A force-based mathematical programming method for the incremental analysis of 3D frames with non-holonomic hardening plastic hinges

摘要

In this work, a fully automated, step-by-step, 1st order matrix force method is developed for the analysis of planar (2D) and spatial (3D) structural frames made of elastic-hardening plastic material. Plasticity (ideal and hardening) is modelled using plastic hinges of zero-length. The proposed automation techniques utilize Lagrange multipliers to model all forms of discontinuities in a simple and efficient way, within the framework of mathematical programming: internal discontinuities (e.g. articulations) as well as element eccentricities are taken into account. The problem may be solved using any quadraticon-linear optimization algorithm with linear constraints; the redundant forces/moments serve as the primary unknowns. A load-controlled numerical strategy that is suitable for any predefined loading scenario analysis is proposed; its efficiency is demonstrated via a set of examples which are compared with existing results from the literature or output from commercial software based on the equivalent direct stiffness method. (C) 2018 Elsevier Ltd. All rights reserved.