Bending Buckling Research Articles

Bending instability of an embedded double-walled carbon nanotube based on Winkler and van der Waals models

The present paper examines the instability of a double-walled carbon nanotube embedded in an elastic medium under pure bending. Effect of surrounding elastic medium and van der Waals forces between the inner and outer nanotubes is taken into consideration. From the point of view of continuum modeling, an elastic double-shell model is presented for the pure bending buckling of a double-walled carbon nanotube. Based on this model, a condition is derived in terms of the buckling modes of the shell, from which the critical bending moment can be predicted. The paper emphasizes bifurcation instability. It is shown that buckling may occur. Finally, a simplified analysis is carried out to estimate the moment causing bifurcation instability of the double-walled carbon nanotube.

Asymptotic Methods in the Buckling Theory of Elastic Shells

Equations of Thin Elastic Shell Theory Basic Equations of Shell Buckling Simple Buckling Problems Buckling Modes Localized Near Parallels Non-Homogeneous Axial Compression of Cylindrical Shells Buckling Modes Localized at a Points Semi-Momentless Buckling Modes Effect of Boundary Conditions on Semi-Momentless Modes Torsion and Bending of Cylindrical and Conic Shells Nearly Cylindrical and Conic Shells Shells of Revolution of Negative Gaussian Curvature Surface Bending and Shell Buckling Buckling Modes Localized at an Edge Shells of Revolution under General Stress State.

Nonlinear bending response and buckling of ring-stiffened cylindrical shells under pure bending

Abstract In this paper, the nonlinear bending response of finite length cylindrical shells with stiffening rings is investigated by using a modified Brazier approach. The basic assumptions for the present study are that the deformation of a shell subjected to pure bending can be simplified into a two-stage process. One is that the shell ovalizes but its axis remains straight; the other is that the bending of the shell is regarded as a beam with nonuniform ovalization. The nonlinear bending response is derived by applying the minimum potential energy principle and the corresponding critical moment, associated with local buckling, is determined by employing the Seide–Weingarten approximation. Numerical results are shown and compared with those obtained from other methods, which demonstrates that the assumptions used in the present study are reasonable.

Bending buckling of an elastoplastic cylindrical shell with a cutout

The buckling behavior of an elastoplastic cylindrical shell with a cutout under pure bending was investigated analytically and experimentally. For analysis, a finite element code based on an updated Lagrangian formulation was established to analyze the problem of bending buckling by considering nonlinear geometric and material properties. An iterative displacement-controlled scheme was adopted in the solution procedure to ensure the pure bending state and to avoid numerical instability near the limiting buckling moment. A testing device was used to perform experiments on bending buckling. The ratio of diameter to thickness of the aluminum specimens was 50; the ratio of length to diameter was 7.9. The shape of the cutout on the shell was circular or rectangular. The influence of the size and location of the cutout on the limiting buckling moment is discussed. Antisymmetric deformation around the cutout in the shells was observed after bending buckling of the shell.

Static Strength of Axially Loaded Tubular K-Joints. I: Behavior

This paper reports the results of an extensive finite-element study into the static behavior of axially loaded tubular K-joints. The emphasis of the study was on the effects of the geometric parameters and the overlap amount on the behavior of overlap joints. The results of some K-joints with small gaps were also included for comparative purposes. The study reveals new insight into how the behavior of axially loaded overlap K-joints varies across the practical range of geometric parameters. Certain overlap geometries were seen to be 100% efficient, with the joints reaching the brace member squash load capacity. Other failure modes of chord bending, brace local buckling, and in particular, combined chord bending and brace local buckling were evident. Examination of the load-deformation characteristics for the sharp falls in the postpeak load—reflecting sudden joint failures, which have been a suggested cause for concern in the past—has revealed that relatively few overlap geometries exhibit such behavior. ...

Load Capacity of Nested, Laterally Braced, Cold-Formed Steel Z-Section Beams

Cold-formed steel Z-purlins were tested in combining bending and shear to evaluate the behavior of lap joints. The tested sections covered a range of web depth-to-thickness ratios ( h /t) from 79 to 131 and lap-to-span ratios from 0.25 to 1.0. The results indicated that the lapping process significantly enhances the load capacity for beams with lap-to-span ratios up to 0.5. Little or no further enhancement was noted for higher ratios. A bending buckling pattern governed the failure of all beams at stresses close to the steel yield stress. Failure was encountered in the single-section zone for beams with lap-to-span ratio less than 0.5, and in the lap zone for higher ratios. Correlations were established to predict the load capacity of lapped beams and were found in agreement with the results of a study cited in the literature. Current American Iron and Steel Institute specifications were also found to be adequate to predict the strength of the single Z-section.

Force-Extension Relation and Plateau Modulus for Wormlike Chains.

We derive the linear force-extension relation for a wormlike chain of arbitrary stiffness including entropy elasticity, bending and thermodynamic buckling. From this we infer the plateau modulus $G^0$ of an isotropic entangled solution of wormlike chains. The entanglement length $L_e$ is expressed in terms of the characteristic network parameters for three different scaling regimes in the entangled phase. The entanglement transition and the concentration dependence of $G^0$ are analyzed. Finally we compare our findings with experimental data.

Analysis of Shear Buckling of Cylindrical Shells. 3rd Report. Postbuckling Behaviors.

Cylindrical shells subjected to lateral loads buckle in shear or bending modes. The bending buckling mode results in a diamond-shaped pattern or elephant-foot bulge at the edge. In this paper, by developing a special-purpose finite-element analysis program using the 8-node isoparametric shell element, the postbuckling behaviors and residual deformations under cyclic lateral loading are investigated in both shear buckling and bending buckling cases. The shear buckling patterns on the shell change according to the direction of loading in the shear buckling case. In the bending buckling case, shear mode also appears in addition to elephant-foot bulge.

Ultimate Load Capacity of Single Steel Angles

Design of single-angle members has been a controversial subject for some time. The design specifications differ considerably with regard to design of these members. The authors are to be thanked for their effort to shed more light in this area that clearly needs additional research. By considering a large range of slenderness ratios (60, 90, 120, 150, 180, and 210) in their experiments, the authors have covered a wide spectrum of single-angle struts. The experimental results are compared with ASCE Manual 52 (1988) for design of latticed transmission towers. This comparison indicates that the manual overpredicts angle capacity by a significant margin for both (L/r 120) struts. As has been emphasized by the authors, full-scale tests are often made on lattice transmission towers in the power industry. These tests indicate that the capacity of the towers is very close to that predicted by ASCE Manual 52. This is a clear indication that individual member tests, while serving a very useful purpose of verifying analytical methods, often fail to model the behavior of members assembled as a structure. The strut tests reported use ball end connections, thus removing all beneficial end restraint effect present in a tower. This may be the reason for the significant difference in capacity predicted by the tests and Manual 52. The paper reports L/r values for the tests. It would be useful to know the location of the points in the test setup between which the length L was measured. This will have an impact on the comparison with Manual 52, particularly for shorter angles. In the design office, typically, L is taken from work point to work point. Another point of interest would be any information about the lateral behavior of the members. Were the lateral deflections and rotations along the length measured in the study? It is the experience of the writers that steel single angles, when loaded through one leg in compression fail by exhibiting a bending (buckling) behavior predominantly about one leg only. This appears to be true whether the loading is through long leg or short leg. Perhaps the authors would like to throw some light on this subject. The tables showing the test and calculated ultimate load of single angles appear to have an error. For example, the test capacities shown in kips in Figs. 4 and 9 for test number 4 and I, respectively, do not convert to the corresponding capacities shown in the tables. The authors might wish to clarify the point. It is also interesting to compare the results of these tests with recently reported tests by Elgaaly et al. (1992) that were performed on the web members of a truss. Tests 18, 19,50,51, and 52 in Elgaaly et al. are similar in slenderness, angle size, and steel strength to test 21 by the authors as shown in Table 10. Manual 52 capacity shown in Table 10 is based on nominal section properties and nominal yield strength (248 MPa). Nominal values are used as will be the case in the design office. It is noteworthy that test 21 has lower slenderness ratio and higher F, and yet, has a test capacity significantly lower than that for the corresponding tests by Elgaaly et al. (1992). This perhaps is because the tests reported by the authors include the detrimental

Studies on the Seismic Buckling Design Guideline of FBR Main Vessels. 2nd Report. Formulae for Evaluating Shear-Bending Buckling Strength.

Although plastic shear-bending buckling of the cylindrical part of FBR main vessels under horizontal earthquake loading is one of the most critical problems in structural design, the evaluation method of buckling strength is not specified in related standards in Japan. The purpose of this paper is to describe the results of static buckling tests of cylindrical shells and to present formulae for determining the allowable buckling strength of FBR main vessels. Shear buckling and bending buckling are evaluated under the assumption that both buckling modes interact slightly with each other. Shape imperfection within the plate thickness regarding shear buckling, and one-half the plate thickness regarding bending buckling is considered in the formulae originally.

“Recoil” Compressive Strength Test and the Evolution of Compressive Behavior in PAN-Based Carbon Fibers

AbstractThe compressive properties of PAN-based carbon fibers were measured with the tensile recoil method. The recoil fracture morphology was also examined. In addition to the axial compression, flexure during recoil affects the test results. Compressive failure may be caused by shear failure and/or bending buckling of the microfibrils/fibrils. Study of the evolution of compressive and other mechanical properties discloses that, in general, the compressive strength bears a similar tendency to the tensile strength and torsion modulus up to the carbonization temperature of 1500 °C. However, the relative rate of evolution is different. To some extent, the bending buckling mechanism may relate to the structural units which govern the tensile strength.

Formulae for Evaluating Buckling Strength of FBR Main Vessels under Earthquake Loading.

Although plastic shear-bending buckling of the cylindrical part of Fast Breeder Reactor (FBR) main vessels under horizontal earthquake loading is one of the most critical problems in structural design, the evaluation method of buckling strength is not specified in related standards in Japan. Central Research Institute of Electric Power Industry (CRIEPI), commissioned by the Ministry of International Trade and Industry of the Japanese government, is carrying out verification tests of fast breeder technologies (from FY 1987 through 1993). The Demonstration Test and Research Program of Buckling of FBR is part of the commissioned research program, and the first half was accomplished after establishing a seismic buckling design guideline (a tentative draft) in FY 1989. The purpose of this paper is to describe the results of static buckling tests and numerical analyses, and to present formulae for determining the buckling strength of FBR main vessels. Shear buckling and bending buckling are evaluated under the assumption that both buckling modes slightly interact with each other. Regarding shear buckling, shape imperfection within the plate thickness is considered in the formulae originally, and a correction factor for larger imperfections is provided

Exact analysis of bending and overall buckling of sandwich beam systems

This paper formulates the stiffness matrix and a procedure for exact solutions of the bending and overall buckling problem of a general class of sandwich beam and frame structures subjected to arbitrary loading and boundary conditions. The solutions for deflections, stresses and buckling load are exact in the sense that they satisfy the governing differential equation, interelement compatibility and all boundary conditions. A preliminary study of the behaviour of sandwich beams using the developed theory shows that the Saint Venant principle may not apply to sandwich beams regarding the effects of applied end moments. Restraint against shear deformations will generally reduce the deflections and shear stresses in the core, and increase stresses in the facings and the buckling load. Quantitative assessment of these and other factors can be easily carried out with the present theory.

Analysis of Shear Buckling of Cylindrical Shells. (2nd Report. Effects of Combined Loadings).

Cylindrical shells subjected to lateral loads buckle in shear or bending buckling modes. The effects of combined loadings are investigated by developing a special-purpose FEM program using the 8-node isoparametric shell element. Three types of loading, lateral and axial loads, and pure bending moments are considered. For short cylindrical shells, shear buckling modes are dominant, but elephant-foot bulges take place with an increase in bending moments. Effects of axial loads on shear buckling and the elephant-foot bulge are investigated. In the case of shear buckling the axial load affects the buckling mode as well as the buckling load. For bending bucklings, the axial loads have great effect on the buckling load.

The effect of specimen size on the bending strength of unidirectional carbon fibre-epoxy

Four-point bending and pinned-end buckling tests were carried out on scaled specimens of 25, 50 and 100 plies. Both types of test gave similar results and showed a significant decrease in strength with increasing specimen size. The smaller specimens tended to fail progressively in tension. The tensile strain to failure decreased by about 8% for each doubling of specimen size. This corresponds to a Weibull modulus of about 25. However the amount of scatter in the results was much smaller than that expected based on Weibull strength theory. The larger specimens tended to fail catastrophically in compression. This suggests a reduction in compressive strength with specimen size which may be even larger than the reduction in tensile strength.

A Service-Life Model for Casing Strings

Summary Conventional casing design is based solely on the achievement of adequate design factors in burst, collapse, and tension from the loads generated by the hanging weight of the pipe, internal and external surface pressures, and fluid densities. The effects of cementing, temperature changes, ballooning, changes in cross-sectional area, bending, and helical buckling are virtually never considered. This paper describes a service-life model for the design analysis of casing strings that includes the significant factors that affect the performance of the string.

Improved finite element models for the large displacement bending and post buckling analysis of thin plates

Triangular finite element models are presented for the large displacement bending and postbuckling analysis of thin plates. The formulation is based upon a general variational theory which offers a wide scope for the selection of valid finite element trial functions. This makes it feasible to model the particular physical actions crucial to the successful calculation of large displacement behaviour. In this paper it is demonstrated by numerical examples that a notable improvement in performance is achieved, without a significant increase in computational effort, when simple inextensional bending deformations are included explicitly in the finite element trial functions.

17—A STUDY OF INELASTIC DEFORMATIONS OF TEXTILE FABRICS

After a phenomenological discussion of elasticity, viscosity, friction, and plasticity in textile structures, rheological models of coupled frictional, elastic, and plastic elements of finite and infinitesimal types are demonstrated, and their stress–strain behaviour is derived. These models are applied to deformation–recovery phenomena of textile fabrics in extension, shearing, bending–buckling, and creasing, and theoretical conclusions are compared with experimental results.

Electron Microscope Investigation of Extinction Line Contours in Copper Oxide Whiskers

Oxide whiskers were grown in dry air on pre-worked and pre-annealed copper and studied by high-magnification transmission electron microscopy. Examinations of individual whiskers at high magnifications revealed a complex array of lines of strong contrast within some of the crystals. Stereoscopic examinations of single whiskers revealed that the lines were not associated with any thickness variation within the crystal. The application of diffraction contrast and dark field techniques indicated that the lines in most cases were a result of loss of illumination due to Bragg reflections, perhaps as a result of bending or elastic buckling of the whisker. Only in a few isolated cases, when line contrast reversals were obtained in the dark field images, was it possible to associate these lines with an inherent strain field in the whisker. The extinction bend contours observed in the broader whiskers formed on pre-worked copper were normally more complex than those exhibited by the thinner whiskers formed on the pre-annealed specimens.

Bending Rigidity and Column Strength of Thin Sections

Abstract It has been found that elementary structural theory cannot be applied with accuracy to problems concerning beams and columns having thin deep webs and thin wide flanges, because of nonuniform stress distribution which exists in the flanges. In this paper the problems of nonuniform axial flange stress are treated by means of efficiency factors which apply to the flange material. These basic factors are evaluated from theoretical considerations. Then, given a particular section and the manner of loading, it is necessary only to apply the proper flange efficiency factor to calculate reduced or effective section properties, which can be used in place of the geometrical properties in the elementary formulas for lateral bending or lateral column buckling. The results are substantiated by empirical data. Practical usage is illustrated with examples. The tangentmodulus column curve is shown to apply to stiffened-skin panels when based on a “true slenderness ratio” which allows for shear lag effects. Conclusions are drawn indicating design for best efficiency.