed to be immovable in the radial and transverse directions and elastically restrained against bending rotation, which allows one to model the boundary conditions between two extremes of clamped and simply supported. The stability analysis is performed by the semi-analytical finite element method, where unknown displacements are approximated by truncated Fourier series in the circumferential coordinate. The geometrical nonlinearity is taken into account in a quadratic approximation using the Fӧppl - von Karman nonlinear plate theory. To find equilibrium states of the plate, an iterative algorithm is proposed which requires determination of the coefficients of the first and second variations of the total potential energy. Stability of the equilibrium states is examined using the criterion of positive defineteness of the Hess matrix of the plate finite-element model. The critical temperature rise at which secondary buckling occurs is determined. The postbuckling nonlinear deformation characterized by local winkling near the plate edge is studied. The effect of boundary conditions and temperature-dependent material properties on the critical thermal load and secondary buckling modes is discussed.