Showing papers in "Thin-walled Structures in 1999"

The strength characteristics of aluminum honeycomb sandwich panels

Abstract: Aluminum sandwich construction has been recognized as a promising concept for structural design of lightweight transportation systems such as aircraft, high-speed trains and fast ships. The aim of the present study is to investigate the strength characteristics of aluminum sandwich panels with aluminum honeycomb core theoretically and experimentally. A series of strength tests are carried out on aluminum honeycomb-cored sandwich panel specimen in three point bending, axial compression and lateral crushing loads. Simplified theories are applied to analyze bending deformation, buckling/ultimate strength and crushing strength of honeycomb sandwich panels subject to the corresponding load component. The structural failure characteristics of aluminum sandwich panels are discussed. The test data developed are documented.

Design formula for axially compressed perforated plates

Abstract: This paper is concerned with post-buckling behaviour and the ultimate load capacity of perforated plates with different boundary conditions and subjected to uniaxial or biaxial compression. Plates were analysed using the finite element method (FEM), and extensive studies were carried out covering parameters such as plate slenderness, opening size, boundary conditions and the nature of loading. A design formula to determine the ultimate load carrying capacity was established based on a best-fit regression analysis using the results from the finite element analyses. The accuracy of the proposed formula was established by comparison with experimental values of ultimate capacity and similar finite element values. Ultimate load values are also presented in the form of charts for various values of plate slenderness and opening size.

Collapse behavior of square thin-walled columns subjected to oblique loads

Abstract: The crush behavior of a square column subjected to oblique loads, which is undergoing both axial and bending collapses, is analyzed. Oblique load conditions in numerical simulations are realized by means of impacting the column on a declined rigid wall with no friction. Mean crush loads corresponding to load angles are investigated with such geometrical parameters as thickness, width and length. Results show that there is a critical load angle at which a transition takes place from the axial collapse mode to the bending collapse mode. The dimensionless mean crush load is employed by normalizing the mean crush load with the analytical axial mean crush load and bending moment equations. It is expressed as a function of only one variable, the load angle. Finally, the formulation for the mean crush load is developed in terms of geometrical parameters and the critical load angle. The equation of the critical load angle is expressed as a function of the ratio of l/b. The value of the mean crush load drops to about 40% of the mean crush load in pure axial collapse after the critical load angle. Some cases of thin-walled columns are examined to verify the formulas of the mean crush load, and the results of numerical simulations are in good agreement with the predicted mean crush loads.

Analytical modelling of tube hydroforming

Abstract: The automotive industry has shown a growing interest in tube hydroforming during the past years. The advantages of hydroforming (less thinning, a more efficient manufacturing process etc.) can, for instance, be combined with the high strength of extra high strength steels, which are usually less formable, to produce structural automotive components which exhibit lower weight and improved service performance. Design and production of tubular components require knowledge about tube material behaviour and tribological effects during hydroforming and how the hydroforming operation itself should be controlled. These issues are studied analytically in the present paper. Hydroforming consists of free forming and calibration. Only the so-called free forming is treated here. The analytical models constructed in this paper are used to show what the limits are during the free forming, how different material and process parameters influence the loading path and the forming result, and what an experimental investigation into hydroforming should focus on. The present study was a part of a larger investigation, in which finite-element simulations and experiments were also conducted. The results of these simulations and experiments will be accounted for in coming papers.

Axial compression of metallic spherical shells between rigid plates

Abstract: Aluminium spherical shells of R/t values between 15 and 240, were axially compressed in an INSTRON machine between flat plates. The modes of their collapse, load-compression and energy-compression curves, and mean collapse loads are presented. A simple analytical model has been developed for the prediction of load-compression and energy-compression curves for the metallic spherical shells, by using the concepts of stationary and rolling plastic hinges. The results thus obtained match well with the experimental results. These results have also been compared with the solutions proposed in earlier studies. Behaviour of these shells is compared with the response of spherical shells (aluminium, mild steel and galvanised steel) of shallow depth, which were also subjected to axial compression between rigid plates. Their load-deformation curves are presented, and their energy-compression behaviour and mean collapse loads are discussed.

Elastic buckling analysis of ring-stiffened cylindrical shells under general pressure loading via the Ritz method

Abstract: This paper presents the Ritz method for the elastic buckling analysis of shells with ring-stiffeners under general pressure loading. The stiffeners may be of any cross-sectional shape and arbitrarily distributed along the shell length. Using polynomial functions multiplied by boundary equations raised to appropriate powers as the Ritz functions, the method can accommodate any combination of end conditions. As far as it is known, the Ritz method has not been automated in this way for the buckling of ring-stiffened shells. By formulating in a nondimensional form, generic buckling solutions for shells with various end conditions, stiffener distributions and under various pressure distributions, were presented. These new buckling solutions should serve as useful reference sources for checking the validity and accuracy of other numerical methods and software for buckling of cylindrical shells. This paper also shows that the appropriate distribution of ring stiffeners can lead to a significant increase in the buckling capacity over that of a stiffened shell with evenly spaced and identical ring stiffeners.

On the buckling of cylindrical shells with through cracks under axial load

Abstract: Presence of cracks or similar imperfections can considerably reduce the buckling load of a shell structure. In this paper, the buckling of cylindrical shells with through cracks has been studied. A general finite element model has been proposed, verified and applied to some novel cracked shell buckling problems for which documented results are not available. A special purpose program has been developed for generating finite elements models of cylindrical shells with cracks of varying length and orientation. The buckling behavior of cracked cylinders in tension and compression has been studied. The results of the analysis are presented in parametric form when it seems to be appropriate. Sensitivity of the buckling load to the crack length and orientation has also been investigated.

Experiments and theory on deck and girder crushing

Abstract: This paper is concerned with theoretical and experimental analysis of deep plastic collapse of a deck or deep girder subjected to an in-plane, concentrated load. A theory is derived which is valid until initiation of fracture in the structure. The presented experimental results show load–deflection curves and modes of deformation for decks, stringer decks and deep thin-walled beams subjected to central or excentric point loads between transverse frames. Based on theory and experiments, various modelling aspects of the local/global failure of the beams are discussed. The agreement between the theoretical closed form solutions and the experimental results is good.

Elastic-plastic collapse of non-uniform cylindrical shells subjected to uniform external pressure

Abstract: The objective of this paper is to derive analytical solutions for the elastic buckling and plastic collapse pressures of a cylindrical shell with reduced thickness over part of its circumference. The section of reduced thickness is used to represent a corroded region in a pipe. The proposed solutions are extensions of Timoshenko's solutions for the elastic-plastic collapse of a linear elastic, perfectly plastic cylindrical shell subjected to uniform external pressure. A modified interaction formula for the fully plastic membrane forces and bending moments in the non-uniform cylinder has been proposed for plastic collapse. A parametric study shows that the elastic buckling pressure decreases smoothly with corrosion angle when the corrosion depth is less than 0.5t. When the corrosion depth is greater than 0.5t, the elastic buckling strength first decreases very rapidly with corrosion angle. Furthermore, the elastic buckling pressure decreases uniformly with corrosion depth when the corrosion angles are greater than 30°, while the elastic buckling strength decreases more rapidly at higher corrosion depths when corrosion angles are less than 30°. Another parametric study on a steel pipe shows that the initial and fully plastic yield pressures both decrease monotonically with corrosion depth for a given corrosion angle and imperfection.

Ultimate strength of aluminium alloy outstands in compression: experiments and simplified analysis

Abstract: An experimental investigation was undertaken to study the stability and ultimate strength of aluminium alloy outstands. In the tests, thin-walled cruciform aluminium extrusions were stressed into the post-buckling range in axial compression. The local buckling behaviour of the flanges of a cruciform section is the same as that of an outstand, i.e. a plate element which is free along one unloaded edge and simply supported along the other. Two tempers of alloy AA6082 with significantly different stress–strain curves were tested for five b / t ratios. The experimental ultimate strengths were compared with theoretical predictions, using the classical Stowell theory for plastic buckling in combination with the effective width concept, and with ultimate strength formulae recommended in the literature.

Behaviour of cold-formed singly symmetric columns

Abstract: An experimental investigation into the behaviour of cold-formed plain and lipped channel columns compressed between fixed and pinned ends is presented in this paper. It is shown experimentally that local buckling does not induce overall bending of fixed-ended singly symmetric columns, as it does of pin-ended singly symmetric columns. Consequently, local buckling has a fundamentally different effect on the behaviour of pin-ended and fixed-ended singly symmetric columns. In order to show this fundamental different effect caused by local buckling, a series of tests was performed on plain and lipped channels brake-pressed from high strength structural steel sheets. Four different cross-section geometries were tested over a range of lengths which involved pure local buckling, distortional buckling as well as overall flexural buckling and flexural-torsional buckling. The different effects of local buckling on the behaviour of fixed-ended and pin-ended channels are investigated by comparing strengths, load–shortening and load–deflection curves, as well as longitudinal profiles of buckling deformations. The purpose of the paper is to demonstrate experimentally the different effects of local buckling on the behaviour and strengths of fixed-ended and pin-ended channels.

Local and distortional buckling of thin-walled short columns

Abstract: This paper assesses the applicability of Eurocode 3 (EC3) to the prediction of the compression capacity of short fixed-ended columns with different cross-sections. This compression capacity is determined by combining the effective width of plane elements due to local buckling and the effective stiffener thickness due to distortional buckling. Numerical calculations have been carried out in order to compare alternative methods for determining the minimum elastic distortional buckling stress in compression. The method given in EC3 does not correlate as well as Lau and Hancock's method with the results given by Generalized Beam Theory (GBT). The end boundary conditions have a significant influence on the distortional buckling strength, and thus also on the compression capacity of short columns. Selected experimental results from compression tests on C-, Hat- and rack upright-sections are compared with the predictions given by EC3. The procedure in EC3 was modified by determining the distortional buckling stress using GBT, taking into account the actual column length and the end boundary conditions. This lead to better agreement between the experimental results and the theoretical predictions.

Global optimum design of cold-formed steel hat-shape beams

Abstract: Using the computational neural network model developed recently by the authors, a comprehensive parametric study is performed for global optimization of cold-formed steel hat-shape beams based on the AISI Specifications. Design curves are presented for global optimum values of the thickness, the web-depth-to-thickness ratio, and the flange width-to-thickness ratio for unbraced beams having steel yield strengths of 250 and 345 N/mm2. The computational neural network model guarantees a local optimum solution. The global optimum is found by an exhaustive search that is guided by a heuristic approach to reduce the search effort. An extensive parametric study yielded insights into the behavior of cold-formed steel beams that are then used as rules to reduce the search space and guide the exhaustive search. The procedure for finding the global optimum design of cold-formed steel beams is presented in a few recursive steps. The optimum design curves presented in this article can be of great value to structural design engineers.

A parametric finite element study of cracked plates and shells

Abstract: The overall behavior of plates and shells as affected by the presence of a through crack in the elastic range has been studied. Due attention has been paid to finite element modeling aspects of the problem. Forty different cracked plate and shell FE models have been generated and analyzed by a special computer program developed for the purpose of this study. The significance of various parameters such as the order of mesh refining at the crack tip, the effect of boundary conditions, Poisson's ratio, crack length and shell curvature are studied. FE model consisting of isoparametric 4-noded shell elements moderately refined at the crack tip predicted the overall stress and displacement field with acceptable precision.

Distortional theory of thin-walled beams

Abstract: The classic thin-walled beam theory for open and closed cross-sections is generalized to include one distortional mode of deformation. Distortional cross-section parameters are introduced and the new orthogonality conditions for uncoupling of the axial displacement modes are given. A normalization technique for the distortional modes leads to unique distortional cross-section properties. The theoretical formulations for torsion and distortion are nearly similar and result in nearly identical equilibrium equations. However, for closed single- or multi-cell cross-sections the torsional and distortional shear flows may couple. A study of the order of magnitude of the governing torsional and distortional parameters shows the difference between open and closed cross-sections and the related solution types. The difference in the order of magnitude of the governing cross-section parameters also leads to approximate solution techniques. In the examples, section three cross-sections are used to illustrate variations of the theoretical parameters.

Two-dimensional analysis of stacked geosynthetic tubes on deformable foundations

Abstract: Stacked geosynthetic tubes resting on a deformable foundation such as soil are analyzed The tubes contain a slurry which applies hydrostatic pressure The material of the tubes is assumed to act like an inextensible membrane and to have negligible weight, and the foundation is assumed to exert a normal upward pressure which is proportional to the downward deflection Friction is neglected between tubes and at the foundation interface Two configurations are considered: (a) one tube on top of another and (b) one tube straddling two tubes underneath it For the latter formation, the case of external fluid acting on one side is analyzed, to simulate an application as a dike, and rigid blocks are utilized to prevent sliding of the tubes Equilibrium shapes of the tubes are obtained numerically from a closed-form integral formulation, and the tension in each tube is computed

Lateral buckling strengths of cold-formed Z-section beams

Abstract: This paper is concerned with the inelastic lateral buckling strengths of cold-formed Z-section (CFZ) beams. The point symmetry of the cross-section of a CFZ beam introduces characteristics that are not encountered in a doubly symmetric I-beam. Firstly, the effective section rotates after yielding, so that a CFZ beam under in-plane bending about the geometrical major principal axis is subjected to bending moments about the effective minor axis and bimoments. Secondly, the minor axis bending and warping strain distributions and therefore the lateral inelastic buckling behaviour and strengths of CFZ beams are related to the twist rotation and minor axis displacement directions. The stress–strain curves, residual stresses, initial imperfections, and lipped flanges of CFZ beams are all different to those of hot-rolled I-beams. This paper develops a realistic finite element model for the analysis of CFZ beams and uses it to investigate the elastic lateral-distortional buckling, inelastic behaviour, and strengths of CFZ beams with residual stresses and initial imperfections. The results of the study are used to develop improved design rules which are suitable for CFZ beams. The effects of moment distribution and load height on the lateral buckling strengths are also studied.

Distortional warping functions and shear distributions in thin-walled beams

Abstract: In the analysis of thin-walled beams it is often necessary to consider the effects of distortion of the cross-section. The distortion in the plane of the cross-section generates axial warping displacements. On the basis of a known in-plane distortional displacement mode it is possible to derive a unique warping function and the related shear stress distributions. Local axial equilibrium is used to derive the main differential equation for determination of the distortional warping function and shear distributions. In closed single- or multi-celled cross-sections it is necessary to introduce circulation shear force flows around the cells to achieve compatibility of the axial displacement. Methods for analysis of open and closed cross-sections are generalized to include distortional displacement modes. It is shown that axial extension, flexure and torsional warping are included as special cases of distortion. A generalization of the conventional orthogonalization procedure and a normalization technique for distortional modes are also presented. A triple cell cross-section is used to illustrate the generalized calculation procedure and computed results are presented.

Spline FSM postbuckling analysis of shear-deformable rectangular laminates

Abstract: A spline finite strip method is developed for the prediction of the geometrically non-linear response of rectangular, composite laminated plates to progressive in-plane loading. The development takes place within the context of the use of the first-order shear deformation plate theory and the non-linearity is introduced in the strain-displacement equations in the manner of the von Karman assumption. A number of applications of the new capability is described, involving laminates subjected to progressive uniform end shortening and to progressive in-plane shearing. In all the applications a close comparison of the finite strip results with independent finite element results is demonstrated.

Measurement and assessment of geometric imperfections in thin-walled panels

Abstract: Thin-walled members may be subject to performance limitations arising through local or distortional buckling of slender elements comprising the cross-section of the member, or overall buckling of the member The effects of structural instability may be aggravated by the presence of geometric imperfections in these elements An investigation is presented into methods of measuring and assessing geometric imperfections in cold-rolled thin-walled steel panels These methods can be used to characterise the geometry of prismatic thin-walled members that exhibit performance sensitivity due to geometric imperfections The measurement procedures investigated include close-range photogrammetry, precise optical levelling, and the use of a co-ordinate measurement machine The assessment procedure comprises a least-squares spectral decomposition of the measurements to characterise the imperfections existent in the panels under investigation, and estimates of the precision of the derived Fourier coefficients are used to inter-compare the three measurement procedures The investigation has demonstrated that statistically significant imperfections may exist in thin-walled members at short and medium wavelengths, leading to a reduction in the load carrying capacity Both optical levelling and the co-ordinate measurement machine technique can yield desirable results, but for high precision work, use of the co-ordinate measurement machine is recommended

Partially stiffened RHS sections under transverse bearing force

Abstract: Concentrated force applied to rectangular hollow sections (RHS) members at loading or reaction points can lead to web crippling of the members. This paper investigates the possibility of improving the web crippling behaviour of RHS sections using internal stiffeners. Tests of RHS sections partially filled with concrete and with wood plus a bolt through the web are described. Both end-bearing and interior-bearing forces were applied. Design models are established for the four failure modes identified in the tests. The parameters varied include section aspect ratio (D/B) which ranges from 1.5 to 3.0, web depth to thickness ratio (D/t) which ranges from 15 to 75, and bearing length to section width ratio (γ=N/B) which ranges from 0.5 to 1.0.

The influence of bend–twist coupling on the shear buckling response of thin laminated composite plates

Abstract: The finite strip method of analysis has been used in this paper to examine the effect of bend–twist coupling on the shear buckling behaviour of laminated composite constructions. The distorted nodal lines of the shear buckling mode and its complex deformation state in general are readily accounted for in the analysis procedure through the multi-term nature of the finite strip buckling displacement field and the appropriate level of structural modelling. The degree of bend–twist coupling in the laminated composite plates is varied by changing the level of anisotropy in the plies and by altering the lay-up configuration of the plies in the laminated stack. Symmetric laminates of a balanced and unbalanced nature are given consideration. It is shown that, for a given degree of anisotropy in the plies of a laminate and for a given laminate thickness, the stacking sequence of the plies significantly alters the degree of bend–twist coupling. The shear buckling performance of composite plates having the same dimensions and being made from the same material are therefore shown in the paper to be quite different. The preclusion of the bend–twist coupling coefficients in the solution procedure of the finite strip method allows the shear buckling orthotropic solution to be determined. Comparisons between the coupled and orthotropic solutions are shown in the paper to be markedly different.

Nonlinear hydroelastic vibration of a cylindrical tank with an elastic bottom containing liquid-analysis using harmonic balance method

Abstract: Theoretical analyses and experimental studies have been carried out on the non-linear hydroelastic vibration of a cylindrical tank with an elastic bottom. In this paper, nonlinear axisymmetric free vibration analysis of the bottom plate of the tank, coupled with that of the liquid contained within it, is presented by means of the harmonic balance method. In the analysis, the effect of an in-plane force in the plate due to static liquid pressure is taken into account. The effect of the liquid on the non-linearity of the backbone curve of the super-harmonic and the sub-harmonic resonances as well as the principal resonance of both sloshing- and bulging-type responses was clarified, and it was found that with an increase of liquid height, the non-linearity with a hard-spring type of the bottom plate decreased in degree, and became close to linear characteristics. The influence of the bottom plate motions on the free surface response amplitude in the first bulging-type resonance region was also investigated.

Elastic distortional buckling of tee-section cantilevers

Abstract: The paper presents the results of a finite element study of the elastic distortional buckling of tee-section cantilevers, which can be thought of as beams fully braced at one end and unbraced at the other. The finite element procedure is described briefly, and then three loading cases, viz., a tip moment, a tip load and a uniformly distributed load are considered. All of these loading cases place the unstiffened or free edge of the stem or web into compression. The effects of distortion are quantified for the three loading cases, as are the effects of fully restraining the top flange against lateral deflection and twist by a discrete brace positioned anywhere along the cantilever. It is shown that the effects of distortion during buckling cannot be ignored in a tee-section cantilever with even a moderately slender web.

Mechanical fasteners for cladding sandwich panels:: Interpretative models for shear behaviour

Abstract: The shear performance of screwed connection systems usually adopted for lightweight sandwich panels is investigated in this paper. First of all, after brief considerations concerning the possibility to use cladding panels as diaphragm in steel building and the corresponding connecting system requirements, the results of available monotonic and cyclic experimental analyses on several connection typologies are summarised. Then mathematical models able to interpret both monotonic and cyclic behaviour of the connections are proposed. In particular, the mathematical cyclic model is based on the previously defined envelope curve, which is expressed by means of a Ramberg-Osgood type law relationship and calibrated trough monotonic tests. Finally, the comparison between experimental and numerical results is carried out, focussing on the actual dissipative capacities of such connection typologies.

Vibration analysis of toroidal panels using the differential quadrature method

Abstract: The free vibration characteristics of linear elastic toroidal shell panels are determined. A solution based on the Mushtari–Vlasov–Donnell shell equations is developed using the Differential Quadrature Method. The work represents the first application of this method to problems in shell theory with variable coefficients in the governing equations. Numerical results are calculated using the method, and these are compared with results found using a Fourier series and a finite element solution.

Analysis of multiple stiffened barrel shell structures by strain-based finite elements

Abstract: In this paper strain-based rectangular cylindrical shell and curved arch finite elements are coupled to straight beam finite elements to analyse multiple stiffened barrel shell structures. The first two finite elements are based on assumed strains rather than displacement fields. The results obtained with this analysis are successfully compared with values derived from several commercial computer codes.

An experiment on elastically compressed frusta

Abstract: It is postulated that pre-buckling elastic stress pattern in axially compressed right frustum will determine its initial and progressive buckling mode. The elastic stress profiles along the generator and around various diameters of aluminium alloy frustum under axial compression were measured under different boundary constraints. The shape of such profiles was found to be periodic and wavy with relatively high peaks and high stress gradients at a number of points. It is thought that these peaks correspond to the number of lobes in multi-lobe collapse modes, which are observed when the axial loading exceeds the elastic range. These peaks are attributed to all possible imperfections in geometry and dimensions such as variations in thickness, symmetry, generator length and deviation of the axis from being perpendicular to the cross-section.

Variational design of open cross-section thin-walled beam under stability constraints

Abstract: A thin-walled beam is in pure bending subjected to couples M 0 . The open cross-section profile has two ribs, with cross-section A 0 and it is shaped symmetrically towards the plane perpendicular to the bending plane. The ribs are located at the profile ends. The shape of the profile line is searched for. Criterion is the minimal value of the cross-section area A 1 of the beam. The problem is described by means of variational calculus. Within the numerical calculations a Runge–Kutta method is used. The optimal shapes of beam profiles are shown graphically.

Prediction of the fatigue life of slender web plates using fracture mechanics concepts

Abstract: The results of a series of fatigue tests, on slender plate girders subjected to repeated shear loading, are summarised and used to establish a lower bound fatigue strength curve for the welded web boundary, based on geometric or principal surface stress ranges. The propagation of a semi-elliptical surface crack, through the thickness of a plate, is studied using fracture mechanics concepts. An extensive parametric study indicates that the initial crack size and aspect ratio, the geometric stress concentration at the weld toe, and the plate thickness, all have a significant influence on fatigue strength. It is concluded that the fracture mechanics approach requires specification of a number of parameters which are difficult to determine in practice. However, having specified a realistic crack size and aspect ratio and an approximate stress concentration at the weld toe, the solution can be calibrated against available experimental fatigue strength curves.