Showing papers in "Thin-walled Structures in 1995"
TL;DR: In this paper, the effect of geometrical nonlinearity, as well as material plasticity, has been investigated for wind-buckling of thin-walled steel cylinders, such as silos and tanks.
Abstract: The wind-induced buckling of thin-walled steel cylinders, such as silos and tanks, was investigated by wind-tunnel testing for a limited range of the parameters. While wind-buckling of short, stocky shells can be well represented by an equivalent uniform external pressure, long shells show quite a different behaviour, which is strongly influenced by the axial compression forces. This paper presents a study of this behaviour, based on numerical analyses and considering various types of imperfection shape. The effect of geometrical nonlinearity, as well as material plasticity, has also been included. A comparison with test results shows good agreement with the numerical results of imperfect shells, provided that special eigenmode-shaped modes of imperfections are excluded.
78 citations
TL;DR: In this article, the authors trace the history of the ideas which have been deployed in order to shed light on what is often referred to as "imperfection-sensitive" buckling behaviour of shells.
Abstract: The buckling of thin-walled shell structures under load is still imperfectly understood, in spite of much research over the past 50 years. In this paper the author traces the history of the ideas which have been deployed in order to shed light on what is often referred to as ‘imperfection-sensitive’ buckling behaviour of shells. The ideas, which recur in various combinations, involve interaction of competing buckling modes, nonlinear behaviour, the growth of initial geometric imperfections under load and the alteration of the distribution of membrane stress as imperfections grow. The author claims that there are strong grounds for supposing that ‘locked in’ initial stresses on account of imperfect initial geometry and the static indeterminacy of boundary conditions of real shells have a pronounced effect on the buckling performance. This effect has been ignored in the past, and is the subject of a current experimental study.
78 citations
TL;DR: In this paper, the authors proposed an optimization procedure based on the methods of path following, direct computation of bifurcation and limit points, and an accurate and efficient sensitivity analysis.
Abstract: The subject of the present study is the optimization of structures with geometrically nonlinear behaviour allowing the inclusion of instability phenomena and imperfection sensitivity in the structural design. The proposed optimization procedure is based on the methods of path following, direct computation of bifurcation and limit points and an accurate and efficient sensitivity analysis. The finite element method is used for the structural analysis. These techniques are used together with mathematical programming schemes and methods of computer-aided geometric, design.
68 citations
TL;DR: The reduced stiffness method for the analysis of shell buckling was developed to overcome a trend towards increasingly sophisticated analysis that has become divorced from its basically simple underlying physics as discussed by the authors, and it is suggested that the method has now reached a stage where it could profitably be adopted as a basis for an improved shellbuckling design methodology.
Abstract: The ‘reduced stiffness method’ for the analysis of shell buckling was developed to overcome a trend towards increasingly sophisticated analysis that has become divorced from its basically simple underlying physics. This paper outlines the developments of the reduced stiffness method from its origins in the late 1960s, through its experimental confirmation, generalisation and elaboration over the past 20 years, to its more recent consolidation using carefully controlled non-linear numerical experiments. It is suggested that the method has now reached a stage where it could profitably be adopted as a basis for an improved shell buckling design methodology.
61 citations
TL;DR: In this article, a comprehensive nonlinear finite element elastic stability analysis was performed with the aim of explaining the effect of a deep single longitudinal initial dent on the load-carrying behaviour of an externally-pressurized cylindrical shell.
Abstract: A comprehensive nonlinear finite element elastic stability analysis was performed with the aim of explaining the effect of a deep single longitudinal initial dent on the load-carrying behaviour of an externally-pressurized cylindrical shell. The numerical results are compared with available test results and agree well, at least qualitatively. Imperfection sensitivity studies were carried out comparing the effect of the single dent with the effect of evenly distributed periodic initial imperfections. Imperfection sensitivity tends to vanish for increasing amplitudes of the idealized case of a single dent.
52 citations
TL;DR: A design methodology which includes the correlation of realistic imperfections with manufacturing techniques is outlined, and ways are indicated of inclusion of the relevant imperfection data into design methods.
Abstract: The development of techniques for measuring geometric imperfections is traced from the sixties to the present day. First, the early laboratory experiments that initiated the concepts and developed the basic techniques are outlined. Imperfection measurements of large and full-scale shells are then considered, including those performed in industry. Modern, more sophisticated, semi-automated measurement techniques as well as imperfection data banks are discussed. Finally, a design methodology which includes the correlation of realistic imperfections with manufacturing techniques is outlined, and ways are indicated of inclusion of the relevant imperfection data into design methods.
48 citations
TL;DR: In this article, a probabilistic methodology was used to design and analysis of cylindrical shells under axial compression, and the results of the statistical analysis were introduced in the imperfection modelling.
Abstract: One possible avenue that may improve design against buckling is to recognise and account for the random nature of initial geometric imperfections introduced by manufacturing. This paper presents the application of a probabilistic methodology to the design and analysis of cylindrical shells under axial compression. Results from two cases are presented and compared: the first involves stringer-stiffened steel cylinders failing elastoplastically, whereas the second examines unstiffened composite cylinders buckling elastically. In both cases, the method is underpinned by statistical analysis of imperfections measured on nominally identical specimens. Nonlinear FE analysis is used for strength assessment and the results of the statistical analysis are introduced in the imperfection modelling. It is demonstrated that the method has advantages over code design based on ‘lower bound’ curves, in terms of the calculated buckling loads but also in offering a systematic and rational way by which randomness in imperfections can be assessed.
46 citations
TL;DR: In this paper, a 3-node triangular shell element with only three translational degrees of freedom per node, in which the out of plane displacement is the only d.o.f. considered for bending, is presented.
Abstract: We present a 3 node triangular shell element with only three translational degrees of freedom per node, in which the out of plane displacement is the only d.o.f. considered for bending. The bending stiffness matrix of the element is derived by assuming constant curvature normal to the boundary with adjacent elements. The method is illustrated for a plate element and then for a triangular shell element. Results are presented for a variety of linear and non-linear problems to illustrate its accuracy compared with three other well-known triangular shell elements we have also implemented.
41 citations
TL;DR: In this article, the stability of cylindrical shells under axial compression, external pressure and/or torsion possessing general nonsymmetric random initial imperfections is evaluated.
Abstract: The establishment of an International Imperfection Data Bank is discussed. Characteristic initial imperfection distributions associated with different fabrication techniques are shown. Using a first-order, second-moment analysis, a stochastic method is presented, whereby the stability of isotropic, orthotropic and anisotropic nominally circular cylindrical shells under axial compression, external pressure and/or torsion possessing general nonsymmetric random initial imperfections can be evaluated. Results of measurements of initial imperfections are represented in Fourier series and the Fourier coefficients are used to construct the second-order statistical properties needed. The computation of the buckling loads is done with standard computer codes and includes a rigorous satisfaction of the specified boundary conditions. It is shown that the proposed stochastic approach provides a means to combine the latest theoretical findings with the practical experiences spanning about 75 years in an optimal manner via the advanced computational facilities currently available.
41 citations
TL;DR: In this paper, a high precision triangular plate bending finite element has been extended to the buckling analysis of laminated skew plates, which involves development of the transformation matrix between global and local degrees of freedom for nodes lying on skew edges and suitable transformation of the element matrices.
Abstract: A general high precision triangular plate bending finite element has been extended to the buckling analysis of laminated skew plates. This procedure involves development of the transformation matrix between global and local degrees of freedom for nodes lying on the skew edges and suitable transformation of the element matrices. The accuracy of the present formulation has been verified against literature values. New results are obtained for antisymmetric angle-ply and cross-ply laminated skew plates. In this analysis, the critical buckling loads for different skew angles with various lamination parameters, such as number of layers, fibre orientation angle, different boundary (simply supported, clamped) and loading (uniaxial, biaxial) conditions, have been presented.
38 citations
TL;DR: Experimental and numerical results on seven 580 mm diameter, spun steel, hemispherical shells subjected to external pressure are discussed in this article, where it is shown that one should use the minimum shell thickness for design purposes and not rely on the average wall thickness.
Abstract: Experimental and numerical results on seven 580 mm diameter, spun steel, hemispherical shells subjected to external pressure are discussed in the paper. The average wall thickness of the shells varied from 0·37mm to 2·5mm. Careful shape and thickness measurements on all the shells were obtained and utilised in several types of analysis (2-D Finite Element, bestfit axisymmetric, axisymmetric with a local fattening, etc.). None of the analysis techniques employed proved to be entirely reliable insofar as predicting the collapse strength of the spun steel hemispheres. For example, the ratios of the experimental to the 2-D FE numerical collapse pressures were between 0·56 and 1·21. The test results were also compared with the ECCS design curve and it is shown that one should use the minimum shell thickness for design purposes and not rely on the average wall thickness (three test results plotted below the design curve when the average wall thickness was used).
TL;DR: In this article, the axi-symmetric folds formed in the deforming specimens extend both inside and outside of the line of original tube radius, and the ratio of the inside to outside fold lengths depends on the tube dimensions.
Abstract: Different size tubes of aluminium and mild steel were subjected to axial compression in an Instron machine. The tubes chosen were such that they collapsed in axi-symmetric concertina mode. Typical load-compression curves and deformed shapes of the collapsed tubes are presented. These reveal that the axi-symmetric folds formed in the deforming specimens extend both inside and outside of the line of original tube radius, and the ratio of the inside to outside fold lengths depends on the tube dimensions. Considering the tube collapse mechanism as observed experimentally, an analysis is presented in an attempt to predict the mean collapse load and the post collapse load-compression curve. The computed values of the mean collapse load and the load-compression curve during a load oscillation, are presented and compared with the experiments, as well as with some existing theoretical results.
TL;DR: A triangular and a rectangular strain-based element is developed for the general plane elasticity problems in this article, which is used in various forms, including statical condensation and satisfying equilibrium, to obtain solutions to two dimensional elasticity problem where the contribution of the shearing stress on the deformation can be significant.
Abstract: A triangular and a rectangular strain based elements are developed for the general plane elasticity problems. The triangular element has the two essential external degrees of freedom at each of the three corner nodes and at a mid-side node. It is based on assumed independent linear direct strains and constant shearing strain. The rectangular element has the same degrees of freedom at each of the four corner nodes as well as at the centroidal node. This element is based on linear variations of all the three components of strains. These elements are used in various forms, including statical condensation and satisfying equilibrium to obtain solutions to two dimensional elasticity problems where the contribution of the shearing stress on the deformation can be significant.
TL;DR: In this paper, the authors investigated the vibrations of inflatable dams and applied the finite element method to determine the equilibrium shape of the dam and then analyzed small vibrations about that configuration.
Abstract: Inflatable dams are used for various purposes, such as controlling flood-waters, diverting water for irrigation, impounding water for recreation, raising the height of existing spillways, and preventing beach erosion. They are flexible, cylindrical structures attached to a rigid, horizontal base. The vibrations of such dams are investigated in this paper. The dam is modelled as an elastic shell inflated with air and anchored along two of its generators. Both infinitely—long dams and dams of finite length are considered. Previous analyses have only considered two-dimensional vibrations and have assumed that the dam is an inextensible membrane. The finite element method is applied, first to determine the equilibrium shape of the dam and then to analyze small vibrations about that configuration. For the numerical examples, the lowest six vibration frequencies and corresponding mode shapes are obtained. The results are compared to those when no external water is present.
TL;DR: In this paper, the accuracy of classical shell theories (CST) according to Flugge, Sanders, Love and Donnell, with respect to the recently available three-dimensional elasticity solution, for cross-ply laminated circular cylindrical shells under static loads was examined.
Abstract: This paper examines the accuracy of classical shell theories (CST) according to Flugge, Sanders, Love and Donnell, with respect to the recently available three-dimensional elasticity solution, for cross-ply laminated circular cylindrical shells under static loads. Further, a study has also been made to examine to what extent incorporation of first order shear deformation (FSDT), in aforementioned shell theories, improves the results. In general, all the basic equations (for both CST and FSDT), of aforementioned shell theories, have been presented in a unified form using tracer coefficients. A Navier type solution has been used to analyse both a simply supported circular cylindrical shell of revolution and an all round simply supported circular cylindrical shell panel. A parametric study has been carried out keeping in view the lamination schemes and geometrical parameters of the shell. From the detailed comparisons of the results it has been shown that (i) Donnell's theory (CST and FSDT) could be in error for certain lamination schemes and geometrical parameters and (ii) improved results for stresses and displacements could be obtained by incorporating shear deformation on more accurate theory like Flugge (CST).
TL;DR: In this paper, different ways of modelling imperfections are discussed and steel silo shells are used as an application. But the assessment of imperfections is most important for determining the loadbearing capacity of a thin-walled shell structure.
Abstract: The assessment of imperfections is most important for determining the load-bearing capacity of a thin-walled shell structure. Different ways of modelling imperfections are discussed in this paper and steel silo shells are used as an application. Buckling tests were performed on different types of model shell - standard quality and high quality with reduced heat input during welding. For the numerical studies two different approaches were used as well: an axisymmetric approach with substitute geometric imperfections and an FEM approach, where the nodal coordinates were derived from surveying the specimen. It was found that there is considerable gain in the buckling strength due to the presence of the granular solid. The larger the initial imperfections in the shell the greater the gain in strength compared to the empty cylinder. The modelling of the uneveness of the edges with uneven dead loading is also discussed.
TL;DR: In this paper, a study on vibration damping by means of partial viscoelastic coating applied to the surface of vibrating panels is presented, where an optimization procedure seeking the location as well as the shape of coverage giving the best damping performance for a given weight of material is established.
Abstract: This paper presents a study on vibration damping by means of partial viscoelastic coating applied to the surface of vibrating panels. An optimization procedure seeking the location as well as the shape of coverage giving the best damping performance for a given weight of material is established. Emphasis is also put on the temperature and frequency dependent characteristics of the viscoelastic material. The results show the effects of the operating temperature and the great potential of using optimized partial coverage, either to reduce the weight while maintaining the same damping level or to increase the performance with the same amount of material.
TL;DR: In this article, the collapse load of aluminum and mild steel tubes between parallel rigid platens was analyzed by considering the out-of-straightness of arms, corner radius, friction between the platens and the specimen and stability of the vertical arms.
Abstract: Experiments to determine the collapse load of aluminum and mild steel tubes, of square and rectangular cross-sections, between parallel rigid platens were carried out in an Instron machine. A two stage analysis for the collapse of these tubes was carried out by considering the out-of-straightness of arms, corner radius, friction between the platens and the specimen and stability of the vertical arms. Results thus obtained compare well with experiments.
TL;DR: In this paper, the general theory of isoparametric spline finite strip for analysis of shell structures is outlined, when applied to most problems, yields a relatively narrow band matrix and requires little computational effort.
Abstract: The isoparametric spline finite strip method for degenerate shells is presented. In the formulation, both the geometry and the displacement field are represented by uniform cubic B-spline curves. In this paper, the general theory of isoparametric spline finite strip for analysis of shell structures is outlined. The method, when applied to most problems, yields a relatively narrow band matrix and requires little computational effort. Solutions of a number of problems using this method are compared with other available analytical and numerical solutions, and in all cases very good agreement is observed.
TL;DR: In this article, the elastic buckling of uniformly in-plane loaded regular polygonal plates with combinations of various edge conditions and internal line/curved supports has been investigated, and the Rayleigh-Ritz method has been adopted.
Abstract: This paper concerns the elastic buckling of uniformly in-plane loaded regular polygonal plates with combinations of various edge conditions and internal line/curved supports. In contrast to the usual practice of using one of the discretization methods such as the finite element method for performing the buckling analysis, the Rayleigh-Ritz method has been adopted. It will be demonstrated how such an approximate continuum method can still be applied for such plates with somewhat complicated boundary conditions. This more comprehensive tabulated set of buckling factors for plates of various regular polygonal shapes should be valuable to designers and may also serve as reference values for testing future software development in plate buckling analysis.
TL;DR: In this article, a general buckling solution under combined axial compression and external pressure was derived for moderate-length orthotropic cylindrical shells loaded by either external pressure or axial compressions.
Abstract: Most papers dealing with the analysis of the buckling behaviour of orthotropic circular cylindrical shells provide solutions which are complex in nature and difficult to use. In this paper the theory has been developed to the point that relatively simple solutions of a general nature have been formulated. Based on Flugge's linear theory for isotropic cylindrical shells, a general buckling solution under combined axial compression and external pressure was derived. For moderate-length orthotropic cylindrical shells loaded by either external pressure or axial compression, buckling loads are formulated in a simple form.
TL;DR: In this paper, it was shown that the presence of a granular solid can increase buckling load remarkably, and also that small modifications in the interaction assumptions have a major influence on the buckling loads.
Abstract: Thin-walled shell structures are likely to buckle under axial loading way below the classical value. In the presence of granular solids (e.g. sand) in cylindrical shells the stiffness of the contents has a positive influence on the buckling load, similar to internal pressure. In practical silo design this effect is not considered. This is because not much is known about the interaction between the shell and the flexible granular contents and about how to handle this in a computational model. The present study will focus on some simple interaction models. It will be seen that the presence of a granular solid can increase the buckling load remarkably, and also that small modifications in the interaction assumptions have a major influence on the buckling loads.
TL;DR: In this paper, the relationship between torsional warping and distortional warping for the analysis of thin-walled beams has been investigated for both open and closed cross-section profiles.
Abstract: This paper considers the relationship between torsional warping and distortional warping for the analysis of thin-walled beams. The paper explains why warping displacement can be defined by a single warping function in special cases, but in more general cases this description is insufficient. The paper also considers the relationships between warping functions and the torsional and distortional angles in thin-walled beam analysis. Finally, in order to demonstrate the essential features of the paper, a numerical example is solved for a thin-walled beam. Both open and closed cross-section profiles are investigated.
TL;DR: In this paper, an analysis of the bifurcation and initial postbuckling behavior of highly imperfection-sensitive large spherical.shells, such as cargo tanks for ship transportation of liquefied natural gas and large spherical containment shells for nuclear power plants, is presented.
Abstract: The paper deals with an analysis of the bifurcation and initial post-buckling behaviour of highly imperfection-sensitive large spherical .shells, such as cargo tanks for ship transportation of liquefied natural gas and large spherical containment shells for nuclear power plants. The numerical analysis procedure has sufficient generality to treat shells of revolution with arbitrary curved generators and with arbitrary variation of the thickness. The shells can be subjected to non-axisymmetric time-varying loadings. The purpose of the paper is to present simple procedures for scantling selections in the initial design phase and to propose an analysis procedure for verification of the final design of optimized thin-walled spherical shells.
TL;DR: In this paper, the authors investigated the large deflection, geometrically nonlinear behaviour of shells and obtained complex load-deflection curves for cylindrical and spherical shells by incrementing loads as well as deflections.
Abstract: An investigation into the large deflection, geometrically nonlinear behaviour of shells is carried out in the present paper. The finite element method is used in conjunction with linearised incrementation and the Newton-Raphson iterative technique. The finite element used is based on independent strain assumptions insofar as it is allowed by the compatibility equations. Strain-displacement relationships based on shallow shell formulation are used and applied to an element having three principal curvatures. The resulting element has the only essential external degrees of freedom, satisfies the exact requirement of strain free rigid body modes of displacements and can be used for the representation of cylindrical, spherical and hyperbolic paraboloid shells. Complex load-deflection curves are obtained for cylindrical and spherical shells by incrementing loads as well as deflections. The relative behaviour of cylindrical and spherical panels having the same overall dimensions are also discussed in terms of stiffness, instability and snap-through phenomena.
TL;DR: In this paper, the results of a systematic numerical investigation of the nonlinear elastic and elastic plastic load-carrying behavior and imperfection sensitivity of torispherical pressure vessel heads under uniform external pressure were presented.
Abstract: The paper deals with the results of a systematic numerical investigation of the nonlinear elastic and elastic plastic load-carrying behaviour and imperfection sensitivity of torispherical pressure vessel heads under uniform external pressure. In particular, the presentation focuses on the qualitative and quantitative influence of the radius-to-thickness ratio R/t, the yield stress σ 0 and the magnitude of initial geometric imperfections (in the shape of the elastic bifurcation mode) on the elastic-plastic load-carrying behaviour. It is found that thinner shells are more sensitive to the value of the yield stress and the magnitude of initial geometric imperfections, but their load-carrying capacity, relative to the elastic bifurcation pressure, may also be significantly higher than that of thicker shells.
TL;DR: In this paper, exact solutions for the torsional analysis of variable and open cross-section bars are given, including the effect of warping, in regions with continuous variation in section properties and loading.
Abstract: This work gives exact solutions for the torsional analysis of variable and open cross-section bars. An analytical method is derived to form the stiffness matrix of the bar, including the effect of warping. Only one element is needed for the exact solution in regions with continuous variation in section properties and loading. Several examples are given and compared to approximate results.
TL;DR: In this article, the displacement function of a flat shell finite strip is made up of two parts, namely, the two in-plane displacement interpolations and the out-of-planar displacement interpolation.
Abstract: This paper presents the application of a new finite strip to the analysis of folded-plate structures. The displacement function of a flat shell finite strip is made up of two parts, namely, the two in-plane displacement interpolations and the out-of-plane displacement interpolation. Each of the three displacement components is interpolated by a set of computed shape functions in the longitudinal direction and, as usual, one-dimensional shape functions in the transverse direction. Only standard beam shape functions are involved in the longitudinal computed shape functions. When compared with other finite strips, the present finite strip is relatively simple in dealing with boundary and internal support conditions. In addition, the method can be easily implemented by incorporating a standard finite strip program with a continuous-beam program. The computation of the stiffness matrix involves no numerical integration. To verify the accuracy and efficiency of the new finite strip, a few numerical experiments are conducted in which the present finite strip results are compared with those using other finite strips and/or finite elements for the vibration and buckling of folded-plate structures with varying complexity.
TL;DR: In this article, the original spline finite strip is modified and generalized in the sense that the formulation is based upon a third-order plate theory and is applicable to thin plates and shear-deformable plates (e.g. thick isotropic plates and laminated composite plates).
Abstract: In this paper, the original spline finite strip, which is based upon the thin-plate theory, is modified and generalized in the sense that the formulation is based upon a third-order plate theory and is applicable to thin plates and shear-deformable plates (e.g. thick isotropic plates and laminated composite plates). To extend its application to nonlinear analysis, displacement formulation is employed with geometric nonlinearity and small initial imperfection taken into account. To demonstrate the performance of the present finite strip in the analysis of plates, a number of numerical examples are given.
TL;DR: In this paper, the authors report the findings of research into the possibility of certain shell forms for elevated reservoirs, initially conducted on the basis of the membrane hypothesis, and present a review of the conditions of applicability of membrane solutions.
Abstract: This paper reports the findings of research into the possibility of certain shell forms for elevated reservoirs, initially conducted on the basis of the membrane hypothesis. In order to place the methods used and the findings obtained firmly into context, the paper begins by a review of the conditions of applicability of membrane solutions. Then, on the basis of a rectangular coordinate system, general expressions for membrane stress resultants are developed for elevated liquid-filled tanks in the form of shells of revolution of arbitrary meridian profiles. These expressions are next applied to selected profiles with zero slope at the pole (consistent with the smoothness requirements of the membrane hypothesis), and of reasonable shape for containment. A general discussion of the validity of the results, particularly for locations around the poles, is followed by a comparison of the membrane-stress variations for tanks of the same height and circular plan area, based on typical values of these dimensions. Finally, by defining a form efficiency parameter η, the tank of most desirable profile (from among the cases studied) is suggested.