In this study, the buckling response of homogeneous circular plates with variable thickness subjected to radial compression based on the first-order shear deformation plate theory in conjunction with von-Karman nonlinear strain-displacement relations is investigated. Furthermore, optimal thickness distribution over the plate with respect to buckling is presented. In order to determine the distribution of the prebuckling load along the radius, the membrane equation is solved using the shooting method. Subsequently, employing the pseudospectral method that makes use of Chebyshev polynomials, the stability equations are solved. The influence of the boundary conditions, the thickness variation profile and aspect ratio on the buckling behavior is examined. The comparison shows that the results derived, using the current method, compare very well with those available in the literature. تفاصيل المقالة

In this study, based on nonlocal differential constitutive relations of Eringen, the first order shear deformation theory of plates (FSDT) is reformulated for vibration of nano-plates considering the initial geometric imperfection. The dynamic analog of the von Kármán nonlinear strain-displacement relations is used to derive equations of motion for the nano-plate. When dealing with nonlinearities, in the frame work of nonlocal theory, challenges are presented because of the coupling between nonlocal stress resultants and displacement terms. Governing equations are solved using differential quadrature method (DQM) and numerical results for free vibration of an imperfect single layered graphene sheet are presented. تفاصيل المقالة