Buckling of Long Thin Plates under Residual Stresses with Application to Strip Rolling

2014 ◽  
Vol 611-612 ◽  
pp. 221-230 ◽  
Author(s):  
Kekeli Kpogan ◽  
Michel Potier-Ferry
Keyword(s):  
Experimental Data ◽  
Finite Elements ◽  
Residual Stresses ◽  
Thin Plates ◽  
Continuous Annealing ◽  
Deflection Curve ◽  
Strip Rolling ◽  
Buckling Mode ◽  
Buckling Behavior ◽  
Post Buckling

We present a simplified numerical method which can be used to predict efficiently the response of long thin plates under effects of residual stresses induced by production process such as rolling or continuous annealing. The principle consists in assuming harmonic buckling mode along the sheet length, and we consider Koiter-Budiansky post-buckling theory to compute the stress-deflection curve. In this way, only the width of the sheet has to be discretized by 1D finite elements. The size and shape of the flatness defects can be predicted efficiently and for a large number of cases. Various types of residual stresses and loadings can be accounted for. In particular, we will see the influence of the global traction on the buckling and post-buckling behavior. The numerical results are compared with experimental data and full numerical computations

Post-Buckling of Piezoelectric Thin Plates

2015 ◽  
Vol 15 (07) ◽  
pp. 1540020 ◽  
Author(s):  
Michael Krommer ◽  
Hans Irschik
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Nonlinear Behavior ◽  
Dirichlet Boundary Conditions ◽  
Thin Plates ◽  
Governing Equations ◽  
Simply Supported ◽  
Buckling Behavior ◽  
Single Term ◽  
Post Buckling ◽  
Special Case

In the present paper, the geometrically nonlinear behavior of piezoelastic thin plates is studied. First, the governing equations for the electromechanically coupled problem are derived based on the von Karman–Tsien kinematic assumption. Here, the Berger approximation is extended to the coupled piezoelastic problem. The general equations are then reduced to a single nonlinear partial differential equation for the special case of simply supported polygonal edges. The nonlinear equations are approximated by using a problem-oriented Ritz Ansatz in combination with a Galerkin procedure. Based on the resulting equations the buckling and post-buckling behavior of a polygonal simply supported plate is studied in a nondimensional form, where the special geometry of the polygonal plate enters via the eigenvalues of a Helmholtz problem with Dirichlet boundary conditions. Single term as well as multi-term solutions are discussed including the effects of piezoelectric actuation and transverse force loadings upon the solution. Novel results concerning the buckling, snap through and snap buckling behavior are presented.

LOCAL/DISTORTIONAL/GLOBAL MODE INTERACTION IN SIMPLY SUPPORTED COLD-FORMED STEEL LIPPED CHANNEL COLUMNS

2011 ◽  
Vol 11 (05) ◽  
pp. 877-902 ◽  
Author(s):  
P. B. DINIS ◽  
D. CAMOTIM
Keyword(s):  
Shell Element ◽  
Mode Interaction ◽  
Buckling Mode ◽  
Global Mode ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Buckling Behavior ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
Cold Formed Steel

This paper reports the results of a numerical investigation concerning the elastic and elastic-plastic post-buckling behavior of cold-formed steel-lipped channel columns affected by local/distortional/global (flexural-torsional) buckling mode interaction. The results presented and discussed are obtained by means of analyses performed in the code ABAQUS and adopting column discretizations into fine four-node isoparametric shell element meshes. The columns analysed (i) are simply supported (locally/globally pinned end sections with free warping), (ii) have cross-section dimensions and lengths ensuring equal local, distortional, and global (flexural-torsional) critical buckling loads, thus maximizing the mode interaction phenomenon under scrutiny, and (iii) contain critical-mode initial geometrical imperfections exhibiting different configurations, all corresponding to linear combination of the three "competing" critical buckling modes. After briefly addressing the lipped channel column "pure" global post-buckling behavior, one presents and discusses in detail numerical results concerning the post-buckling behavior of similar columns experiencing strong local/distortional/global mode interaction effects. These results consist of (i) elastic (mostly) and elastic-plastic equilibrium paths, (ii) curves and figures providing the evolution of the deformed configurations of several columns (expressed as linear combinations of their local, distortional, and global components) and, for the elastic-plastic columns, (iii) figures enabling a clear visualization of (iii1) the location and growth of the plastic strains, and (iii2) the characteristics of the failure mechanisms more often detected in this work.

scholarly journals Numerical Simulation of Buckling and Post-Buckling Behavior of a Central Notched Thin Aluminum Foil with Nonlinearity in Consideration

Metals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 582 ◽  
Author(s):  
Mahdieh Shahmardani ◽  
Per Ståhle ◽  
Md Shafiqul Islam ◽  
Sharon Kao-Walter
Keyword(s):  
Mode Shape ◽  
Tensile Loading ◽  
Width Ratio ◽  
Plastic Behavior ◽  
Yield Limit ◽  
Buckling Mode ◽  
Buckling Stress ◽  
Buckling Behavior ◽  
Sheet Width ◽  
Post Buckling

In thin notched sheets under tensile loading, wrinkling appears on the sheet surface, specifically around the cracked area. This is due to local buckling and compression stresses near the crack surfaces. This study aims to numerically study the buckling behavior of a thin sheet with a central crack under tension. A numerical model of a notched sheet under tensile loading is developed using the finite element method, which considers both material and geometrical nonlinearity. To overcome the convergence problem caused by the small thickness-to-length/width ratio and to stimulate the buckling, an imperfection is defined as a small perturbation in the numerical model. Both elastic and elasto-plastic behavior are applied, and the influence of them is studied on the critical buckling stress and the post-buckling behavior of the notched sheet. Numerical results for both elastic and elasto-plastic behavior reflect that very small perturbations need more energy for the activation of buckling mode, and a higher buckling mode is predominant. The influences of different parameters, including Poisson’s ratio, yield limit, crack length-to-sheet-width ratio, and the sheet aspect ratio are also evaluated with a focus on the critical buckling stress and the buckling mode shape. With increase in Poisson’s ratio. First, the critical buckling stress reduces and then remains constant. A higher yield limit results in increases in the critical buckling stress, and no change in the buckling mode shape while adopting various crack length-to-sheet-width ratios, and the sheet aspect ratio changes the buckling mode shape.

Onset and Post Buckling of Pipe-in-Pipe’s Helical Buckling Using Improved Energy Method

2018 ◽  
Author(s):  
Lixin Gong
Keyword(s):  
Potential Energy ◽  
Energy Method ◽  
Normal Force ◽  
Horizontal Wells ◽  
Energy Methods ◽  
Buckling Mode ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Helical Buckling ◽  
Remarkable Agreement

The purpose of this paper is to present theoretical solutions based on an improved energy method for predicting the helical buckling (HB) behavior of pipes in vertical, inclined, and horizontal wells. The energy method has been applied to solve the pipe-in-pipe’s (PIP) helical buckling behavior since Lubinski, et al [2] in the 1950’s. However, in the preceding studies, the energy methods are not yet completely correct because the pipe’s potential energy of the distributed contact normal force induced by the helical buckling was considered to be negligible. This deficiency caused improper deductive procedures. In this paper, the energy method is improved by adding the term of the potential energy of the distributed contact normal force. With this improvement, not only can the PIP’s critical helical buckling forces be successfully derived, but it also provides a deeper insight on the PIP’s helical buckling onset, as well as the post helical buckling behavior. For inclined and horizontal wells, equations are provided to determine the critical forces required to initiate the helical buckling mode for both “long” and “short” pipes. In addition, the post buckling behavior is also described, and a new concept of helical buckling zone (HBZ) for “short” pipes is introduced based on the force-pitch plots as an area in-between the helical buckling’s onset curve and the classical Lubinski curve. Finite element ABAQUS models have also been utilized to confirm the analysis using the improved energy method. And the ABAQUS results show remarkable agreement with the theoretical solutions.

Pure Bending Test on a Box Girder With Low Panel’s Slenderness

2018 ◽  
Author(s):  
José Manuel Gordo ◽  
Carlos Guedes Soares
Keyword(s):  
Residual Stresses ◽  
Progressive Collapse ◽  
Bending Moment ◽  
Bending Test ◽  
Box Girder ◽  
Buckling Behavior ◽  
Linear Characteristic ◽  
Collapse Mode ◽  
Post Buckling ◽  
The Moment

The results of a four points bending test on a box girder are presented. The experiment is part of series of tests with similar configuration but different thickness, spacing between longitudinal stiffeners and span between frames. The present work refers to the stockiest plate box girder with a plate’s thickness of 4 mm and a span between frames of 800 mm. The experiment includes initial loading cycles allowing for residual stresses relief. It also includes a series of cycles close to collapse load allowing the analysis of linear characteristic at high levels of load. The moment curvature relationship is established for a large range of curvatures. The ultimate bending moment of the box is evaluated and compared with the first yield moment and the plastic moment allowing the evaluation of the efficiency of the structure. The post buckling behavior and collapse mode are characterized. Comparison of the experiment with a progressive collapse method is made taking into consideration the effect of residual stresses on envelop of the moment curvature curve of the structure.

Effects of symmetric imperfections on the behavior of bistable struts

2016 ◽  
Vol 22 (12) ◽  
pp. 2240-2252 ◽  
Author(s):  
Jianguo Cai ◽  
Xiaowei Deng ◽  
Jian Feng
Keyword(s):  
Virtual Work ◽  
Variable Geometry ◽  
Equilibrium Equations ◽  
Buckling Mode ◽  
Concentrated Load ◽  
Virtual Work Principle ◽  
Shallow Arches ◽  
Buckling Behavior ◽  
Nonlinear Equilibrium ◽  
Post Buckling

The behavior of a bistable strut for variable geometry structures was investigated in this paper. A three-hinged arch subjected to a central concentrated load was used to study the effect of symmetric imperfections on the behavior of the bistable strut. Based on a nonlinear strain–displacement relationship, the virtual work principle was adopted to establish both the pre-buckling and buckling nonlinear equilibrium equations for the symmetric snap-through buckling mode. Then the critical load for symmetric snap-through buckling was obtained. The results show that the axial force is in compression before the arch is buckled, but it becomes in tension after buckling. Thus, the previous formulas cannot be used for the analysis of post-buckling behavior of three-hinged shallow arches. Then, the principle of virtual work was also used to establish the post-buckling equilibrium equations of the arch in the horizontal and vertical directions as well as the static boundary conditions, which are very important for bistable struts.

On the Use of the Hole-Drilling Technique for Residual Stress Measurements in Thin Plates

1992 ◽  
Vol 114 (3) ◽  
pp. 292-299 ◽  
Author(s):  
R. W. Hampton ◽  
D. V. Nelson
Keyword(s):  
Experimental Data ◽  
Residual Stress ◽  
Residual Stresses ◽  
Strain Gage ◽  
Surface Preparation ◽  
Thin Plates ◽  
Hole Drilling ◽  
Thick Plates ◽  
Analysis Methodology ◽  
Drilling Technique

The strain gage blind hole-drilling technique may be used to determine residual stresses at and below the surface of components. In this paper, the hole-drilling analysis methodology for thick plates is reviewed, and experimental data are used to evaluate the methodology and to assess its applicability to thin plates. Data on the effects of gage pattern, surface preparation, hole spacing, hole eccentricity, and stress level are also presented.

Buckling Behavior of Elliptical Shells of Changing Thickness under Uniform Axial Compression

2013 ◽  
Vol 351-352 ◽  
pp. 492-496 ◽  
Author(s):  
Li Wan ◽  
Lei Chen
Keyword(s):  
Axial Compression ◽  
Cylindrical Shells ◽  
Imperfection Sensitivity ◽  
Buckling Mode ◽  
Buckling Strength ◽  
Shell Buckling ◽  
Buckling Behavior ◽  
Structural Applications ◽  
Post Buckling ◽  
Shell Geometry

Many elliptical shells are used in structural applications in which the dominant loading condition is axial compression. Due to the fact that the radius varies along the cross-section midline, the buckling behavior is more difficult to identify than those of cylindrical shells. The general concerned aspects in cylindrical shell buckling analyses such as the buckling mode, the pre-buckling deformation and post-buckling deformation are all quite different related to specific elliptical shell geometry. The buckling behavior of elliptical cylindrical shells with uniform thickness has been widely studied by many researchers. However, the thickness around the circumference may change for some specific structural forms, the femoral neck for example, which makes the buckling behavior more complex. It is known that the buckling strength of thin cylindrical shells is quite sensitive to imperfections, so it is natural to explore the imperfection sensitivity of elliptical shells. This paper explores the buckling behavior of imperfect elliptical shells under axial compression. It is hoped that the results will make a useful contribution in this field.

scholarly journals Dynamic Post-Buckling Behavior

2017 ◽  
Vol 17 (2) ◽  
pp. 131-150
Author(s):  
Ľuboš Šnirc ◽  
Alžbeta Grmanová ◽  
Ján Ravinger
Keyword(s):  
Residual Stresses ◽  
Linear Theory ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Buckling Behavior ◽  
Non Linear ◽  
Post Buckling ◽  
Non Destructive

Abstract Geometric non-linear theory has been used to describe the post-buckling behavior of slender web. Hamilton’s principle in increments has been used. Examples of dynamic post-bucking behavior of slender web loaded in compression are presented. Influence of residual stresses to frequency of slender web is a base for non-destructive method of investigation of structures.

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