Secondary Buckling Research Articles

Finite element analysis of the secondary buckling of a flat plate under uniaxial compression

Uemura and Byon (Int. J. Non-Linear Mech. 13, 1–14, 1978) presented experimental results and a numerical analysis about the secondary buckling of clamped flal plates under uniaxial compression. However, their numerical analysis is based upon an inconsistent flat plate finite element and it does not take into account the important influence of antisymmetric imperfections. This paper presents and discusses F.E.M. results obtained by two computer codes using very different approaches, and compares these results with the experimental ones.

Secondary States of Rectangular Plates

The secondary buckling of rectangular elastic plates is studied as a problem of secondary bifurcation. The nonlinear von Kármán plate theory is used in the analysis. The secondary bifurcation points, and the secondary states that bifurcate from them are determined by a previously developed perturbation method. Secondary buckling is related to the phenomenon of “mode-jumping” that is observed in buckling experiments with elastic plates.

The secondary buckling and post-secondary-buckling behaviours of rectangular plates

Secondary buckling and post-secondary-buckling behaviours are theoretically studied for simply-supported rectangular plates, whose primary buckling modes of deflection contain more than half-waves in the load acting direction. Modal coupling effects more complex than one two-term-coupling effects are incorporated into the secondary buckling and post-secondary-buckling analyses. Then, unstable or stable symmetric secondary branching points are found on the post-primary-buckling paths and “snap through” motions involving an abrupt change in wave-form are shown to be possible. Wave-form variations along post-secondary-buckling paths are also disclosed by means of a numerical analysis of equilibrium paths.

Coloboma of optic nerve with overlay of peripapillary retina.

An eye that had the clinical appearance of a tumour of the nerve head was found on histological examination to have a congenitally large scleral canal with secondary buckling of the overlying retina.

Secondary buckling of a flat plate under uniaxial compression: Part 2. Analysis of clamped plate by F.E.M. and comparison with experiments

In Part 1, a theoretical analysis was used to study the secondary buckling of a simply supported plate. In Part 2, a clamped plate is analysed by the finite element method. The stability criterion for a non-linear post-buckling equilibrium state is evaluated by the sign of the determinant of the stiffness matrix. It should be noted that the secondary buckling loads of clamped plates are unexpectedly smaller than those of simply supported plates and are only one and a half times the primary buckling loads. In previous analyses, only a quarter segment of the plate was considered by assuming a stable equilibrium state with symmetrical mode. However, instability can also be predicted by considering the unsymmetrical mode over the whole plate. Results of experimental analysis of secondary instability of clamped square plates under uniaxial compression agreed with the numerical results.

Minimum Stiffness Ratio of a Stiffener against Ultimate Strength of a Plate (2nd report)

In the previous report, the authors clarified the existence of the minimum stiffness ratio, γUmin, of a stiffener against the ultimate strength of a stiffened plate in similar to the buckling strength, γBmin. In this report, elastic large deflection analysis is performed on the stiffened plate, and the phenomenon of the secondary buckling after the primary buckling is indicated. Then, a series of experiment is conducted to confirm the phenomena predicted by the theory.From these theoretical and experimental results, an approximate analytical method to determine γUmin is newly proposed as the intersection of the secondary buckling strength curve and ultimate strength curve of a locally failured plate, when there exists no initial deflection. When there exists initial deflection, the effective minimum stiffness ratio effγUmin is defined as the intersection of a curve of the initial yielding of bending stress of a stiffener and that of membrane stress of a plate. This method can also be applied to determine γUmin of a stiffened plate with arbitary aspect ratio and arbitary number of stiffeners.The effect of welding residual stresses on the buckling and ultimate strength is also discussed, together with on γUmin and effγUmin and the minimum stiffness ratio against the buckling strength, γBmin.

Secondary buckling of a flat plate under uniaxial compression: Part 1: theoretical analysis of simply supported flat plate

While studies of post-buckling behavior and load-carrying capacities of thin plates subjected to uniaxial compression have been limited to stable conditions, further post-buckling loading generates an unstable condition. The secondary buckling which occurs with snap-through to higher-order deflections under such unstable conditions has not been analyzed in detail as yet. In the first part of this paper, a thin square plate under uniaxial compression, which is simply supported along four edges, is considered. A method based on the second variation of the total potential energy is then proposed for evaluating the stability of the post-buckling equilibrium state and inevitable secondary buckling is derived analytically. The effects of various factors, such as initial imperfections, assumed virtual displacement pattern, post-buckling deflection pattern and in-plane boundary conditions, on the secondary buckling values are discussed. In part 2, secondary buckling of clamped plates is analyzed by use of the finite element method and the resultant numerical results are compared with experimental results.

Secondary Buckling of Thin Plate under Uniaxial Compression : 2nd Report, Analysis of Clamped Plate by F.E.M. and Comparison with Experiments

Secondary Buckling of Thin Plate under Uniaxial Compression : 2nd Report, Analysis of Clamped Plate by F.E.M. and Comparison with Experiments

Secondary Buckling of Thin Plate under Uniaxial Compression : 1st Report, Analysis of simply Supported Plate by Analytical Method

Secondary Buckling of Thin Plate under Uniaxial Compression : 1st Report, Analysis of simply Supported Plate by Analytical Method

Secondary Buckling of Circular Plates

It is shown by using a formal perturbation expansion, that unsymmetric equilibrium states branch from axisymmetric buckled states of the uniformly compressed and clamped circular plate. The process is called secondary buckling and the edge thrusts at which the branchings occur are called the secondary buckling loads. In the neighborhoods of the secondary buckling loads that are studied, the secondary states exist for thrusts less than the secondary buckling loads. The minimum secondary buckling load is approximately 7.5 times the primary buckling load of the plate. The linear boundary value problems that are obtained in the application of the perturbation method are solved numerically.

On the Plastic Buckling of Stiffened Panels under Axial Compression

The general instability of a stiffened flat plate under axial compression is a problem of primary buckling of a bending type of deformation of the stiffener about an axis parallel to the plane of the sheet and a twisting type of deformation in which the stiffener rotates about an axis in the plane of the sheet. The paper treats the primary buckling of stiffened plates in the strain-hardening range as well as in the elastic range. The secondary or local buckling of the stiffener or plate such as crippling of the stiffener or interfastener buckling of plate are excluded.From consideration of the yielding process of structural steel it has been shown that the material becomes anisotropic when strained into the strain-hardening range. Introducing appropriate moduli the problem may then be treated as buckling of an orthotropic plate.Buckling in the elastic range, then, is a particular case of the orthotropic solution with the elastic moduli of steel. The application of the integral equation to the buckling of a stiffened plate simplifies the problem and saves labor and time for computation. The single basic integral equation covers the whole domain of the plate. The stiffener reactions enter as transverse or twisting loads but do not introduce new boundary conditions.The required minimum bending rigidity of a stiffener is obtained in both elastic and strainhardening range. The effect of torsional resistance of a stiffener on buckling strength is investigated for the stifener with a symmetric type of thin-walled open cross-section.