A Robust Elastoplastic Analysis of Plate Structures via Mathematical Programming

This paper presents a robust mathematical programming framework for elastoplastic analysis of plate structures, addressing critical limitations of traditional nonlinear analysis and Newton-Raphson-based methods. By recasting the nonlinear structural problem as a mathematical programming task, the proposed approach eliminates iterative equilibrium corrections, stiffness matrix updating and inversions, and ad hoc stabilization techniques. The core analysis mechanism is the consideration of the effect of nonlinearities occurring in some parts of the structure on the whole structure and formulating the yield condition in the form of a mathematical problem that can be solved by Linear Programming (LP) solution scheme. The method’s efficacy is demonstrated through three numerical examples: a rectangular plate, a horizontally curved plate, and a circular plate exhibiting material softening. Results show close agreement with Yield-Line Theory and ABAQUS simulations while achieving exact responses and naturally capturing softening behavior without displacement-control algorithms. This work bridges a critical gap in extending mathematical programming methods beyond frame structures, offering a foundation for efficient large-scale elastoplastic analyses in practical engineering.