Elastic/plastic buckling of isotropic thin plates subjected to uniform and linearly varying in-plane loading using incremental and deformation theories

The present study is concerned with the elastic/plastic buckling of thin rectangular plates under various loads and boundary conditions. The in-plane loads are placed uniformly and linearly varying in the uniaxial compression and biaxial compression/tension. The equilibrium and stability equations are derived and analyses are carried out based on two theories of plasticity, i.e. deformation theory (DT) and incremental theory (IT). The elastic/plastic behavior of plates is described by the Ramberg–Osgood model. Generalized Differential Quadrature (GDQ) discretization technique is used to solve the buckling of plate equation. To examine accuracy of the present formulation and procedure, several convergence and comparison studies are investigated and new results are presented. The differences between the IT and DT results increase by increasing loading parameter in linearly varying in-plane loading. Some new consequences are achieved regarding the validation range of two theories. Furthermore, effects of aspect, thickness to length and loading ratios, boundary condition, type of plasticity theory and linearly varying in-plane loading on the buckling coefficient are discussed. Contour plots of buckling mode shapes for various loading parameters are also illustrated.