Generalized finite element formulation for efficient first-order plastic hinge analysis

Abstract

This article presents generalized finite element formulation for plastic hinge modeling based on lumped plasticity in the classical Euler-Bernoulli beam. In this approach, the plastic hinges are modeled using a special enrichment function, which can describe the weak discontinuity of the solution at the location of the plastic hinge. Furthermore, it is also possible to insert a plastic hinge at an arbitrary location of the element without modifying its connectivity or adding more elements. Instead, the formations of the plastic hinges are achieved by hierarchically adding more degrees of freedom to existing elements. Due to these features, the proposed methodology can efficiently perform the first-order plastic hinge analysis of large-frame structures. A generalized finite element solution technique based on the static condensation scheme is also proposed in order to reduce the computational cost of a series of linear elastic problems, which is in general the most time-consuming portion of the first-order plastic hinge analysis. The effectiveness and accuracy of the proposed method are verified by analyzing several representative numerical examples.

A co-rotational finite element with embedded plastic discontinuities consistently accounting for distributed loads

“…In addition, a generalized Euler-Bernoulli formulation for plastic hinge modeling based on lumped plasticity was proposed by [25], which uses special enrichment functions to describe the weak discontinuity of the solution at the location of the plastic hinge. Juárez-Luna and Tenorio-Montero [26] developed a thick beam-column element with embedded discontinuities for modeling hinges in a simple and double-lined tunnel.…”

Elastic-plastic analysis with pre-integrated beam finite element based on state diagrams: Elastic-perfectly plastic flow

“…The most straightforward approach is the plastic-hinge method [17][18][19], which detects if plastic hinges occur at a given load level; if this happens, the kinematic evolution of the frame is analysed to check possible subsidence mechanisms consequent to instability. Some FE formulations encompass lumped plastic-hinge elements (Fig.…”

“…Fig 18. Pinned-pinned tapered trapezoidal beam subjected to linear variable distributed load and a concentrated moment applied at the right end…”

On the Formulation of an Elastic-Plastic Beam Model: the Pre-Integration Idea

“…A shortcut often considered in beam structures is the lumped plastic-hinge method [9,10] that, although unable to accurately describe the elastic-plastic state within the sections, is capable to estimate the overall collapse of a frame structure. This analysis takes the name of first order plastic hinge.…”