Nonstandard Models for Thin-Walled Beams With a View to Applications

1996 ◽  
Vol 63 (2) ◽  
pp. 399-403 ◽  
Author(s):  
N. Rizzi ◽  
A. Tatone
Keyword(s):  
Cross Sections ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Lateral Buckling ◽  
Simply Supported Beam ◽  
One Dimensional ◽  
Simply Supported ◽  
Flexural Buckling ◽  
Nonstandard Models ◽  
Thin Walled

A direct theory of a one-dimensional structured continuum is introduced in order to study the postbuckling behavior of thin-walled beams. A simply supported beam bent by end couples is analyzed showing that, in the case of nonsymmetric cross sections, lateral buckling gives rise to imperfection sensitivity. Then an axially loaded beam is studied taking also into account the interaction between torsional and flexural buckling. The results obtained prove that in this case imperfection sensitivity, though slighter than in the previous case, arises also for symmetric cross sections.

Torsional and Flexural Buckling of Bars of Thin-Walled Open Section Under Compressive and Bending Loads

1942 ◽  
Vol 9 (3) ◽  
pp. A103-A107 ◽  
Author(s):  
J. N. Goodier
Keyword(s):  
Lateral Buckling ◽  
Flexural Buckling ◽  
Open Section ◽  
Bending Loads ◽  
Thin Walled ◽  
General Section ◽  
Observed Behavior

Abstract The observed behavior of torsionally weak columns in buckling by twisting rather than, or as well as, bending is analyzed in this paper on the basis of a hypothesis due to Wagner. The theory is simplified, and extended to the general section, where results simpler than some already obtained by Kappus are given. It is further extended to bars, restrained by flexible sheets, and bars with constrained axes of rotation. Wagner’s hypothesis is applied to the problem of lateral buckling, where it yields the accepted theory for symmetrical sections, but indicates results of novel form for unsymmetrical cases. Similar results are obtained in the problem of eccentric thrust, whatever the section.

scholarly journals On incorporating warping effects due to transverse shear and torsion into the theories of straight elastic bars

2020 ◽  
Author(s):  
T. Lewiński ◽  
S. Czarnecki
Keyword(s):  
Cross Sections ◽  
Transverse Shear ◽  
Explicit Construction ◽  
Effective Characteristics ◽  
Warping Function ◽  
Torsional Buckling ◽  
Lateral Buckling ◽  
First Order ◽  
Thin Walled ◽  
Scientific Tool

Abstract By endowing El Fatmi’s theories of bars with first-order warping functions due to torsion and shear, a family of theories of bars, of various applicability ranges, is effectively constructed. The theories thus formed concern bars of arbitrary cross-sections; they are reformulations of the mentioned theories by El Fatmi and theories by Kim and Kim, Librescu and Song, Vlasov and Timoshenko. The Vlasov-like theory thus developed is capable of describing the torsional buckling and lateral buckling phenomena of bars of both solid and thin-walled cross-sections, which reflects the non-trivial correspondence, noted by Wagner and Gruttmann, between the torsional St.Venant’s warping function and the contour-wise defined warping functions proposed by Vlasov. Moreover, the present paper delivers an explicit construction of the constitutive equations of Timoshenko’s theory; the equations linking transverse forces with the measures of transverse shear turn out to be coupled for all bars of asymmetric cross-sections. The modeling is hierarchical: the warping functions are numerically constructed by solving the three underlying 2D scalar elliptic problems, providing the effective characteristics for the 1D models of bars. The 2D and 1D problems are indissolubly bonded, thus forming a unified scientific tool, deeply rooted in the hitherto existing knowledge on elasticity of elastic straight bars.

Analysis of Thin-Walled Closed Beams With General Quadrilateral Cross Sections

1999 ◽  
Vol 66 (4) ◽  
pp. 904-912 ◽  
Author(s):  
J. H. Kim ◽  
Y. Y. Kim
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Distortion Function ◽  
Element Formulation ◽  
Numerical Work ◽  
New Approach ◽  
One Dimensional ◽  
Static And Dynamic Analysis ◽  
Thin Walled ◽  
The One

This paper deals with the one-dimensional static and dynamic analysis of thin-walled closed beams with general quadrilateral cross sections. The coupled deformations of distortion as well as torsion and warping are investigated in this work. A new approach to determine the functions describing section deformations is proposed. In particular, the present distortion function satisfies all the necessary continuity conditions unlike Vlasov's distortion function. Based on these section deformation functions, a one-dimensional theory dealing with the coupled deformations is presented. The actual numerical work is carried out using two-node C0 finite element formulation. The present one-dimensional results for some static and free-vibration problems are compared with the existing and the plate finite element results.

Buckling and Postbuckling of Imperfect Cylindrical Shells: A Review

1986 ◽  
Vol 39 (10) ◽  
pp. 1517-1524 ◽  
Author(s):  
George J. Simitses
Keyword(s):  
Critical Conditions ◽  
Offshore Platforms ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Combined Application ◽  
Round Cylinder ◽  
Load Carrying ◽  
Thin Walled ◽  
Complex Structural ◽  
Structural Configurations

Thin-walled cylinders of various constructions are widely used in simple or complex structural configurations. The round cylinder is commonly found in tubing and piping, and in offshore platforms. Depending on their use, these cylinders are subjected (in service) to individual and combined application of external loads. In resisting these loads the system is subject to buckling, a failure mode which is closely associated with the establishment of its load-carrying capacity. Therefore, the system buckling and postbuckling behavior have been the subject of many researchers and investigators both analytical and experimental. The paper is a state-of-the-art survey of the general area of buckling and postbuckling of thin-walled, geometrically imperfect, cylinders of various constructions, when subjected to destabilizing loads. The survey includes discussion of imperfection sensitivity and of the effect of various defects on the critical conditions.

scholarly journals Catastrophic Influence of Global Distortional Modes on the Post-Buckling Behavior of Opened Columns

Materials ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3314
Author(s):  
Andrzej Teter ◽  
Zbigniew Kolakowski
Keyword(s):  
Cross Sections ◽  
Carrying Capacity ◽  
Strong Interactions ◽  
Load Carrying Capacity ◽  
Buckling Modes ◽  
Flexural Buckling ◽  
Load Carrying ◽  
Post Buckling ◽  
Global Modes ◽  
Thin Walled

The multimodal buckling of thin-walled isotropic columns with open cross-sections under uniform compression is discussed. Column lengths were selected to enable strong interactions between selected eigenmodes. In the case of short columns or very long ones subjected to compression, single-mode buckling can be observed only and the effect under discussion does not occur. In the present study, the influence of higher global modes on the load-carrying capacity and behavior in the post-buckling state of thin-walled structures with open cross-sections is analyzed in detail. In the literature known to the authors, higher global modes are always neglected practically in the analysis due to their very high values of bifurcation loads. However, the phenomenon of an unexpected loss in the load-carrying capacity of opened columns can be observed in the experimental investigations. It might be explained using multimode buckling when the higher global distortional-flexural buckling modes are taken into account. In the conducted numerical simulations, a significant influence of higher global distortional-flexural buckling modes on the post-buckling equilibrium path of uniformly compressed columns with C- and TH-shaped (the so-called “top-hat”) cross-sections was observed. The columns of two lengths, for which strong interactions between selected eigenmodes were seen, were subject to consideration. Two numerical methods were applied, namely, the semi-analytical method (SAM) using Koiter’s perturbation approach and the finite element method (FEM), to solve the problem. The SAM results showed that the third mode had a considerable impact on the load-carrying capacity, whereas the FEM results confirmed a catastrophic effect of the modes on the behavior of the structures under analysis, which led to a lack of convergence of numerical calculations despite an application of the Riks algorithm. All elastic-plastic effects were neglected.

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