Initial Postbuckling Behavior Research Articles

Stability and initial post-buckling behavior of reinforced cylindrical shells made of composites

Stability and initial post-buckling behavior of reinforced cylindrical shells made of composites

On the stability and postbuckling behaviour of multilayered sandwich-type plates

This paper gives the governing equations and natural boundary conditions for the stability of multilayered sandwich-type rectangular flat plates with orthotropic (constructionally orthotropic) hard and transversally isotropic soft layers. It shows the solution of these equations and the problem of initial postbuckling behaviour for the regularly multilayered plates with Navier-type boundary conditions.

Buckling and Initial Post-Buckling Behavior of Laminated Oval Cylindrical Shells Under Axial Compression

Buckling and Initial Post-Buckling Behavior of Laminated Oval Cylindrical Shells Under Axial Compression

Calculation of the stability, initial post-buckling behavior, and flaw sensitivity of laminated cylingrical shells made of composites

Calculation of the stability, initial post-buckling behavior, and flaw sensitivity of laminated cylingrical shells made of composites

Initial Postcritical Behavior of Thin‐Walled Angle Section Columns

This work deals with the overall flexural instability of an angle section column under axial load, taking into account deformations of the cross section as buckling occurs. A nonlinear differential formulation with two variables is considered. The perturbation method is used to follow the initial postbuckling behavior from the bifurcation point. Deformations of the cross section do not modify the Euler critical load, but they may significantly affect the nature of the postcritical path. Unlike the well-known behavior of columns with solid cross sections, the angle section may exhibit unstable postbuckling deformations typical of the light-gauge sections, as reported in previous studies on thin circular arc sections.

Asymptotic analysis considerations on the initial postbuckling behavior of delaminated composites

An asymptotic analysis for the initial postbuckling behavior of delaminated beam/plates is performed. Under the assumptions of inextensional deformation, the exact expressions that govern the plane elastic deformation of the different parts of the system are expanded in a Taylor series in terms of the distortion variable. Order of magnitude arguments are used to relate the distortion variables and these are subsequently used in an asymptotic solution for the deflections and the load. Finally, a comparison with experiments is performed.

Initial postbuckling behavior of beams on non-linear elastic foundations

Hypothese de dependance lineaire de la partie lineaire du module de la fondation sur la compression asciale exercee sur la poutre. Modelisation d'un fibre dans un composite a un fibre, la fondation etant la matrice

Some thoughtd on mode interaction in thin-walled columns under uniform compression

Interaction of nearly simultaneous buckling modes in the presence of imperfections is studied. The investigation is concerned with thin-walled trapezoidal columns under uniform compression. The asymptotic expansion established by Byskov and Hutchinson is also used here. The present paper is devoted to an improved study of the equilibrium path in the initial post-buckling behaviour of imperfect structures. The results obtained include the effect of interaction of the ‘primary’ local mode and a ‘secondary’ local mode having the same wavelength as the primary. In this paper the analysis of a few buckling mode interactions is presented.

The initial postbuckling behavior of ring stiffened shells under hydrostatic pressure

In this article the initial postbuckling behavior of ring stiffened cylindrical shells under hydrostatic pressure is analyzed by Koiter's theory. The nonlinear bending equations consistent with boundary conditions have been used in prebuckling state. The eigenvalue problem is solved by Galerkin's method. The obtained buckling loads are compared with the results which are based on classical stability theory. As calculating examples, three typical outside-stiffened cylinders with different ring stiffener parameters are chosen. The results show that the strength of stiffener not only influences buckling load obviously, but also changes the imperfection-sensitivity of cylindrical shells.

Initial Postbuckling Behavior of Imperfect, Antisymmetric Cross-Ply Cylindrical Shells Under Torsion

This paper deals with the initial postbuckling of antisymmetric cross-ply closed cylindrical shells under torsion. Under the assumptions employed in Koiter’s theory of elastic stability, the structure is imperfection-sensitive in certain intermediate ranges of the reduced-Batdorf parameter (approx. 4 ≤ ZH ≤ 20.0). Due to different material bending-stretching coupling behavior, the (0 deg inside, 90 deg outside) two-layer clamped cylinder is less imperfection sensitive than the (90 deg inside, 0 deg outside) configuration. The increase in torsional buckling load due to a higher value of Young’s moduli ratio is not necessarily accompanied by a higher degree of imperfection-sensitivity. The paper is the first to consider imperfection shape to be identical to the torsional buckling mode and presents concise parameter variations involving the reduced-Batdorf paramter and Young’s moduli ratio.

Post-Buckling Analysis of Heavy Columns with Application to Marine Risers

The post-buckling behavior of heavy tubular columns following static instability under the combined action of weight, tension/compression at the top, and fluid static pressure forces in the gravity field is studied. A two-dimensional nonlinear small-strain large-deflection model of the column is derived, consisting of an integrodifferential equilibrium equation and two end rotation conditions. The equation of equilibrium is discretized using a finite-element method. An approximate solution valid in the neighborhood of the bifurcation point and an incremental solution are used to determine the secondary equilibrium path. The results of both methods are corrected by Newton-Raphson iteration. Conditions for unstable initial post-buckling behavior and existence of limit points on the secondary equilibrium path are presented. The numerical solution is applied to the problem of the elastica and is found to be in good agreement with the analytical solution. The secondary equilibrium path for a 500-m-long (1640 ft) marine drilling riser is calculated for two sets of boundary conditions and various values of the drilling mud density. The effect of the drilling mud density and the boundary conditions on the riser's post-buckling behavior is discussed.

Collapse of long, noncircular, cylindrical shells under pure bending

This paper describes an extension of a method developed in a previous paper to determine the moment carrying capacity of elastoplastic noncircular cylindrical shells with infinite length by the finite element method. As a result of the shape change in the cross section of a shell during deformation, the bending moment reaches a global maximum value and then decreases as the bending curvature further increases. The shell would consequently collapse at the maximum moment. However, a bifurcation buckling may occur before the maximum moment can be developed. This bifurcation buckling could induce collapse of the shell under a moment less than the maximum. Determination of the likelihood that the bifurcation buckling would generate shell collapse may be made from the initial post-buckling behavior. An initial post-buckling analysis based on the J 2 deformation theory of plasticity has been developed in this paper. The finite element method with one spatial variable is used to locate the bifurcation point as well as to analyze the initial post-buckling behavior. Numerical examples of cylindrical shells with various cross-sectional shapes are shown. In particular, for a shell of square cross section, the moment at the bifurcation is much lower than the maximum value; however, the initial post-buckling analysis reveals that the state of equilibrium is still stable. Deep post-buckling analysis is required to determine the moment carrying capacity of a shell with such cross section.

Asymmetric postbuckling of symmetrically laminated cross ply, short cylindrical panels under compression

Buckling and initial postbuckling behavior of symmetrically laminated, thin cross ply cylindrical panels under axial compression are investigated. The panels are simply supported at all four edges. Closed form solutions are obtained for the buckling loads. The initial asymmetric postbuckling behavior is demonstrated by computing the postbuckling coefficients within the context of Koiter's theory of elastic stability. Parameter studies involving the flatness parameter, the length-to-width ratio, number of layers and Young's moduli ratio are presented for typical cross ply cylindrical panels likely to be encountered in practice.

Geometrically Nonlinear Analysis of Plates and Shells Using Perturbation Techniques and Incremental Procedures

The numerical performance of incremental solution techniques in geometrically nonlinear analysis is often subjected to a lack of convergence in the vicinity of critical equilibrium states, in order to get qualitative and quantitative information about the initial post-buckling behaviour, reliable algorithms should take account of the properties of a perturbation approach. This paper deals with the Lagrangian description of the virtual work principle and shows how both methods can be worked out for the study of plates and shells. Some numerical applications are included to verify the validity of these techniques.

Postbuckling of Rings under Two Uniform Loads

The interaction effect of the normal and centrally directed pressures on the initial postbuckling behavior of a thin elastic circular ring buckling freely in its own plane is investigated by means of the perturbation method applied to the exact nonlinear differential equations of the engineering theory of curved beams. A dimensionless value of the postbuckling deflection is employed as the perturbation parameter. The analysis has yielded a simple formula representing the relationship between small increases in the buckling loads. This formula characterizes the initial postbuckling behavior of the ring subjected to the two interacting, uniformly distributed loads. Heretofore, the limited technical literature on the postbuckling characteristics of rings has dealt only with single distributed external pressure loads. In practice, the two types of static loads considered can be realized by compressing the ring by means of closely spaced, perfectly flexible spokes and simultaneously applying a gas pressure.

Stability and postbuckling analysis of nonlinear structures

The complementary energy approach for stability analysis of elastic structures under conservative loading is based on Fraeijs de Veubeke's variational principle. The associate equations of neutral equilibrium and stability criterium are presented for arbitrarily large deformations and rotations. When specialized to the structural behavior of thin plates in moderate rotations this functional yields the von Karman equations. Efficient mixed flat shell finite elements are derived from this functional. If the fundamental path is moderately nonlinear, the buckling load and the initial postbuckling behavior can be obtained by an iterative process of Rayleigh-Ritz type, which is based on Koiter's asymptotic approach. Development of the iterative method within the complementary energy principle allows improvement of computational effectiveness and of the rate of convergence, as shown by means of numerical examples.

Mode Interaction of Axially Stiffened Cylindrical Shells: Effects of Stringer Axial Stiffness, Torsional Rigidity, and Eccentricity

This paper deals with the effect of stringer axial stiffness, torsional rigidity, and eccentricity on the panel initial postbuckling behavior and mode interaction of axially stiffened cylindrical shells. As far as the local panel mode is concerned, the cylinder is taken to be integrally stiffened and the postbuckling redistribution of the axial load-carrying capacity between the skin and stringers is investigated. It is found that although the buckling analysis is more or less identical to previous analyses, there are significant changes in the quartic term of the potential energy of the local mode and hence, the imperfection-sensitivity of the structure is altered. These changes are due to the interaction between the stringers and the skin in the postbuckling analysis. In addition, to assess the effect of a nonlinear prebuckling state resulting from the presence of local imperfections, Koiter’s theory of amplitude modulation of the local mode is applied to an example problem of interest.

Postbuckling behavior of a periodically laminated medium in compression

A theory is constructed for geometrically nonlinear behavior of a periodically laminated medium for a class of planar deformation modes which are macroscopically homogeneous in the direction normal to the material interfaces. The theory is used to study microbuckling and initial postbuckling behavior of the medium under compression along the laminates. The results indicate that the bifurcation is of the stable symmetric type so that geometrical imperfections in the form of initial waviness of the reinforcements are not expected to reduce the microbuckling stress significantly.

Buckling and initial post-buckling behavior of thin-walled I columns

The behavior of axially compressed thin-walled I columns after torsional buckling is discussed. At first the state of strain in a column subjected to a large angle of twist is outlined. The considerations are based on the following assumptions: (1) cross section is non-deformable in its own plane, (2) shear deformation is negligible, and (3) strains are small and elastic. The initial post-buckling equilibrium paths are determined by utilizing a perturbation approach. The finite-element and analytical procedure is presented. It has been shown that the point of bifurcation for simply supported, or clamped I column with constant cross section is symmetric and stable. Two examples of I columns of variable cross section are also considered. It is worthwhile noticing that in these examples the critical loads are beyond the limits described by the critical force for column with the minimum and the maximum cross section. The points of bifurcation in these cases are also symmetric and stable. This property of the bifurcation point is very important with regard to the sensitivity to the initial geometrical imperfections. In the case of the unstable point of bifurcation a drastic decrease of the value of the critical loads is possible, which does not hold for stable point.

Initial postbifurcation behavior of a one-hinged circular arch

Herein, the initial postbuckling behavior of one-hinged, symmetric, elastic, circular arches of uniform cross section, subjected to an external gas pressure load, is investigated on the basis of a highly accurate nonlinear theory of thin curved beams with arbitrarily large in-plane deflections, by means of an asymptotic (perturbation) method. The final result is presented in the form of a formula as well as in tabular form.