Elastic-plastic Buckling Research Articles

Methodology For Design Of Earthquake ResistantSteel Liquid Storage Tanks

Steel shells of cylindrical liquid storage tanks are initially designed using a factor of safety specified in the prevailing code. When the safety of tanks under seismic loading is assessed, the capacity of the shell against buckling is computed. There are two types of shell buckling: membrane and elastic-plastic. Although the latter is not accounted for in most codes, it may limit the seismic design especially at higher values of total liquid pressure. The elastic-plastic buckling capacity is eventually depleted when the ratio of total-to-hydrostatic pressures is equal to the employed factor of safety. Numerous tank dimensions were selected for an extensive parametric study, and such tanks were evaluated under varying earthquake intensities. Tanks with larger height-to-radius ratio when subjected to high peak earthquake accelerations tend to be unsafe, if originally designed under commonly specified factor of safety. A formula is suggested to modify the factor of safety according to the height-to-radius ratio and the expected peak earthquake acceleration. This may form the core for developing enhanced seismic design code methodology for steel liquid-filled tanks.

Degradation and Buckling of I-Beams under Cyclic Pure Bending

This paper presents experimental and numerical results of the elasticplastic response and buckling of S3 x 5.7 steel and aluminum I-beams subjected to cyclic pure bending. A special 4-point bending device was designed and built for this purpose. The emphasis of the work is on the description of the response and buckling of the beams. The numerical results were obtained using a commercial finite element program that implements the nonlinear kinematic hardening plasticity model. Results indicate that the beams considered, most of which had length-to-height ratio of 5, buckled first in a global mode involving either twisting or lateral deflections of the beams. The prevailing deflection mode seems to be determined by the nature of the initial geometric imperfections. The deformations induced by the global deflections could induce a local buckle at mid-span. The finite element predictions yield results that qualitatively reproduce the development of most of the aspects of the response of the beams, but generally at a slower rate.

Dynamic buckling of elastic–plastic square tubes under axial impact—II: structural response

Dynamic elastic–plastic buckling of thin-walled square tubes is studied from the viewpoint of elastic–plastic stress wave propagation, which originates from an axial impact loading. The influence of the impact velocity and the striking mass on the development of the buckling shape is discussed when considering the transient deformation process. It is shown that the maximum load, which results from a high velocity impact load and occurs at t=0, is a function of the impact velocity and is related to the speed of the elastic–plastic stress waves propagating along the tube. The predictions for the initiation of buckling based on a numerical simulation of the axial impact of strain rate insensitive square tubes using the FE code ABAQUS show good agreement with the results from experiments on aluminium alloy tubes impacted at various initial velocities. A comparison between the buckling initiation in square tubes and geometrically equivalent circular tubes reveals differences in the response, which are attributed to the stress wave propagation phenomena and to the structural differences between the two structures.

Elastic–plastic buckling of annular circular plate with linear material hardening

AbstractThe contribution treats the buckling problem of a circular annular plate where the unstable state and the buckling process occurs when the stress state in the most loaded points of the plate is already in the elastic–plastic region. It is supposed that the plate buckles axisymmetrically (m = 0) or nonaxisymmetrically with m > 0, m ∈ ℕ waves in the circumferential direction. Using the equilibrium method, the critical buckling loads are calculated. The results show the influence of the material hardening coefficient 0 ≤ f ≤ 1 on the buckling load. The comparison between calculations with the consideration of flow and deformation theory of plasticity is given.

Elastic-Plastic Dynamic Response and Buckling of Steel Columns under Strong Vertical Ground Motion

Elastic-Plastic Dynamic Response and Buckling of Steel Columns under Strong Vertical Ground Motion

引張荷重を受ける傾斜き裂板の座屈特性−弾塑生解析および実験検証

A cracked plate under tension could manifest a local buckling along the crack due to a compressive stress field in the crack’s vicinity. Crack length and location, loading condition, as well as aspect ratio, thickness, and overall dimensions of the plate are among the contributing parameters to the local buckling characteristics. In this study, the buckling characteristics of a cracked plate on whick the crack’s orientation is not perpendicular to the tensile loading were xs examined. Elastic-plastic buckling analyses of a plate with an oblique crack were conducted by taking into account the effect of the plasticity of the crack tip regions on the local buckling. The elastic-plastic analysis results were compared with experimental results as well as with an elastic buckling analysis. This study reveals that the oblique angle of the crack contributes significantly to the characteristics of the buckling behavior.

A study of elastic-plastic buckling of cylindrical shells under torsion

The elastic-plastic buckling of cylindrical shells under torsion is analysed with a deep thick-shell model under various boundary conditions. The word ‘deep’ means that in the general equations of equilibrium the three non-linear terms that involve the torsional force are all retained for the buckling analysis. In the Donnell-type shallow-shell theory, however, only one of such terms is retained. The word ‘thick’ means that in calculating strains and stress resultants the factor (1+ z/ R) is retained. This factor results from the trapezoid-like shape of the cross-section and is usually neglected in the thin-shell theory. For boundary conditions, not only the conventional geometrical boundary conditions, which are in terms of displacements and rotations, but also the mechanical boundary conditions, which are in terms of forces and moments, are considered. The numerical results of examples assess the effect of the additional non-linear terms, the effect of the factor (1+ z/ R), and the effect of the mechanical boundary conditions.

Finite element torsional buckling analysis of shafts with non-concentric bores

The demand for more powerful and efficient aeroengines results in the need to design improved main driveshafts. The design requirement may be to increase the torque capacity of the shafts, to reduce the outer diameter or to reduce the weight. Meeting these requirements tends to increase the likelihood of the shaft buckling and research was carried out to investigate the factors influencing the torsional buckling of shaft sections in order to provide an improved analysis method applicable to typical gas turbine aeroengine shafts. This paper uses finite element analysis to examine the effect of bore concentricity on the elastic-plastic buckling of shafts subjected to pure torsional loading. Equations were developed to predict the buckling torque for a range of shaft geometries and levels of bore eccentricity.

On buckling of toroidal shells under external pressure

The paper presents results of a numerical study into the buckling resistance of geometrically perfect and imperfect steel toroidal shells with closed cross-sections. Elastic and elastic-plastic buckling analyses of shells subjected to uniform external pressure were carried out for a range of geometries, boundary conditions and material properties. Toroids with circular and elliptical cross-sections were investigated. Elastic-plastic analyses carried out for toroids with circular cross-sections allowed identifying shell configurations, which fail by bifurcation buckling or by collapse. An appropriate equation is proposed for identification of configurations for which either bifurcation or collapse governs the shell's stability. The proposed equation supplements Jordan's long-standing design formula, which is applicable to elastic buckling only. The obtained results show that toroids with an elliptical cross-section can be much stronger than shells with a circular cross-section. Calculations identified geometries possessing the largest load carrying capacity. It was found numerically that on both sides of ‘the peak performance geometry’ there is a different failure mechanism which in turn, as it is discussed in the paper, leads to different imperfection sensitivity. A simple design curve is provided for the separation of these two regions. Within each region, the paper provides simple design equations for the elastic buckling strength of geometrically perfect toroids with elliptical cross-sections. Imperfection sensitivities of elastic and elastic-plastic buckling loads to initial, localised and global shape deviations from perfect geometry are given for typical shells with circular and elliptical cross-sections. Initial geometric imperfections in the form of the eigenmode, ‘a single wave’ extracted from the eigenmode and inward dimple modelled by a cosine function in both R-circumferential and r-meridional directions are studied.

Elastic-plastic buckling analysis of rectangular plates subjected to biaxial loads

Elastic-plastic buckling analysis of rectangular plates subjected to biaxial loads

Elastic–plastic buckling behaviour of shafts in torsion

AbstractThe development of more powerful and efficient aero-engines requires ways of increasing the torque transmitted by shafts, whilst also restricting their dimensions and weight. Thin-walled designs can assist this objective, but their use is limited by their torsional collapse behaviour. Of particular interest are conditions leading to buckling instability. The paper investigates the factors influencing this behaviour in order to provide the basis for an improved analysis method applicable to typical gas turbine aero-engine components.The Riks finite element algorithm has been successfully applied to both plain shafts and shafts with holes. In the former case, it is shown that the perfect cylindrical geometry must be given an initial perturbation in order to give accurate predictions. The perturbation imposed is obtained by scaling the mode shape from an eigenvalue solution so that the maximum radial deformation is a percentage of the wall thickness. The predictions for both plain and holed shafts have been validated experimentally.

Dynamic elastic–plastic buckling of circular cylindrical shells under axial impact

Dynamic axisymmetric buckling of circular cylindrical shells struck axially by a mass is studied in order to clarify the initiation of buckling and to provide some insight into the buckling mechanism as a transient process. It is assumed that the material is elastic–plastic with linear strain hardening and displaying the Bauschinger effect. The deformation process is analysed by a numerical simulation using a discrete model. Particular attention is paid to the influence of stress wave propagation on the initiation of buckling. It is found that the development of the buckling shape depends strongly on the inertia properties of the striker and on the geometry of the shell. The theoretical method is used to clarify some experimental data and good agreement is obtained with results on aluminium alloy tubes.

A shell finite element for large strain elastoplasticity with anisotropies—: Part I: Shell theory and variational principle

A shell model for finite elastic and finite plastic strains is derived taking into account initial and induced anisotropies. A corresponding eight-node C 0 shell element with three displacement and three director degrees-of-freedom at each node is developed, which combines the advantages of an isoparametric description of geometry and deformation with an effective plane stress formulation. The element accounts for isochoric or approximately isochoric deformation due to finite plastic strains. Because of the three displacement and three director degrees-of-freedom at each node, it is easily possible to link different parts of a composed irregular shell structure or to connect the derived shell element with solid (brick) elements. This paper presents the shell theory based on the kinematics of finite elastoplasticity proposed in Schieck and Stumpf (1995) and the special geometric concept of the derived shell model. The Lagrange multiplier method is applied to introduce into the virtual work principle the transverse normality constraint and the condition of isochoric deformation, where the Lagrange multipliers can be condensed inside the element procedure. Various assumed strain techniques designed to avoid the membrane locking are compared with known methods in the literature. According to the numerical experience so far the proposed shell finite element is free of locking effects and spurious modes. Part II presents the constitutive equations for finite elastic–plastic strains accounting for initial and induced anisotropies and the implementation of the model into the FE-code. A comprehensive set of numerical examples is provided, involving the tension of a plane specimen with necking and shear-band localization, the elastic–plastic response of a simply supported plate with a localization of the plastic bending strains in the four corner zones, the elastic–plastic deformation mode of the so-called Scordelis-Lo roof, and the elastic–plastic buckling of a cylindrical shell showing an essential influence of the anisotropic material behavior. The results illustrate the performance of the proposed shell finite element for a wide range of engineering applications.

Elastic buckling of ring-stiffened cone–cylinder intersections under internal pressure

Cone–cylinder intersections are commonly found in pressure vessels and piping. Examples include conical end closures to cylindrical vessels and conical reducers between cylinders of different radii. In the case of a cone large end-to-cylinder intersection under internal pressure, the intersection is subject to a large circumferential compressive force. Both the cone and the cylinder may be thickened near the intersection to resist this compression, but it is often convenient and necessary to augment further the strength of the intersection using an annular plate ring stiffener. Under this large circumferential compression, the intersection may fail by elastic buckling, plastic buckling or plastic collapse. This paper describes an investigation of the elastic buckling strength of ring-stiffened cone–cylinder intersections. Two buckling modes are identified: a shell mode for thin intersections with a shallow cone (a cone with its apex half angle approaching 90°) and/or a relatively stocky ring stiffener, and a ring mode for other cases. An existing elastic buckling approximation for annular plate rings in steel silos is found to be applicable to the intersection when it buckles in the ring mode. New approximate design equations are also established for the shell mode. In addition, simple expressions are identified which relate the number of circumferential buckling waves to the geometric parameters of the intersection.

Dynamic Buckling of Simply Supported Columns under Axial Slamming

Dynamic buckling properties of simply supported columns under axial fluid-solid slamming are experimentally investigated in this study. By observing the elastic-plastic responses of columns, the dynamic buckling criterion and the dynamic plasticity criterion of columns are defined and the relevant critical impulses are determined. The effect of the slenderness ratio of the column on the elastic-plastic dynamic buckling properties is also examined. The dynamic buckling characteristics of fluid-solid slammed columns are compared and discussed with respect to those of columns under solid-solid impact. It is found that they are different from those of columns subjected to either impulsive impact or impact owing to suddenly applied load.

On the Thermo-Plastic Deformation for One-Piece Brake Disks.

Braking tests under overloading were carried out using large one-piece brake disks having eyebrow-shaped holes as decoration. When the number of braking was greater than five, permanent deflection of the disks was observed. When the number of braking was less than six, no appreciable deflection occured. The experiment revealed that such deflection occurred during the cooling process after the final braking cycle. The mechanism for this phenomenon is explained based on the deflection-time record in conjunction with the temperature distribution of disks and its variation with respect to time. The key for this phenomenon is yielding in tension at the bridges between holes. The deflection occurs due to elastic-plastic buckling caused by shrinkage of the flange. Numerical simulations were successfully conducted by using a general 3 D FEM in consideration of geometrical and material non-linearities.

Elastic-plastic buckling analysis of rectangular plates subjected to biaxial loads

In order to calculate the buckling load of a rectangular plate, the analytical approach is used in this study. The plate is assumed to be simply supported on four edges and loaded by uniform stresses along the edges. If the plate is slender, the buckling is elastic. However, if the plate is sturdy, it buckles in the plastic range. Then, the instantaneous moduli in the constitutive equations depend on the external loading.

コンクリート充填円形鋼管柱の非線形解析法に関する研究

A numerical method for elastic-plastic buckling analysis of concrete-filled tubular columns with hollow circular section is presented. The elastic-plastic tangent stiffness matrix in the method is constructed by using the tangent coefficient matrix obtained by the numerical integration of the handening moduli of the fibers about the member section to calculate the generalized plastic strain increments. The assumptions that a column deforms in a body and behaves according to the Bernoulli-Euler hypothesis are made in the analysis. The accuracy of the method is examined by comparing the results with available experimental results.

Elastic-Plastic Dynamic Buckling Analysis of Reticular Domes Subjected to Earthquake Motion

Static and Dynamic characteristics of shell-like structures such as reticular domes vary depending on their configuration. There is, however, very little information available concerning dynamic buckling collapse or dynamic buckling analysis. This paper presents a method for dynamic buckling analysis with emphasis on dynamic buckling behaviour subjected to vertical earthquake motion. The study focuses on the elastic-plastic buckling of the members of a large dome as well as on the global shell-like buckling of the dome. Through the analyses, the efficiency of the proposed analytical method is discussed while a method for estimating collapse accelerations is proposed.

Dynamic elastic-plastic buckling phenomena in a rod due to axial impact

Dynamic elastic-plastic buckling phenomena which might develop in a rod from an axial impact loading are studied in order to identify the conditions for quasi-static behaviour. A discrete model for dynamic elastic-plastic buckling, which retains the axial and the lateral inertia forces, is proposed, and the relationship between the model parameters and the characteristics of an actual structure is given. Examples of different external loadings and boundary conditions are considered in order to clarify the influence of elastic-plastic axial wave propagation on the buckling process. The critical time for the initiation of buckling is obtained and the post-buckling behaviour of the model is analysed. Particular attention is paid to the role of the striking mass on the characteristics of the buckling process and on the development of the buckling shape. The numerical study reveals that the inertia of the striking mass affects considerably the development of the buckling shape causing different patterns of axial strain distributions at the initiation of buckling. The comparisons which are made between the model predictions and some previously published experimental data show that the buckling process is governed by the impact velocity as well as by the external loading history provided by the experimental technique.