Showing papers in "Thin-walled Structures in 1991"

Hysteretic characteristics of unstiffened plate shear panels

Abstract: A series of quasi-static cyclic loading tests on unstiffened plate shear panels is described. All the panels tested exhibited adequate ductility and stable S-shaped hysteresis loops, with the energy absorbed per cycle increasing with the maximum amplitude of shear displacement. A theoretical model for predicting the hysteretic characteristics is presented, which incorporates the influences of shear buckling of the web plate and plastic yielding of the web plate and surrounding frame. Theoretical predictions are compared and show satisfactory agreement with the experimental results. The simplicity of the theoretical model is such that it can be readily incorporated in nonlinear dynamic analyses of steel plate shear walls.

An experimental investigation of the degradation and buckling of circular tubes under cyclic bending and external pressure

Abstract: Cyclic bending of tubes into the plastic range of the material leads to a progressive accumulation of ovalization of the tube cross-section. Persistent cycling leads to local catastrophic buckling of the tube. This paper presents an experimental study of the problem. The main objective of the study was to establish the effect of the cyclic bending history and of the external presdure on the rate of accumulation of ovalization and on the onset of instability. The cyclic loading histories examined include curvature symmetric bending, bending about a mean value of curvature and moment-controlled bending about a mean value of moment. The rate at which ovalization accumulates in curvature-controlled cyclic bending was found not to be significantly affected by a mean curvature in the cycles. Moment-controlled bending about a mean moment leads to ratcheting in curvature as well as in ovalization. External pressure accelerates the accumulation of ovalization and leads to buckling in fewer cycles than in the corresponding pure bending cases. This was found to be true for all bending histories considered. Significant similarities were observed between the response and onset of instability in the monotonic bending case and all cyclic bending cases. For a group of aluminum tubes instability was found to occur when the ovalization of the cross-section reached a critical value. This critical value was found to be relatively independent of the bending history followed.

Buckling and postbuckling behaviour of cylindrical shells under combined external pressure and axial compression

Abstract: Buckling and postbuckling behaviour of perfect and imperfect cylindrical shells of finite length subject to combined loading of external pressure and axial compression are considered. Based on the boundary layer theory which includes the edge effect in the buckling of shells, a theoretical analysis for the buckling and postbuckling of circular cylindrical shells under combined loading is presented using a singular perturbation technique. Some interaction curves for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, and it is shown that both agree well. The effects of initial imperfection on the interactive buckling load and postbuckling behaviour of cylindrical shells have also been discussed.

Energy dissipation and associated failure modes when axially loading polygonal thin-walled cylinders

Abstract: The crumpling mechanisms of thin-walled octagonal steel tubes subjected to axial static compression and their efficiency as energy absorbing components under impact conditions are investigated and compared with the equivalent circular and square tubes of same material. Both inextensional and extensible collapse mechanisms are theoretically analysed. Theoretically predicted values based on the deformation modes encountered, as well as experimentally obtained ones, are compared and found to be in good agreement.

A geometrically nonlinear theory of transversely isotropic laminated composite plates and its use in the post-buckling analysis

Abstract: A higher-order, geometrically nonlinear theory of transversely isotropic symmetrically laminated composite plates is formulated and their post-buckling behavior is analysed. The numerical illustrations emphasize the role played by transverse shear deformation, transverse normal stress, higher-order effects and the character of in-plane boundary conditions. The results obtained within the present higher-order theory are compared with those of first-order transverse shear deformation and classical (Kirchhoff) theory, and conclusions on their range of applicability and the influence of various parameters are outlined.

A nonlinear elastic spline finite strip analysis for thin-walled sections

Abstract: A nonlinear elastic analysis based on the spline finite strip method has been developed for studying the post-buckling behaviour of thin-walled sections. The method can handle local, distortional and overall buckling modes in the post-buckling range and the interaction between them. It allows for geometric imperfections, arbitrary loading and non-simple boundary conditions. By comparison, the semi-analytical finite strip method is restricted to simply supported end boundary conditions and a single buckle half-wavelength. The two incremental-iterative strategies adopted in the nonlinear analysis are the arc-length method and the improved iteration method based on displacement control. Switching between load and displacement control can occur automatically as the need arises in an analysis. Numerical examples are presented for comparison with and verification against solutions for the nonlinear behaviour of plates, plate assemblies and cylindrical shells.

Application of integrated fluid-thermal-structural analysis methods

Abstract: Hypersonic vehicles operate in a hostile aerothermal environment which has a significant impact on their aerothermostructural performance. Significant coupling occurs between the aerodynamic flow field, structural heat transfer, and structural response creating a multidisciplinary interaction. Interfacing state-of-the-art disciplinary analysis methods is not efficient, hence interdisciplinary analysis methods integrated into a single aerothermostructural analyzer are needed. The NASA Langley Research Center is developing such methods in an analyzer called LIFTS (Langley Integrated Fluid-Thermal-Structural) analyzer. The evolution and status of LIFTS is reviewed and illustrated through applications.

Stability of rack structures

Abstract: Standard commercial pallet racking is used in warehouses, factories, shops and a multitude of other places where palletised goods are to be stored. The structural analysis of this type of structure is complicated by the semi-rigid nature of the beam-to-upright connection, which is different from one manufacturer to another. In the present paper an attempt has been made to provide a simple design approach to the stability of pallet rack structures, and the effect that the form of the moment-rotation characteristic has on the type of stability demonstrated by the system. Finally the role of small imperfections is studied, and the effect that they have on the maximum load carrying capacity of the structure is shown.

Buckling of plates with a hole under tension

Abstract: An FEM analysis is made on the elastic buckling of plates, each of which has a hole and is subjected to tensile loading. In a general way, no attention is paid to the buckling of plates if they are subjected to a tensile load. However, when a plate has a hole, compressive stresses appear near the hole under a tensile load, and the stress may cause local buckling of the plate. In this paper, stress distributions and buckling behaviours of such plates under tension are studied. Aspect ratios, shapes of holes and so on, are adopted as parameters. Through the analysis, variations of buckling coefficients and buckling modes against aspect ratios are obtained. The effects of the hole shapes on the buckling strength are also discussed.

Interactive buckling of beams in bending

Abstract: A discrete model involving a limited number of degrees of freedom is presented, for analyzing the interaction between overall lateral-torsional buckling and local flange buckling, qualitatively. The results are compared with experiments and show a good qualitative agreement. The results suggest that a quantitative numerical analysis based on Koiter's asymptotic approach may have a wide range of validity.

Natural shape functions of a compressed Vlasov element

Abstract: To approximate a tube building by thin-walled Vlasov beam, it is unreasonable to neglect the axial force due to dead and live loads. The axial compression makes the lateral displacements (Y, Z) coupled with the torsional displacement (Φ) when warping is concerned. The resulting twelve-order differential equation is customarily solved by finite element method assuming independent cubic shape functions for Y, Z and Φ. It is pointed out here that the displacement functions are not completely independent. Indeed, if one takes the static solutions of the governing ordinary differential equations as shape functions, for the same number of degrees of freedom, one can approximate the Vlasov beam by quintic polynomials plus six hyperbolic-trigonometric functions. For static problems without distributed force, the resulting stiffness equation is exact. For dynamic problems, the resulting finite element converges rapidly.

Delamination buckling of cylindrical laminates

Abstract: 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.

The shear strain influence on the dynamics of thin-walled beams

Abstract: The influence of middle-surface shear strains on the dynamics of thin-walled beams is analyzed. By means of a suitable choice of the axial displacement field, shear lag effects in bending and torsion are taken into account for open and closed cross-sections. The equations of motion are obtained via Hamilton's principle. The flexural-torsional natural frequencies in the presence of warping which varies along the beam axis are compared with those given by Timoshenko-Vlasov models. The solution to the problem is pursued by means of the most natural choice, i.e. the classical trigonometric series expansion. A suitable algorithm is developed to solve the resulting eigenvalue problem which turns out to be strongly ill-conditioned.

Multi-level optimization of aircraft shell structures

Abstract: Various aspects of multi-level optimization are reviewed, and the application to problems typical of aircraft wing and fuselage structures is discussed. A three-level optimization is proposed, as this relates in a convenient way to the design of a shell structure in which stiffened panels are assembled into individual cross-sections which are in turn linked together to form the complete structure. Furthermore, the different tasks which the designer has to perform can then retain their separate identity, and a considerable degree of ‘local’ optimization can be carried out. The suitability of multi-level optimization in more complex design problems is tested on a structure representative of a wing box in composite material, with buckling limitations in each panel, and another problem in which aeroelastic requirements are included. Proposals are made for a simplified approach to the sensitivity data used in multi-level optimization.

Structural optimization of aircraft

Abstract: After a general presentation of the CATIA-ELFINI tool, developed by Dassault, where CAD, structural analysis and optimization are fully integrated, a detailed description of the optimization algorithm is focused upon. The special features of optimization with composite materials is shown, and two relevant examples of structural and aeroelastic optimization on carbon structures of a wing and a fin are presented. The new organization of design resulting from use of optimization techniques is described, and techniques of neighbouring optimization as model adjustment and computation with uncertain data is reviewed. In conclusion further developments are presented.

Interactive and local buckling of thin-walled members

Abstract: A new p-version finite element, especially suited for high-precision modeling of structures consisting of a fabricated three-dimensional assembly of plates, is used to study the local and interactive buckling behaviour of such members when subjected to axial compression and bending. A deeper understanding of the elastic phenomenon of such thin-walled structures is realized through a series of parametric studies on a number of test problems.

Plate bending analysis by unequally spaced splines

Abstract: A cubic B-spline finite strip method (BFSM) is developed to analyze thin plates in bending. The basic mathematical relationships are derived for a direct stiffness formulation using a series type strip displacement function. Longitudinal behavior is modeled by a spline series in which unequal spline spacing is permitted. This feature allows local refinement of the discretization near patch and concentrated loads. Accuracy and convergence vis-a-vis alternative methods are compared. These include various finite element models, the conventional finite strip method and the BFSM with equally spaced splines. Comparisons show comparable accuracy with improved convergence. Oscillatory convergence due to Gibb's phenomenon, evident in some of the models, is avoided in the BFSM.

On torsional and warping stiffness of thin-walled girders

Abstract: The torsional and warping stiffness of the beam idealization of thin-walled girders is defined from equivalence of their natural frequencies for torsional vibration of sinusoidal modes. The membrane and plate strip theory are employed for the girder structural members. The stiffness parameters are determined analytically for a few girders of simple cross-section, while for those of complex cross-section a numerical procedure is formulated.

Beam-column welded RHS connections

Abstract: T- or X-shape joints are the predominant member connections used for orthogonal plane frames. When rectangular hollow sections (RHS) are used as frame members, experiments show that the most common mode of joint failure is the push-pull local mechanism. This arises in the contact flange and webs of the column member. Over 250 such connections have been tested internationally and some of the theoretical estimations of the joints' resistance are available. On this basis design methods are suggested. The comparison between the actual and predicted strength of joints is given. A regression analysis has been used to obtain the design load.

Postbuckling interaction analysis of cold-formed thin-walled channel sections by finite strip method

Abstract: An elastic-plastic large-deflection finite strip method has been set up to compute the interaction behaviour of initially deflected and eccentrically loaded cold-formed thin-walled channel sections. The ultimate loads of the sections are estimated under the loading of a constant compression eccentricity and a constant load eccentricity, respectively. A series of conclusions, which are valuable for channel section design, are obtained through many numerical calculations. A test programme associated with the Moire fringe technique is performed. Comparisons of analytical and experimental results reveal that the finite strip method possesses a high accuracy in elastic-plastic large-deflection analysis of plates and sections.

Buckling and strength characteristics of some CFRP stiffened curved panels

Abstract: This paper describes the initial and post-buckling behaviour of CFRP stringer-stiffened curved panels. The panels are of 500-mm radius, 2-mm thickness and have either three or four blade stringers. Initial buckling loads were calculated using the finite strip code VIPASA within the design optimisation program PASCO. An unstiffened, externally supported panel is also considered. Stringer stiffening gave higher buckling loads than external supports. The initial buckling behaviour was influenced by geometric imperfections, and methods of modelling these with PASCO are discussed. The imperfections caused scatter in buckling load, but there was minimal scatter in failure load, despite the presence of impact damage in some cases. The failure loads were about 50% higher than the buckling loads.

A static solution of stiffened plates

Abstract: Rectangular plates with periodic stiffening ribs which are symmetrical about the middle plane of the plate and with all edges simply supported are considered. The exact solution for the deflection function of a stiffened plate subjected to uniform load is derived by using the U-transformation method. Solutions for other loading cases can also be derived in a similar manner. A comparison between the results obtained by this exact model and the orthotropic plate model is made.

Web crippling of multi-web deck sections

Abstract: This paper presents the results of an extensive experimental investigations of web crippling loads for multiple web deck sections. One flange loading and two flange loading conditions were tested for both end and interior reactions. Based on the test data, it can be concluded that satisfactory conformity was obtained with the Canadian cold formed steel standard for interior support conditions. For end support conditions, a slightly modified expression from the Canadian standard is recommended.

Reaction allotment of continuous curved box girders

Abstract: To design load-bearing diaphragms (or support diaphragms) the magnitude of reaction forces on the support must be known. This paper considers such reaction forces on the intermediate support of two-span continuous curved box girders. When a continuous curved box girder has two shoes in the section of its support, these two shoes are subjected to reaction forces which are generally different. In this paper, the reaction forces at such shoes are numerically analyzed by the finite strip method, and the allotment of reaction forces to the two shoes is studied. The number or stiffness of intermediate diaphragms and the dimensions of the box section are used as parameters.

Transient response of cylindrical shells with arbitrary shaped sections

Abstract: A new coordinate transformation function is presented, with the help of which a cylindrical shell of arbitrary cross-section can be mapped approximately into a circular cylindrical shell. Using this method, the transient response of a non-circular cylindrical shell subjected to a shock wave is obtained by the finite strip method. The versatility and accuracy of the method are amply demonstrated through a number of numerical examples.

Vibration of circular cylinders containing water

Abstract: A theoretical and an experimental investigation were carried out on three circular cylinders in air and also with the cylinders containing water. The investigations consisted of experimentally determining the circumferential eigenmodes and accompanying frequencies of these vessels, and then comparing the experimental results with the theoretical predictions. The theoretical analysis was based on the finite element method. Comparison between theory and experiment was found to be good for the higher eigenmodes, but less satisfactory for the lower eigenmodes.

An experimental and theoretical study of multi-cell structures curved in plan

Abstract: The paper describes an experimental and theoretical study of the behaviour of multi-cell structures curved in plan. A technique adopted to make perspex models of multi-cell box girders that are curved in plan is briefly described. The results of eight tests on two perspex models of different span/radius ratios subjected to different loading conditions are presented. The experimental results are compared with theoretical values obtained by employing the finite element method and good agreement between the results can be observed.

Variational principle of combined energy―mechanics of laminated structures

Abstract: The conventional approaches for stress analysis of composite laminates have encountered discontinuity problems. In this paper, the C 1 continuity of displacements in the in-plane directions and C 0 continuity of displacement along the thickness direction are discussed. Also, the global continuity of transverse stresses and local continuity of in-plane stresses are examined. Then, the formulations of stress analysis in both differential equation form and variational functional form are presented.

Viscoelastic effects on the vibration of structural elements liable to buckling

Abstract: The influence of the material creep on the stability and vibration characteristics of axially compressed structural elements is investigated by means of a simplified rheological model. The stability and the vibration characteristics are illustrated, respectively, by the equilibrium paths along the creep process and the natural frequencies corresponding to each equilibrium configuration. The results obtained contribute to a better understanding of the behavior of structural elements under compressible loading, taking into account the time-dependent characteristics of the material.

Cyclic shear loading of aluminium panels with regard to buckling and plasticity

Abstract: Theoretical and experimental results from a series of tests on thin-walled aluminium panels under cyclic shear-load are presented. The test specimens consisted of nearly 30 sheets (thicknesses varying from t = 1·2 to t = 3·0 mm ) of the aluminium alloy 2024 T3 (or T351). Experimental investigations were performed with a special device that applies nearly pure shear. Theoretical results were obtained by using a finite element code. The model used takes into account geometric as well as material non-linearities. In the case investigated — the deeply post-buckled region — interest focused on the material law. Good agreement of experimental and theoretical results was found by using two-surface models.