Narrow Results

The paper presents a Rayleigh–Ritz based non-discretization method of analysis for the inelastic local buckling of rectangular steel plates subjected to applied in-plane axial, bending and shear actions with various boundary conditions. Use is made of the pb-2 representation of the displacement function as the product of a domain polynomial and a boundary polynomial. The constitutive model for the plate is an adaptation of the von Mises yield criterion and the associated flow rule presented in an infinitesimal form, and which leads to an incremental and iterative method of solution. The convergence and accuracy of the solutions are demonstrated, and it is shown that the method of analysis is computationally feasible for the solution of inelastic bifurcative plate instability problems. A parametric study is then undertaken for a range of plate boundary conditions under various regimes of applied loading.

This study proposes an innovative computational strategy to predict the initiation of elastoplastic buckling in shell structures. This strategy is developed in connection with ABAQUS/Standard Finite Element (FE) code. Toward this objective, two constitutive frameworks are implemented as User MATerial subroutines (UMATs) into this FE code; namely, the incremental flow theory of plasticity and the total deformation theory. These frameworks are formulated under the plane-stress condition, which is particularly suitable for modeling sheet structures and which enhances computational efficiency. Elastoplastic buckling is detected by the Hill loss of uniqueness criterion, which establishes that buckling occurs when the global stiffness matrix, derived from the finite element computations, becomes singular. To determine this matrix and investigate its singularity, a Python script is developed and combined to the ABAQUS computations. The reliability and accuracy of this computational strategy are assessed through various representative numerical examples. The effect of some geometric and material parameters on the onset of elastoplastic buckling in both thin and thick plates, as well as cruciform columns, is investigated and compared to reference results from the literature. The findings of the present contribution can serve as useful reference guidelines for ABAQUS/Standard users, offering valuable insights for predicting the occurrence of elastoplastic buckling, even in metallic structures characterized by complex mechanical behavior and geometric configurations.