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.

Analysis of thin-walled frames considering joint flexibilities

2007 ◽  
Vol 221 (10) ◽  
pp. 1221-1229 ◽  
Author(s):  
P R Marur
Keyword(s):  
Beam Theory ◽  
Frame Structure ◽  
Elastic Response ◽  
Joint Flexibility ◽  
One Dimensional ◽  
Static And Dynamic Analysis ◽  
Out Of Plane ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Good Agreement

TAnalytical models are developed for static and dynamic analysis of thin-walled frames representing the automotive side structures. The model is based on one-dimensional beam theory that considers joint flexibility to compute stiffness and frequency response of the whole frame structure. The computed out-of-plane displacements under static and impact loading are in good agreement with those obtained from the shell finite element method. Using the validated analytical model, the influence of joint flexibility on the elastic response of the side structure is studied.

On a One-Dimensional Theory of Finite Torsion and Flexure of Anisotropic Elastic Plates

1981 ◽  
Vol 48 (3) ◽  
pp. 601-605 ◽  
Author(s):  
E. Reissner
Keyword(s):  
Linear Theory ◽  
Beam Theory ◽  
Bending Moment ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Cross Sectional ◽  
One Dimensional ◽  
Slender Beams ◽  
Anisotropic Elastic

Equations for small finite displacements of shear-deformable plates are used to derive a one-dimensional theory of finite deformations of straight slender beams with one cross-sectional axis of symmetry. The equations of this beam theory are compared with the corresponding case of Kirchhoff’s equations, and with a generalization of Kirchhoff’s equations which accounts for the deformational effects of cross-sectional forces. Results of principal interest are: 1. The equilibrium equations are seven rather than six, in such a way as to account for cross-sectional warping. 2. In addition to the usual six force and moment components of beam theory, there are two further stress measures, (i) a differential plate bending moment, as in the corresponding linear theory, and (ii) a differential sheet bending moment which does not occur in linear theory. The general results are illustrated by the two specific problems of finite torsion of orthotropic beams, and of the buckling of an axially loaded cantilever, as a problem of bending-twisting instability caused by material anisotropy.

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.

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.

scholarly journals Quantitative Experimental and Theoretical Investigations on the Interaction of Shock Waves with Magnetic Fields

1969 ◽  
Vol 24 (10) ◽  
pp. 1449-1457
Author(s):  
H. Klingenberg ◽  
F. Sardei ◽  
W. Zimmermann
Keyword(s):  
Magnetic Fields ◽  
Shock Waves ◽  
Physical Model ◽  
Spectroscopic Method ◽  
Experimental Results ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Theoretical Investigations ◽  
Theoretical Predictions ◽  
Interaction Of Shock Waves

Abstract In continuation of the work on interaction between shock waves and magnetic fields 1,2 the experiments reported here measured the atomic and electron densities in the interaction region by means of an interferometric and a spectroscopic method. The transient atomic density was also calculated using a one-dimensional theory based on the work of Johnson3 , but modified to give an improved physical model. The experimental results were compared with the theoretical predictions.

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