Elastoplastic analysis of thin-walled bars in the context of Generalised Beam Theory

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Nuno Silvestre
Keyword(s):  
Finite Element ◽  
Beam Theory ◽  
Finite Element Models ◽  
Inelastic Analysis ◽  
Arbitrary Loading ◽  
Steel Bars ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Global Deformation ◽  
Generalised Beam Theory

A formulation of the Generalised Beam Theory (GBT) is presented for the 1st order inelastic analysis of thin-walled steel bars subjected to arbitrary loading and boundary conditions. Five illustrative examples are shown to validate the theory for cases involving global deformation only, namely uniform bending, non-uniform bending, combined bending and axial compression, and non-uniform torsion. Lastly, the results are validated against ABAQUS using beam and shell finite element models. The correlation is typically great concerning equilibrium paths, deformed configurations, and stress diagrams. In those cases where results do not compare so well, possible causes are pointed out.

Post-buckling inelastic analysis of thin-walled metal members using the Generalised Beam Theory

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Miguel Abambres
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Beam Theory ◽  
Flow Theory ◽  
Promising Alternative ◽  
Inelastic Analysis ◽  
Post Buckling ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalised Beam Theory

A 2nd order inelastic Generalised Beam Theory (GBT) formulation based on the J2 flow theory is proposed, being a promising alternative to the shell finite element method. Its application is illustrated for an I-section beam and a lipped-C column. GBT results were validated against ABAQUS, namely concerning equilibrium paths, deformed configurations, and displacement profiles. It was concluded that the GBT modal nature allows (i) precise results with only 22% of the number of dof required in ABAQUS, as well as (ii) the understanding (by means of modal participation diagrams) of the behavioral mechanics in any elastoplastic stage of member deformation .

Nonorthogonal solution for thin-walled members – applications and modelling considerations

2006 ◽  
Vol 33 (4) ◽  
pp. 440-450 ◽  
Author(s):  
R Emre Erkmen ◽  
Magdi Mohareb
Keyword(s):  
Finite Element ◽  
Beam Theory ◽  
Companion Paper ◽  
Finite Element Models ◽  
Element Analysis ◽  
Steel Members ◽  
Longitudinal Stiffeners ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Orthogonal Coordinates

In a companion paper (R.E. Erkmen and M. Mohareb. 2006. Canadian Journal of Civil Engineering, 33: 421–439.), three finite elements based on the Vlasov thin-walled beam theory were formulated using a nonorthogonal coordinate system. Although the associated derivations are more elaborate than in more conventional solutions based on orthogonal coordinates, the new elements offer more modelling capabilities and flexibility in modelling structural steel members, a feature that is illustrated in this paper. In this context, the current paper presents four details in steel construction that were conveniently modelled within the new solution scheme. The applications involve thin-walled members with coped flanges, rectangular holes reinforced with longitudinal stiffeners, and eccentric supports. Comparisons with established shell finite element models using ABAQUS suggest the validity of the new solution. Key words: open sections, finite element analysis, thin-walled members, coped flanges, rectangular holes, eccentric supports.

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

Generalised Beam Theory (GBT) for Shear Deformable Stiffened Sections

2014 ◽  
Vol 553 ◽  
pp. 600-605
Author(s):  
Gerard Taig ◽  
Gianluca Ranzi
Keyword(s):  
Cross Sections ◽  
Beam Theory ◽  
Element Model ◽  
Elastic Behaviour ◽  
Structural Behaviour ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Linear Elastic Behaviour ◽  
Generalised Beam Theory ◽  
Shear Deformable

A Generalised Beam Theory (GBT) formulation is presented to analyse the structural behaviour of shear deformable thin-walled members with partially stiffened cross-sections located at arbitrary locations along their length. The deformation modes used in the formulation are taken as the dynamic eigenmodes of a planar frame representing the unstiffened cross-section. Constraint equations are derived and implemented in the GBT member analysis to model the influence of rigid stiffeners on the member response. The accuracy of the approach is validated against a shell finite element model developed in Abaqus. A numerical example describing the linear elastic behaviour of partially stiffened thin-walled member is provided to outline the usability and flexibility of the proposed method.

INFLUENCE OF INCLINED STIFFENERS IN I-BEAM CONNECTIONS ON BIMOMENT TRANSFERRING

2021 ◽  
Vol 95 (3) ◽  
pp. 47-58
Author(s):  
I.N. SERPIK ◽  
◽  
R.O. SHKOLYARENKO ◽  
Keyword(s):  
Finite Element ◽  
Point Of View ◽  
Frame Structures ◽  
Engineering Practice ◽  
Finite Element Models ◽  
Free Theory ◽  
Scientific Papers ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Finite Element Schemes

Shear-free theory of V.Z. Vlasov remains one of the most reasonable approaches to calculating thin-walled bars taking into account constrained torsion. At the same time, the use of this theory for the analysis of deformations of frame structures still requires research in terms of the conditions for transferring forces in bar connections. As noted in some scientific papers, the balance of bimoments can be significantly broken at the joints of thin-walled bars of an open profile in some designs. This paper deals with this phenomenon for steel I-beam profiles, associated with the presence of inclined stiffeners in joint units. Using shell finite element models, the influence of inclined stiffeners on the appearance of bimoment jumps at the pairwise connection of bars is shown. A dependence is derived that makes it possible to take into account the stiffness of the inclined edge in the bar models from the point of view of the restraint of cross-section warping. On the basis of numerical experiments, it was determined that the introduction of such stiffness into the bar finite element schemes of frame structures allows to reflect the condition of bars interaction in the transferring of bimoments with a sufficiently high accuracy for engineering practice.

scholarly journals GBT-Based Structural Analysis of Elastic-Plastic Thin-Walled Members

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Nuno Silvestre
Keyword(s):  
Finite Element ◽  
Structural Response ◽  
Beam Theory ◽  
High Strength ◽  
Elastic Plastic ◽  
Collapse Mechanisms ◽  
Non Linear ◽  
Steel Grades ◽  
Thin Walled ◽  
Shell Finite Element

Structural systems made of high-strength and/or high-ductility metals are usually also rather slender, which means that their structural behavior and ultimate strength are often governed by a combination of plasticity and instability effects. Currently, the rigorous numerical analysis of such systems can only be achieved by resorting to complex and computationally costly shell finite element simulations. This work aims at supplying to designers/researchers an efficient and structurally clarifying alternative to assess the geometrically and/or materially non-linear behavior (up to and beyond the ultimate load) of prismatic thin-walled members, such as those built from cold-formed steel. The proposed approach is based on Generalized Beam Theory (GBT) and is suitable for members exhibiting arbitrary deformation patterns (e.g., global, local, distortional, shear) and made of non-linear isotropic materials (e.g., carbon/stainless steel grades or aluminum alloys). The paper begins by providing a critical overview of the physically and geometrically non-linear GBT formulation recently developed and validated by the authors (Abambres et al. 2012a), which is followed by the presentation and thorough discussion of several illustrative numerical results concerning the structural responses of 4 members (beams and columns) made of distinct (linear, bi-linear or highly non-linear) materials. The GBT results consist of equilibrium paths, modal participation diagrams and amplitude functions, stress contours, displacement profiles and collapse mechanisms some of them are compared with values obtained from ABAQUS shell finite element analyses. It is shown that the GBT modal nature makes it possible (i) to acquire in-depth knowledge on the member behavioral mechanics at any given equilibrium state (elastic or elastic-plastic), as well as (ii) to provide evidence of the GBT computational efficiency, which is achieved by excluding from the analyses all the deformation modes that do not play any role in a particular member structural response.

Nonorthogonal solution for thin-walled members – a finite element formulation

2006 ◽  
Vol 33 (4) ◽  
pp. 421-439 ◽  
Author(s):  
R Emre Erkmen ◽  
Magdi Mohareb
Keyword(s):  
Finite Element ◽  
Computational Cost ◽  
Beam Theory ◽  
Torsional Stiffness ◽  
Element Formulation ◽  
Field Equations ◽  
Cross Sectional ◽  
Special Cases ◽  
Thin Walled ◽  
Shell Finite Element

Conventional solutions for the equations of equilibrium based on the well-known Vlasov thin-walled beam theory uncouple the equations by adopting orthogonal coordinate systems. Although this technique considerably simplifies the resulting field equations, it introduces several modelling complications and limitations. As a result, in the analysis of problems where eccentric supports or abrupt cross-sectional changes exist (in elements with rectangular holes, coped flanges, or longitudinal stiffened members, etc.), the Vlasov theory has been avoided in favour of a shell finite element that offer modelling flexibility at higher computational cost. In this paper, a general solution of the Vlasov thin-walled beam theory based on a nonorthogonal coordinate system is developed. The field equations are then exactly solved and the resulting displacement field expressions are used to formulate a finite element. Two additional finite elements are subsequently derived to cover the special cases where (a) the St.Venant torsional stiffness is negligible and (b) the warping torsional stiffness is negligible. Key words: open sections, warping effect, finite element,thin-walled beams, asymmetric sections.

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