Buckling analysis and shape optimization of elastic variable thickness circular and annular plates—I. Finite element formulation

This paper deals with the buckling analysis of circular and annular plates using the finite element method. A family of variable thickness, curved, C(0), Mindlin–Reissner axisymmetric finite elements is developed which include shear deformation and rotary inertia effects. The accuracy, convergence and efficiency of these elements are explored through a series of buckling analyses of plate structures and the results are compared with those obtained by other analytical and numerical methods. The comparisons show that the method yields very good results with a relatively small number of elements and that estimates for the higher modes can be obtained without any difficulties. In a companion paper these accurate and efficient finite elements are used in the context of structural shape optimization.