A unified nonlocal nonlinear higher-order shear deformable plate model for postbuckling analysis of piezoelectric-piezomagnetic rectangular nanoplates with various edge supports

Abstract

By considering the small-scale effect based on the nonlocal elasticity theory, the nonlinear postbuckling of thick and moderately thick rectangular piezoelectric-piezomagnetic nanoplates with various edge supports subjected to the magneto-electro-thermo-mechanical loading is investigated. For this objective, a unified nonlinear higher-order shear deformable plate model is proposed. By adopting the nonlocal theory to capture the small-scale effect and utilizing a generalized displacement field to consider the influence of transverse shear deformation, unified size-dependent nonlinear governing equations and related boundary conditions are derived based on the virtual work principle in conjunction with von Kármán geometric nonlinearity. By choosing appropriate shape functions, the developed plate model can be reduced to the size-dependent Kirchhoff, Mindlin, Reddy, parabolic, trigonometric, hyperbolic and exponential shear deformable plate models. The nonlinear governing equations and boundary conditions are discretized using the generalized differential quadrature method first. Then, the pseudo arc-length continuation technique is used to solve the discretized equations and obtain the secondary equilibrium path of nanoplate in the postbuckling regime. In addition to providing significant guidelines for accurate prediction of the stability conditions nanoplates, extracting various plate models on the basis of any existing shear deformable plate theory becomes readily attainable by utilizing the proposed unified plate model.