Use of Ritz technique to investigate the sensitivity of the postbuckling response of FG microplates to geometric imperfections

Abstract

The present study examines the postbuckling behavior of imperfect microplates made from functionally graded (FG) materials using modified strain gradient theory (MSGT) and modified couple stress theory (MCST). Geometric nonlinearity is incorporated by using von-Karman’s assumptions, and the first-order shear deformation theory is used for modeling the microplates. Modified strain gradient theory defines three length scale parameters, and modified couple stress theory (MCST) reduces it to one parameter. To approximate the unknown displacement fields of the problems, the Ritz technique with Legendre polynomials is employed. The solution is derived by minimizing the total potential energy and solving the nonlinear system of equations using the Newton–Raphson technique. The nonlinear postbuckling response of imperfect FG microplates is investigated by considering the effects of various boundary conditions, different values of initial imperfection, material gradient index.