Limitation of Simplified Hypotheses for the Prediction of Torsional Oscillations for Thin-Walled Beams

1985 ◽  
Vol 107 (1) ◽  
pp. 117-122 ◽  
Author(s):  
A. Potiron ◽  
D. Gay ◽  
C. Czekajski ◽  
S. Laroze
Keyword(s):  
Natural Frequencies ◽  
Beam Theory ◽  
Refined Theory ◽  
Warping Function ◽  
Thin Wall ◽  
Relative Thickness ◽  
Torsional Oscillations ◽  
Dynamic Torsion ◽  
Thin Walled

The study of uniform torsion of thin walled beams is done fairly easily in the thin wall beam case, the effects of thickness being neglected. Then, the classical Saint-Venant warping function simplifies to the double sectorial area. The dynamical case needs the use of a more refined theory involving nonuniform warping, and characterized by supplementary dynamic torsion constants. The computed values obtained from BIEM for those constants are compared with those deduced from thin walled beam theory, and from the measurements of experimental natural frequencies. It is shown that the relative thickness acts significantly on the results in both static and dynamic torsion cases.

Thin-Walled Multicell Beam Analysis for Coupled Torsion, Distortion, and Warping Deformations

2000 ◽  
Vol 68 (2) ◽  
pp. 260-269 ◽  
Author(s):  
J. H. Kim ◽  
Y. Y. Kim
Keyword(s):  
Shear Flows ◽  
Systematic Approach ◽  
Beam Theory ◽  
Warping Function ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Superior Result ◽  
Beam Analysis ◽  
Thin Walled

Due to the complicated deformations occurring in thin-walled multicell beams, no satisfactory one-dimensional beam theory useful for general quadrilateral multicells appears available. In this paper, we present a new systematic approach to analyze the coupled deformations of torsion, distortion, and the related warping. To develop a one-dimensional thin-walled multicell beam theory, the method to determine the section deformation functions associated with distortion and distortional warping is newly developed. In order to guarantee the singlevaluedness of the distortional warping function in multicells, distortional shear flows have been utilized. The superior result by the present one-dimensional theory is demonstrated with various examples.

Dynamic Response of Thin-Walled Composite Material Timoshenko Beams

1990 ◽  
Vol 112 (2) ◽  
pp. 149-154 ◽  
Author(s):  
L. C. Bank ◽  
C.-H. Kao
Keyword(s):  
Natural Frequencies ◽  
Fiber Composite ◽  
Beam Theory ◽  
Composite Beams ◽  
Mode Shapes ◽  
Structural Members ◽  
Timoshenko Beams ◽  
Conventional Steel ◽  
Thin Walled ◽  
Offshore Industry

Thin-walled structural members are used extensively in the offshore industry in applications ranging from marine risers to platforms and frames. Advanced fiber composite structural members may offer advantages over their conventional steel counterparts in certain situations. Use of composite members will require modifications to existing structural analysis codes. This paper presents a beam theory for thin-walled composite beams that can be incorporated into existing codes. Timoshenko beam theory is utilized to account for shear deformation effects, which cannot be neglected in composite beams, and for the variability in material properties in different walls of the beam cross section. The theory is applied to the analysis of the free vibration problem and shows the dependence of the natural frequencies and mode shapes on the in-plane properties of the laminates that form the walls of the beam. Forced periodic and forced arbitrary problems are also discussed and the deflected shapes and maximum deflections are shown as functions of wall layups.

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.

Analysis of Deformation for PC Thin-Wall Box Girders Exposed to Fire

2011 ◽  
Vol 368-373 ◽  
pp. 930-933
Author(s):  
Wei Hou ◽  
Shuan Hai He ◽  
Cui Juan Wang ◽  
Gang Zhang
Keyword(s):  
Finite Element ◽  
Thin Wall ◽  
Fire Load ◽  
Box Girders ◽  
Conduction Model ◽  
Load Model ◽  
Deformation Problem ◽  
Finite Element Procedure ◽  
Thin Walled

Being aimed to deformation problem of pre-stressed concrete thin-walled multi-room box girders exposed to co-action of fire and load, on the basis of enthalpy conduction model and thermo-mechanics parameters, the finite element procedure was applied to analyze the deformation of three spans pre-stressed concrete thin-walled multi-room box girders exposed to co-action of fire and load. In conclusion, the deflection is obvious under action of the variation width and fire load model.

Stresses in Curved, Circular Thin-Wall Tubes

1963 ◽  
Vol 30 (1) ◽  
pp. 134-135
Author(s):  
E. A. Utecht
Keyword(s):  
Thin Wall ◽  
Bending Moments ◽  
Circular Tubes ◽  
Out Of Plane ◽  
Thin Walled ◽  
Plane Bending

Curves are presented which give stress intensification factors for curved, thin-walled circular tubes under various combinations of in-plane and out-of-plane bending moments.

scholarly journals A Refined Theory for Bending Vibratory Analysis of Thick Functionally Graded Beams

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1422
Author(s):  
Youssef Boutahar ◽  
Nadhir Lebaal ◽  
David Bassir
Keyword(s):  
Beam Theory ◽  
Functionally Graded ◽  
Effective Characteristics ◽  
Hyperbolic Function ◽  
Transverse Displacement ◽  
Refined Theory ◽  
Distribution Law ◽  
Fg Beam ◽  
The Impact ◽  
Beam Theories

A refined beam theory that takes the thickness-stretching into account is presented in this study for the bending vibratory behavior analysis of thick functionally graded (FG) beams. In this theory, the number of unknowns is reduced to four instead of five in the other approaches. Transverse displacement is expressed through a hyperbolic function and subdivided into bending, shear, and thickness-stretching components. The number of unknowns is reduced, which involves a decrease in the number of the governing equation. The boundary conditions at the top and bottom FG beam faces are satisfied without any shear correction factor. According to a distribution law, effective characteristics of FG beam material change continuously in the thickness direction depending on the constituent’s volume proportion. Equations of motion are obtained from Hamilton’s principle and are solved by assuming the Navier’s solution type, for the case of a supported FG beam that is transversely loaded. The numerical results obtained are exposed and analyzed in detail to verify the validity of the current theory and prove the influence of the material composition, geometry, and shear deformation on the vibratory responses of FG beams, showing the impact of normal deformation on these responses which is neglected in most of the beam theories. The obtained results are compared with those predicted by other beam theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of FG beams.

Sign in / Sign up

Export Citation Format

Share Document