Elastic buckling of plates containing eccentrically located circular holes

The finite elements method is used to obtain the elastic buckling loads for flat square panels containing eccentrically located circular holes. The applied inplane loads considered are uniaxial and biaxial compressions as well as pure shear. In all cases the load is distributed uniformly along the simply supported or clamped outer edges. The effect of the degree of eccentricity and the size of the hole on the buckling load is obtained.The triangular and rectangular finite elements used for calculating the inplane stresses prior to buckling are based on assumed strain, rather than displacement, fields and satisfy the exact representation of strain free rigid body modes of displacements. The combination of these elements with existing well-known bending elements is shown to produce results of acceptable accuracy without the use of an inordinately large number of elements.     

Elastoplastic buckling of circular annular plates under uniform in-plane loading

This paper deals with the elastoplastic buckling of a circular annular plate, with various axially symmetric boundary conditions and uniform axially symmetric in-plane radial loads on the inner and outer edge. The analysis is based on the standard linear buckling equations and the material behaviour is modelled by the small strain J₂ flow and deformation theories of plasticity where an elastic linear hardening rheological model of the material is considered. The solutions are obtained using the equilibrium approach where the governing differential equation is solved by the finite difference method which leads to the determination of eigenvalues of a homogeneous system of linear equations. Elastoplastic buckling loads for axially symmetric and asymmetric buckling shape modes with m waves in the circumferential direction are calculated and compared for both theories of plasticity. For one case, an experiment was performed and the results were compared with theoretical predictions.     

Why local damage increases the buckling load of circular plates

Local material damage is often characterised as degradation of material properties. A recent study has discovered a paradoxical phenomenon that clamped circular plates with a local axisymmetric damage may have a buckling load above that of a corresponding perfect plate. This paper describes a finite element investigation into the buckling behaviour of circular plates with a local axisymmetric damage. The paradoxical results of previous researchers are explained, and observations are made regarding the appropriate modelling of local damage.     

Delamination buckling of cylindrical laminates

Models for predicting delamination buckling of laminated complete thin cylindrical shells and cylindrical panels are presented. The load cases are uniform axial compression and uniform pressure, applied individually. The models are different for the two load cases and by design they are kept as simple as possible, to keep the mathematical representation of the model and the associated solution simple enough to permit extensive parametric studies. Through these studies one can identify important structural parameters and fully assess their effect on the critical load. Among the general conclusions are the following: (a) the most influential parameters for a given laminated geometry are the size of the delamination and its through-the-thickness position for both load cases; and (b) the effect of boundary conditions (along the straight edges) is important for the case of pressure, whereas for axial compression the effect of boundary conditions (ends) is small for large delaminations.     

Delamination buckling for composite laminated cylindrical shells in Hamilton system

In this article, a semi-analytical three-dimensional model based on the modified Hellinger–Reissner (H–R) variational principle and a nonlinear spring-layer model are presented for the buckling analysis of composite laminated cylindrical shells with a delamination. The method allows the effect of transverse shear deformation in the control equations of the composite laminated structures. In addition, it uses a two-dimensional mesh and can ensure that the number of variables is independent of the layer number. The nonlinear spring-layer model between the exterior and interior sub-laminates ensures the continuity of transverse stresses and displacements in the undelaminated region by specifying infinite values of springs and therefore avoids the possibility of material penetration phenomenon in the delaminated region. As an application of the present method, the influence of the delamination length on the critical buckling loads of delaminated composite laminated stiffened cylindrical shells is investigated.     

Local buckling restraint condition for core plates in buckling restrained braces

Buckling Restrained Braces (BRBs) are commonly used as bracing elements in seismic zones. A key limit state governing BRB design is to prevent flexural buckling. However, when the wall thickness of the steel tube restrainer is relatively small compared to the cross-section of the core plate, the restraint conditions against the local buckling of the core plate can be critical for the stability and strength of the BRB. In this study, cyclic loading tests and numerical analyses of BRBs were carried out using various tube restrainer configurations to investigate the influence of local buckling of the restrainer on BRB strength and ductility.     

Unilateral buckling of point-restrained triangular plates

In this paper the unilateral buckling behavior of point restrained triangular plates is studied. Firstly, the energy functional of a general triangular plate with elastic foundation is calculated. The Rayleigh–Ritz method for investigating the local buckling of unilaterally restrained triangular plates is applied. The displacement functions and restraining medium are modeled as polynomials and tensionless foundation respectively. The results are obtained for different boundary conditions, aspect ratios and various in-plane compressive and shear loadings. Confirming the validity of this investigation, convergence and comparison studies are undertaken. The comparisons show the efficiency and accuracy of the presented method.     

四边简支层合板在剪切作用下的稳定分析

采用伽辽金变分法分析了四边简支的FRP复合材料层合板在纯剪作用下的屈曲荷裁,得出了四边简支层合板的剪切屈曲解析解,并使用有限元软件ANSYS对解析解进行了数值验算与对比分析。所得公式适合长宽比≤4的正交异性层合板,与数值分析结果吻合良好,所得理论公式对实际工程有一定的参考价值,并在一定程度上丰富了复合材料层合板屈曲公式的理论研究。     

Local buckling and post-local buckling redistribution of stress in slender plates and sections

Cold-formed open steel sections are comprised of component plates termed stiffened elements (webs) and unstiffened elements (flanges). The local buckling and post-local buckling behaviour of sections may be determined from the behaviour of the component plates. Much research effort has documented the theoretical elastic local buckling of plates and sections, however until recently few experimental studies have been reported on the local buckling and post-local buckling behaviour of unstiffened plates. This paper presents experimental and numerical studies of unstiffened plates and sections that contain them in both compression and bending, and in particular analyses the mechanism that provides post-buckling strength. It is shown that, as with stiffened elements, the mechanism is the post-local buckling redistribution of stress, however unlike stiffened elements this redistribution can occur to such an extent that tensile stresses commonly form in axially compressed slender elements. The stress distributions at ultimate are compared with current international cold-formed steel specifications.     

Nonlinear buckling of microfabricated thin annular plates

Annular plate structures are commonly used in MEMS devices, particularly in pumps and valves. In MEMS applications, large nonlinear deflections are routinely achieved. In this paper, the nonlinear buckling of a thin elastic annular plate under a compressive radial force acting in the plane of the plate is considered. Although the critical loads at which buckling starts can be determined by solving a linear eigenvalue problem, the large deflection behavior of a buckled plate beyond the critical loads can be described by the nonlinear theory proposed by von Kármán. The buckling loads of the annular plate for various boundary conditions are calculated and the post-buckling behaviors are examined. Interestingly, the buckling of an annular plate exhibits a supercritical pitchfork bifurcation. Thus, the post-buckling behavior is stable and will not collapse catastrophically. Several design implications for microfabricated structures, in particular microvalves, are also given.     

Plastic shear buckling of unstiffened stocky plates

A number of moderate to stocky steel and aluminum plates, with various slenderness ratios and boundary conditions are numerically analyzed under the action of pure in-plane shear and the results are validated against available analytical methods. Numerical non-linear finite element analyses are performed to assess different theoretical approaches and to picture buckling behaviors of moderate stocky plates. It is observed that while thick stocky plates possess some post-yield capacity during the hardening stage prior to plastic buckling, moderately thick plates yield and buckle concurrently followed by softening due to sudden loss of stiffness. It is also concluded that changes in the modulus of elasticity and shear modulus should be considered in the analysis and that the secondary bending stresses induced by initial out-of-plane curvature can cause significant reduction in the post-yield capacity and ultimate resistance of stocky plates.     

Thermal buckling of clamped symmetric laminated plates

The buckling behavior of moderately thick symmetric angle-ply laminates having clamped edges and subject to a uniform temperature rise is investigated. Transverse shear deformation is accounted for by employing the Reissner-Mindlin theory. The exact solution to the coupled differential equations is obtained using the general double Fourier series approach. Calculated values of the critical temperature are compared with corresponding finite element results.     

Elastic buckling of perforated plates under shear

Finite element studies aimed at computing the buckling coefficient for plates containing cut-outs and subjected to shear are reported. The cases considered are:

1. 1. Square and rectangular plates with central circular cut-outs.

2. 2. Square plates with centrally placed rectangular cut-outs.

3. 3. Square plates with eccentrically placed circular cut-outs.

4. 4. Square plates with reinforced circular cut-outs.

5. 5. Square plates with reinforced rectangular cut-outs.

Simply supported plates as well as clamped plates have been studied and approximate formulae for the use of designers have been suggested for the practical cases where the hole dimension is generally not greater than half the width of the plate.     

FRP加固的钢筋混凝土梁剥离破坏研究综述

本文介绍了FRP加固的钢筋混凝土梁剥离破坏的试验研究、理论研究分析方法，提出了一些建议。     

Thermal buckling load optimization of laminated composite plates

In this study, the applicability of the Modified Feasible Direction (MFD) method on the thermal buckling optimization of laminated plates subjected to uniformly distributed temperature load is investigated. The objective function is to maximize the critical temperature capacity of laminated plates and the fiber orientation is considered as design variable. The first-order shear deformation theory is used in the mathematical formulation. For this purpose, a program based on FORTRAN is used for the optimization of laminated plates. Finally, the effect of aspect ratio, antisymmetric lay-up, boundary condition, material anisotropy, ratio of coefficients of thermal expansion, and hybrid laminates on the results is investigated and the results are compared.     

Plastic buckling of axially compressed circular cylindrical shells

For elastic-plastic cylindrical shells with initial axisymmetric imperfections bifurcation into a non-axisymmetric shape is analysed. The shell material is represented by a phenomenological plasticity theory that accounts for the formation of a vertex on subsequent yield surfaces. The influence of various geometric and material parameters is investigated for a wide range of radius-to-thickness ratios. It is shown that for the thicker shells bifurcation generally occurs beyond the maximum axial compressive load. A few analyses for shells with additional non-axisymmetric imperfections show the unstable post-bifurcation behaviour and the sensitivity to imperfections of more general shapes.     

Axial crushing of circular tubes with buckling initiators

This paper presents a study of the effectiveness of adding a buckling initiator which is used to reduce the initial peak force of a thin-walled circular tube under axial impact loadings. The buckling initiator is installed near the impact end of the circular tube and is composed of a pre-hit column along the axis of the tube and several pulling strips uniformly distributed around the top edge of the tube. This device functions just before the impact happens and does not affect the structural stiffness under its normal working conditions. By using two kinds of aluminum-alloy circular tubes, a series of quasi-static compression tests were conducted. The deformation mode, the initial peak force and the mean crushing force of the tubes with different number of pulling strips N, pre-hit height h and inclined angle of the pulling strips θ₀ were studied in the experiments. The results reveal that by using this buckling initiator, the large progressive deformation of the axially crushed circular tube switches from ring mode or mixed mode to diamond mode. Although specimens with N=2, 3 and 4 were tested, the stable deformation tended to diamond mode with lobe number N=3. With suitable selection of pre-hit height h, the initial peak force could be reduced by more than 30%. In addition, a simplified theoretical analysis is conducted to illustrate the reduction of the initial force as well as the energy dissipation mechanisms, leading to good agreements with the experimental results.     

Thickness optimization of circular annular plate at buckling

This work deals with thickness optimization of a circular annular plate at buckling. The plate is loaded with uniform, axially symmetric, in-plane loads on the inner and outer edge. The variable thickness of the plate is approximated by a function of radial coordinates and design variables. An optimization problem is defined to find optimal sets of design variables which maximize buckling loads at constant weight/volume of the plate. The required buckling loads are determined according to the standard linear buckling equations, and the material is modelled by the small strain J₂ flow and deformation theories of plasticity where an elastic linear hardening rheological model is considered. Optimal thickness functions are determined for different support and load cases and the numerical results show that buckling loads can be increased significantly.     

Axi-symmetrical deflection and buckling of circular porous-cellular plate

The main goal of this paper is a solution of the problem of buckling and deflection. A circular porous plate with simply supported edge under radial uniform compression and uniformly distributed load (pressure) is considered. Mechanical properties of the isotropic porous material vary across the thickness of the plate. Middle plane of the plate is its symmetry plane. A field of displacements (geometric model of nonlinear hypothesis) is described. The principle of stationarity of the total potential energy allowed to get a system of differential equations that govern the plate stability. A critical load and a deflection are determined. The results obtained for porous plates are compared to homogeneous circular plates.     

Compression tests of longitudinally stiffened plates undergoing distortional buckling

This paper describes a series of compression tests performed on longitudinally stiffened plates fabricated from a mild steel plate of thickness of 4.0 mm with nominal yield stress of 235.0 MPa. The stiffened plates with longitudinal stiffeners of a range of rigidities were tested to failure. The ultimate strengths and performances of the longitudinally stiffened plates in compression undergoing distortional buckling or interaction between local and distortional buckling were investigated experimentally and theoretically. The compression tests indicated that the critical buckling mode was dependent mainly on the rigidity of the longitudinal stiffeners and the width-to-thickness ratio of the sub-panels. A noticeable interaction between local and distortional buckling was also observed for some stiffened plates. A significant post-buckling strength reserve was shown for those sections with distortional buckling and for those sections showing interaction between local and distortional buckling. A limiting strength curve for distortional buckling of longitudinally stiffened plates was studied. Simple design strength formulas in the direct strength method are proposed to account for the distortional buckling and the interaction between local and distortional buckling of longitudinally stiffened plates. The strength curves were compared with the test and FE results conducted. The adequacy of the strength curve was confirmed. A set of conclusions on the buckling behavior of longitudinally stiffened plates was drawn from the experimental studies.