A KINEMATIC ALGORITHM FOR PLASTIC ANALYSIS OF BEAM STRUCTURES BY DIRECT METHOD

Abstract

A kinematic-based direct method is proposed for evaluating limit and shakedown loads of beam structures subjected to proportional and cyclic loading. Conventional incremental elastoplastic analyses require detailed knowledge of the entire loading history and may involve high computational cost, which limits their application to complex structures. In contrast, direct methods allow the determination of critical load levels without tracing the full loading path. In this work, an upper bound formulation for limit and shakedown analysis of beam structures is developed using admissible plastic generalized strain fields within a kinematic framework. The resulting problem is formulated as a nonlinear optimization problem with compatibility and normalization constraints. A combined penalty–Lagrange technique is employed, and the corresponding Karush–Kuhn–Tucker conditions are solved using Newton iterations. The formulation is implemented within a finite element framework using the von Mises yield criterion. Several numerical examples involving statically indeterminate beams subjected to concentrated loads under proportional and cyclic loading are presented. The results show good agreement with analytical solutions and demonstrate fast and stable convergence of the proposed algorithm. These findings indicate that the proposed method provides an efficient and reliable tool for limit and shakedown analysis of beam structures.