Compressive strength of edge-loaded corrugated board panels

Postbuckling strength of simply supported corrugated board panels subjected to edge compressive loading has been studied experimentally using a specially developed test fixture. Although the load versus out-of-plane displacement response was highly sensitive to the presence of initial imperfections in the panels, the collapse loads did not vary much, which is attributed to the stable postbuckling behavior of the plates. Thin plates collapsed at nearly twice the buckling load, while thick panels collapsed at loads below the elastic critical buckling load. Local buckling of the facing on the concave side of the buckled plate was observed at load levels close to the collapse load. The plate collapse was triggered by compressive failure of the facings that initiated at the unloaded edges. A simplified design analysis was derived based on approximate postbuckling analysis and compared with an existing design formula for corrugated board panels and boxes.     

Buckling and postbuckling of size-dependent cracked microbeams based on a modified couple stress theory

The elastic buckling analysis and the static postbuckling response of the Euler–Bernoulli microbeams containing an open edge crack are studied based on a modified couple stress theory. The cracked section is modeled by a massless elastic rotational spring. This model contains a material length scale parameter and can capture the size effect. The von Kármán nonlinearity is applied to display the postbuckling behavior. Analytical solutions of a critical buckling load and the postbuckling response are presented for simply supported cracked microbeams. This parametric study indicates the effects of the crack location, crack severity, and length scale parameter on the buckling and postbuckling behaviors of cracked microbeams.     

Test fixture for eccentricity and stiffness of corrugated board

Of particular importance for the mechanical response and load-bearing capacity of corrugated board boxes is the manner in which load is introduced in the vertical panels through the horizontal flaps and the adjoining creases (folding lines). This study reports on a test fixture developed to measure the effective eccentricity moment acting on the vertical panels of corrugated board boxes. The axial compressive response of the creased board can also be measured using the new test fixture. The deformation mechanism of the board was monitored by visual inspection and photographically recorded and related to the measured eccentricity moment. The results show that significant eccentricity of the load path exists, which depends on the degree of lateral constraint and amount of axial deformation in a quite complex manner. The axial compressive response was found to be independent of the degree of lateral constraint and unsupported length of the specimen, which is evidence for the majority of the axial deformation occurring in the creased region. Photographic recording of the deformation mechanism of the creased region during compressive loading verified that the board is loaded unevenly as evidenced by kink zone formations appearing at opposite sides at different axial deformation levels.     

Non-linear response of geometrically imperfect sandwich curved panels under thermomechanical loading

This paper deals with the non-linear response of sandwich curved panels exposed to thermomechanical loadings. The mechanical loads consist of compressive/tensile edge loads, and a lateral pressure while the temperature field is assumed to exhibit a linear variation through the thickness of the panel. Towards obtaining the equations governing the postbuckling response, the Extended Galerkin’s Method is used. The numerical illustrations concern doubly curved, circular cylindrical and as a special case, flat panels, all the edges being simply supported. Moveable and immoveable tangential boundary conditions in the directions normal to the edges are considered and their implications upon the thermomechanical load-carrying capacity are emphasized. Effects of the radii of curvature and of initial geometric imperfections on the load-carrying capacity of sandwich panels are also considered and their influence upon the intensity of the snap-through buckling are discussed. It is shown that in special cases involving the thermomechanical loading and initial geometric imperfection, the snap-through phenomenon can occur also in the case of flat sandwich panels.     

开孔平板的剪切稳定性实验

对四边简支和四周边受均匀剪切力的矩形薄平板的屈曲失稳,作了实验分析及数值计算.用作者所设计的剪切试验装置,对一组开孔及开孔后加强的薄平板进行了剪切稳定性试验,求得薄平板失稳时的载荷——挠度曲线及失稳波形,由曲线上拐点来确定平板失稳临界载荷,并将实验结果与有限元数值计算结果作了比较.     

Postbuckling of long unsymmetrically laminated composite plates under axial compression

An approximate solution is given for the postbuckling of infinitely long and unsymmetrically laminated composite plates. This solution is obtained by superposing a polynomial transverse displacement given by bending due to unsymmetric laminate configurations and a simple functional representation for the buckling mode in conjunction with the Galerkin method. Nondimensional parameters are used to express the approximate solution in a very simple and clear formulation. The results given by this solution for axial compression in the longitudinal direction are compared with the results given by the nonlinear finite element method (FEM) for finite length rectangular long plates. The influence of the boundary conditions on postbuckling response is also studied. For the FEM analysis, two different simply supported boundary conditions on the long edges of the plate are considered. It is found that these two sets of boundary conditions give different results for the buckling and postbuckling finite element analysis. In most cases the FEM analysis overestimate and, respectively, underestimate the approximate closed form solution, depending on the type of simply supported boundary condition considered. Thus, the approximate solution appears useful for design purposes as an averaged quantity between the two FEM analyses. Also, it is found that the reduced bending stiffness method can be successfully used for determining the approximate solution.     

Creep buckling of cross-ply symmetric laminated cylindrical panels

A creep buckling analysis of cross-ply symmetric laminated cylindrical panels is given in this paper.By means of theoretical analysis,a method to determine the critical load of creep buckling of the panels with simply supported boundary conditons is obtained.     

Non-linear buckling and postbuckling behavior of thin-walled beams considering shear deformation

The static stability of thin-walled composite beams, considering shear deformation and geometrical non-linear coupling, subjected to transverse external force has been investigated in this paper. The theory is formulated in the context of large displacements and rotations, through the adoption of a shear deformable displacement field (accounting for bending and warping shear) considering moderate bending rotations and large twist. This non-linear formulation is used for analyzing the prebuckling and postbuckling behavior of simply supported, cantilever and fixed-end beams subjected to different load condition. Ritz's method is applied in order to discretize the non-linear differential system and the resultant algebraic equations are solved by means of an incremental Newton-Rapshon method. The numerical results show that the beam loses its stability through a stable symmetric bifurcation point and the postbuckling strength is in relation with the buckling load value. Classical predictions of lateral buckling are conservative when the prebuckling displacements are not negligible and the non-linear buckling analysis is required for reliable solutions. The analysis is supplemented by investigating the effects of the variation of load height parameter. In addition, the critical load values and postbuckling response obtained with the present beam model are compared with the results obtained with a shell finite element model (Abaqus).     

Postbuckling of imperfect rectangular composite plates under inplane shear closed-form approximate solutions

In this paper, the postbuckling behavior of rectangular orthotropic laminated composite plates with initial imperfections under inplane shear load is investigated in a closed-form analytical manner. The plates under consideration are assumed to be infinitely long in the longitudinal direction. At the longitudinal edges, two different sets of boundary conditions are considered, specifically 1) simply supported edges and 2) fully clamped edges. Using Timoshenko-type shape functions for both the initial bifurcational buckling analysis and the subsequent Marguerre-type postbuckling studies, closed-form analytical solutions for the buckling loads and for the postbuckling state variables are derived. A comparison with geometrically non-linear finite element computations shows that the derived analysis approaches are suitable for postbuckling studies in load ranges not too far beyond bifurcational buckling as they are currently relevant for e.g., composite airframe structural analysis and design. Due to their strictly closed-form analytical nature, the presented analysis methods can be used conveniently in engineering practice for all application purposes where computational time is a crucial factor, especially for preliminary analysis and design or optimization procedures.     

In-plane shear test of thin panels

Efficient application of thin-gage composite materials to helicopter fuselage structures necessitates that the materials be designed to operate at loads several times higher than initial buckling load. Methods are required to accurately measure and predict the response of thin-gage composites when subjected to these loads. This paper presents the results of an analytical and experimental study of the behavior of thin-gage composite panels subjected to in-plane shear loads. Finite-element stress analyses were used to aid in the design of an improved shear fixture that minimizes adverse corner stresses and tearing and crimping failure-modes characteristic of commonly used shear fixtures. Tests of thick buckle-resistant aluminum panels and thin aluminum and composite panels were conducted to verify the fixture design. Results of finite-element stress and buckling analyses and diagonal-tension-theory predictions are presented. Correlation of experimental data with analysis indicated that diagonal-tension theory can be used to predict the load-strain response of thin composite panels.     

The effect of a centrally located midplane delamination on the instability of composite panels

The buckling loads of eight-ply graphite-epoxy cylindrical panels with midplane delamination were determined experimentally. The study included two different ply orientations, two different aspect ratios, two different delamination sizes, and one set of boundary conditions; clamped along the top and bottom edges and simply supported along the vertical sides. The experimental test results are compared to the linear bifurcation and nonlinear collapse loads of panels with square cutouts obtained from the STAGSC-1 finite-element computer code. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

ELASTO-PLASTIC DYNAMIC BUCKLING AND POSTBUCKLING OF SQUARE PLATES UNDER SOLID-FLUID SLAMMING

The elasto-plastic dynamic buckling and postbuckling phenomena ofsquare plates subjected to in-plane solid-fluid slamming are investigated.According tothe plate's response,the critical criteria for dynamic buckling,dynamic plasticity andplasti(?)collapse are defined,and the corresponding critical impulses are presented.Meanwhile,dynamic buckling modes and collapse models are observed.The effects ofdifferent boundary conditions and loading histories on the properties of buckling andpostbuckling are discussed.     

Imperfection sensitivity of curved panels under combined compression and shear

The initial buckling load of curved panels under compressive loads is substantially reduced by the existence of imperfections, in particular geometric imperfections. It is therefore essential that these imperfections are considered in analysing components which incorporate such panels in order to accurately predict their buckling behaviour. Finite element analysis allows fully non-linear analysis of shells containing geometric imperfections, however, to obtain accurate results information is required on the exact size and shape of the imperfection to be modelled. In most cases this data is not available. It is therefore generally recommended that the imperfections are modelled on the first eigenmode and have an amplitude selected according to the manufacturing procedure. This paper presents the effects of varying imperfection shape and amplitude on the buckling and postbuckling behaviour of one specific case, a curved panel under combined shear and compression, to test the accuracy of such recommendations.     

复合材料层合板蠕变屈曲与变形的优化问题

将瞬时弹性失稳荷载、持久临界荷载和后屈曲持久变形刚度作为复合材料层合板蠕变屈曲与变形的优化指标,对几组纤维铺设方式进行讨论,构造多目标优化模型,就纤维铺设角进行优化分析.考虑横向剪切变形效应,分别利用Lap lace变换和准弹性方法,导出了这三个优化指标的计算公式.     

Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions

The paper studies the axisymmetric compressive buckling behavior of multi-walled carbon nanotubes (MWNTs) under different boundary conditions based on continuum mechanics model. A buckling condition is derived for determining the critical buckling load and associated buckling mode of MWNTs, and numerical results are worked out for MWNTs with different aspect ratios under fixed and simply supported boundary conditions. It is shown that the critical buckling load of MWNTs is insensitive to boundary conditions, except for nanotubes with smaller radii and very small aspect ratio. The associated buckling modes for different layers of MWNTs are in-phase, and the buckling displacement ratios for different layers are independent of the boundary conditions and the length of MWNTs. Moreover, for simply supported boundary conditions, the critical buckling load is compared with the corresponding one for axial compressive buckling, which indicates that the critical buckling load for axial compressive buckling can be well approximated by the corresponding one for axisymmetric compressive buckling. In particular, for axial compressive buckling of double-walled carbon nanotubes, an analytical expression is given for approximating the critical buckling load. The present investigation may be of some help in further understanding the mechanical properties of MWNTs.     

Imperfection sensitivity of axially compressed stringer reinforced cylindrical sandwich panels

This paper presents some numerical results of the effects of several nondimensional parameters on the buckling and initial post buckling behaviors of shallow sandwich panels under axial compression. Results are presented that show these effects due to transverse shearing resistance of the core material, different face-sheet thicknesses, and different core thicknesses. Further effects on the buckling and initial postbuckling behaviors of sandwich panels are presented due to the torsional resistance of longitudinal edge stiffeners.The results show that the range of flatness parameter, δ/d, for which sandwich panels remain imperfection-insensitive increases with increases in transverse shearing resistance of the core material and with larger core thicknesses. These results also indicate that this range of δ/d is smallest when the face-sheet thicknesses are equal. Finally, as in the case of homogeneous panels, torsional resistance of the longitudinal edge stiffeners has the effect of making the sandwich panel less imperfection-sensitive.     

An experimental investigation of how accurate,simply supported boundary conditions can be achieved in compression testing of panels

How accurate, simply supported boundary conditions can be obtained experimentally in the testing of rectangular panels subjected to uniaxial compression has been investigated. Experimental buckling loads are obtained using the Southwell method and are compared with theoretical predictions. Several support arrangements are examined and compared to the idealized support conditions.     

Experiments on the postbuckling behavior of circular cylindrical shells under compression

Detailed experimental studies are performed on the postbuckling behavior of circular cylindrical shells under compression, by using polyester test cylinders with the geometric parameterZ ranging from 20 to 1000. In each case, variations of the equilibrium load, circumferential wave number and maximum inward and outward deflections, with applied edge shortenings, are clarified. Contour lines for typical postbuckling configurations are also shown. It is found that, as the cylinder is compressed beyond the primary buckling, secondary bucklings take place successively with diminishing wave numbers, and that postbuckling equilibrium loads become significantly lower than those at buckling asZ increases. Further, for short shells withZ≦100, the buckled waveforms are always symmetric with one-tier diamond buckles, while for longer shells, asymmetric postbuckling patterns with two tiers of buckles dominate.     

Stability and behavior of an annular plate under uniform compression

The behavior of an annular plate, free at its inner edge and simply supported at the outer one, is investigated experimentally. The loading is a compressive implane force which is uniformly applied at the outer boundary. Deformations and strains are explored over sub, trans and postbuckling regions. Experimental results for the buckling loads, obtained by different methods, are compared. Comparison is also made with existing theoretical data. Fair to good agreement is found between theory and experiments, especially with respect to circumferential strains. The important influence that initial geometrical imperfections can have on the behavior of the compressed plate is also discussed.