GBT-BASED BUCKLING ANALYSIS OF THIN- WALLED STEEL FRAMES WITH ARBITRARY LOADING AND SUPPORT CONDITIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 363-385 ◽  
Author(s):  
CILMAR BASAGLIA ◽  
DINAR CAMOTIM ◽  
NUNO SILVESTRE
Keyword(s):  
Finite Element ◽  
Beam Theory ◽  
Mode Shapes ◽  
Shear Stresses ◽  
Transverse Beam ◽  
Space Frames ◽  
Buckling Behavior ◽  
Global Buckling ◽  
Thin Walled ◽  
Support Conditions

This paper is concerned with the development and application of a Generalized Beam Theory (GBT) formulation to analyse the local and global buckling behavior of thin-walled steel plane and space frames with arbitrary loadings and various support conditions. This formulation takes into account the geometrical effects stemming from the presence of longitudinal normal stress gradients and also the ensuing pre-buckling shear stresses. Following a description of the main concepts and procedures involved in determining the finite element and frame linear and geometric stiffness matrices (incorporating the influence of joints, applied loading and support conditions), one presents and discusses some numerical results concerning the local and global buckling behavior of (i) simple "L-shaped" frames and (ii) space frames formed by two symmetrical portal frames joined through a transverse beam. For validation purposes, the GBT-based results are compared with those obtained by rigorous shell finite element analyses using ANSYS. An excellent correlation, for both the critical buckling loads and mode shapes, is found in all cases.

GBT FORMULATION TO ANALYZE THE BUCKLING BEHAVIOR OF THIN-WALLED MEMBERS SUBJECTED TO NON-UNIFORM BENDING

2007 ◽  
Vol 07 (01) ◽  
pp. 23-54 ◽  
Author(s):  
RUI BEBIANO ◽  
NUNO SILVESTRE ◽  
DINAR CAMOTIM
Keyword(s):  
Finite Element ◽  
Major Axis ◽  
Shear Stresses ◽  
Longitudinal Stress ◽  
Stress Gradients ◽  
Stiffness Reduction ◽  
Buckling Behavior ◽  
Global Buckling ◽  
Thin Walled ◽  
Uniformly Distributed Loads

In this paper, one investigates the local-plate, distortional and global buckling behavior of thin-walled steel beams subjected to non-uniform bending moment diagrams, i.e. under the presence of longitudinal stress gradients. One begins by deriving a novel formulation based on Generalized Beam Theory (GBT), which (i) can handle beams with arbitrary open cross-sections and (ii) incorporates all the effects stemming from the presence of longitudinally varying stress distributions. This formulation is numerically implemented by means of the finite element method: one (i) develops a GBT-based beam finite element, which accounts for the stiffness reduction associated to applied longitudinal stresses with linear, quadratic and cubic variation, as well as to the ensuing shear stresses, and (ii) addresses the derivation of the equilibrium equation system that needs to be solved in the context of a GBT buckling analysis. Then, in order to illustrate the application and capabilities of the proposed GBT-based formulation and finite element implementation, one presents and discusses numerical results concerning (i) rectangular plates under longitudinally varying stresses and pure shear, (ii) I-section cantilevers subjected to uniform major axis bending, tip point loads and uniformly distributed loads, and (iii) simply supported lipped channel beams subjected to uniform major axis bending, mid-span point loads and uniformly distributed loads — by taking full advantage of the GBT modal nature, one is able to acquire an in-depth understanding on the influence of the longitudinal stress gradients and shear stresses on the beam local and global buckling behavior. For validation purposes, the GBT results are compared with values either (i) yielded by shell finite element analyses, performed in the code ANSYS, or (ii) reported in the literature. Finally, the computational efficiency of the proposed GBT-based beam finite element is briefly assessed.

Buckling Analysis of Thin-Walled Steel Structural Systems Using Generalized Beam Theory (GBT)

2015 ◽  
Vol 15 (01) ◽  
pp. 1540004 ◽  
Author(s):  
Cilmar Basaglia ◽  
Dinar Camotim
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Beam Theory ◽  
Mode Shapes ◽  
Structural Systems ◽  
Hollow Section ◽  
Buckling Behavior ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

This paper deals with the application of beam finite element models based on generalized beam theory (GBT) to analyze the buckling behavior of four thin-walled steel structural systems, namely (i) beams belonging to storage rack systems, (ii) pitched-roof industrial frames, (iii) portal frames built from cold-formed rectangular hollow section (RHS) profiles and (iv) roof-supporting trusses, exhibiting different support conditions and subjected to various loadings. In particular, taking advantage of the GBT unique and structurally clarifying modal features, it is possible to assess how different geometries and/or bracing arrangements affect (improve) the local, distortional and/or global buckling behavior of the above structural systems. The accuracy of the GBT-based buckling results is assessed through the comparison with values yielded by rigorous shell finite element analyzes carried out in the code ANSYS. In spite of the disparity between the numbers of degrees of freedom involved, which are orders of magnitude apart, there is a virtual coincidence between the critical loads and mode shapes provided by the GBT (beam) and ANSYS (shell) finite element analyzes.

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 .

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.

Free Flexural Vibrations Response of Composite Mindlin Plates or Panels With a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint)

2005 ◽  
Author(s):  
U. Yuceoglu ◽  
O. Gu¨vendik ◽  
V. O¨zerciyes
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Solution Technique ◽  
Shear Stresses ◽  
Lap Joint ◽  
Adhesive Layers ◽  
Present Solution ◽  
Flexural Vibrations ◽  
Support Conditions ◽  
Interpolation Polynomials

The present study is concerned with the “Free Flexural Vibrations Response of Composite Mindlin Plates or Panels with a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint). The plate “adherends” and the plate “doublers” are considered as dissimilar, orthotropic “Mindlin Plates” with the transverse and the rotary moments of inertia. The relatively, very thin adhesive layers are taken into account in terms of their transverse normal and shear stresses. The mid-center of the bonded region of the joint is at the mid-center of the entire system. In order to facilitate the present solution technique, the dynamic equations of the plate “adherends” and the plate “doublers” with those of the adhesive layers are reduced to a set of the “Governing System of First Order ordinary Differential Equations” in terms of the “state vectors” of the problem. This reduced set establishes a “Two-Point Boundary Value Problem” which can be numerically integrated by making use of the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. In the adhesive layers, the “hard” and the “soft” adhesive cases are accounted for. It was found that the adhesive elastic constants drastically influence the mode shapes and their natural frequencies. Also, the numerical results of some parametric studies regarding the effects of the “Position Ratio” and the “Joint Length Ratio” on the natural frequencies for various sets of support conditions are presented.

scholarly journals Dynamic Analysis of Tapered Thin-Walled Beams Using Spectral Finite Element Method

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yiping Shen ◽  
Zhijun Zhu ◽  
Songlai Wang ◽  
Gang Wang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Wind Turbine ◽  
Element Model ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Modal Frequency ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Spectral Finite Element

Tapered thin-walled structures have been widely used in wind turbine and rotor blade. In this paper, a spectral finite element model is developed to investigate tapered thin-walled beam structures, in which torsion related warping effect is included. First, a set of fully coupled governing equations are derived using Hamilton’s principle to account for axial, bending, and torsion motion. Then, the differential transform method (DTM) is applied to obtain the semianalytical solutions in order to formulate the spectral finite element. Finally, numerical simulations are conducted for tapered thin-walled wind turbine rotor blades and validated by the ANSYS. Modal frequency results agree well with the ANSYS predictions, in which approximate 30,000 shell elements were used. In the SFEM, one single spectral finite element is needed to perform such calculations because the interpolation functions are deduced from the exact semianalytical solutions. Coupled axial-bending-torsion mode shapes are obtained as well. In summary, the proposed spectral finite element model is able to accurately and efficiently to perform the modal analysis for tapered thin-walled rotor blades. These modal frequency and mode shape results are important to carry out design and performance evaluation of the tapered thin-walled structures.

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