Buckling of plates and shells is a very important concern in many industrial applications. For example, in military and some other sensitive industries, such as aerospace and submarine industries, due to special application and the loading which is imposed on the plates/shells, buckling is potentially a common failure mode of structures. If before the buckling is initiated, at least one material point of the structure experiences yielding, then buckling is called elastic-plastic, or briefly, plastic buckling. On the other hand, thin plates are usually produced by cold rolling process. As it is well known, the cold-rolled plates are intrinsically anisotropic in plastic deformation. Therefore when cold-rolled plates are used in the so-called applications, where the buckling phenomenon is a potential risk, the plastic anisotropy should be taken into account, if plastic buckling to be studied. In this thesis, plastic buckling of a rectangular thin plate, with plane anisotropy in plastic deformation, under uniform normal edge traction, is studied. For this purpose, the critical buckling load was determined based on minimizing the integral criterion of uniqueness of the solution. A polynomial Rayleigh-Ritz approach was used to approximate transversal displacement of the plate. Hill’s 48 orthotropic yield criterion was employed to derive elastic-plastic constitutive equations for both Incremental and Deformation (IT and DT) plasticity theories. The uniaxial behavior of the material was modeled by a bilinear stress-strain curve. A bilinear model, compared with Ramberg-Osgood model, which has been extensively used in previous researches, allows to introduce a specific yield stress in the material properties. To study the effect of boundary conditions on the critical buckling load, different combinations of simply supported and clamped boundary conditions was examined for different edges of the plate. Substituting the increment of stress and strain components in terms of trial transverse displacement, in uniqueness criterion, the integral can be computed as a function of unknown coefficients. The result of the integral should be then minimized with respect to unknown coefficients. This procedure results in a homogeneous system of algebraic in terms of the unknown coefficients. For non-trivial solution, the determinant of the coefficient matrix should be equated to zero. The critical buckling load is then determined as the lowest root of the matrix determinant. A MTLAB code has been developed to derive the matrix determinant and solve for critical buckling load. The results show that the buckling load increases as the all anisotropy (Lankford) coefficients increase. The greatest difference between buckling load for isotropic and anisotropic plate was found to be around 10% which was occurred for CSCS boundary conditions. Keywords: Elastic-Plastic Buckling, Rectangular Thin Plate, Plane Plastic Anisotropy, Hill’s 48 Yield Criterion, Bilinear Stress-Strain Curve
