Enhanced geometrically non-linear Generalized Beam Theory (GBT) formulation: derivation, numerical implementation and application

Dinar Camotim, André Martins, Rodrigo Gonçalves, Pedro Borges Dinis

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Traditionally, the non-linear behavior of prismatic thin-walled members could only be rigorously assessed by resorting to time-consuming and computation-intensive shell finite element simulations, providing outputs not easy to apprehend/interpret. However, in the last decade, higher-order/advanced beam models emerged as very promising alternatives to obtain similarly accurate results. Generalised Beam Theory (GBT) is one of such models, able to analyze the non-linear behavior of thin-walled structural members in an efficient and (mostly) clarifying manner (only a few structurally meaningful d.o.f. are required). Indeed, by performing GBT-based geometrically non-linear imperfect analyses (GNIA) of prismatic thin-walled members, it becomes possible to unveil and quantify the contributions of the various deformation modes to the member structural response. This feature enables acquiring much deeper insight on that response, thus contributing towards obtaining a clearer picture of the mechanics involved - i.e., it makes GBT GNIA an ideally suited numerical tool to investigate complex instability problems. GBT GNIA formulations were previously developed by Miosga (1976) and, much more recently, by Silvestre (2005), Basaglia (2010) and Silva (2013). These authors adopted a total Lagrangian kinematic description and an additive decomposition of the strain terms into Green-Lagrange membrane strains and small-strain bending. However, they disregarded several non-linear membrane strain terms that were found to play an important role in the non-linear behavior of thin-walled members, particularly in the moderate-to-large displacement range, which must be considered when dealing with mode coupling problems (e.g., Martins et al. 2016)  in such problems, neglecting the above non-linear strain terms leads to inaccurate results, sometimes by a fairly large margin. The aim of this work is to enhance the GBT GNIA formulations mentioned in the previous paragraph, by including the whole set of non-linear membrane strain terms - this is equivalent (but not similar) to the formulation proposed by Gonçalves & Camotim (2012). After presenting, in some detail, the main steps involved in the development and numerical implementation of the novel/enhanced GBT GNIA formulation, several illustrative numerical results are presented and discussed, in order to (i) enable a better grasp of the concepts and procedures involved, and (ii) assess the relevance of the added non-linear membrane strain terms. Such results concern columns and beams subjected to uniform stress resultant diagrams and buckling in local, distortional and/or global modes. For validation purposes, several GBT-based results are compared with values yielded by ABAQUS shell finite element analyses - a virtually perfect match is invariably found. Enhanced Geometrically Non-Linear Generalized Beam Theory (GBT) Formulation: Derivation, Numerical Implementation and Application | Request PDF. Available from: https://www.researchgate.net/publication/317335615_Enhanced_Geometrically_Non-Linear_Generalized_Beam_Theory_GBT_Formulation_Derivation_Numerical_Implementation_and_Application [accessed Sep 26 2018].
Original languageEnglish
Title of host publicationProceedings of the 2017 Engineering Mechanics Institute Conference (San Diego, USA, 4-7 june)
PublisherAsce American Society of Civil Engineers
Number of pages1
Publication statusPublished - 4 Jun 2017


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