On Numerical Results of Reticulated Shell Buckling (original) (raw)
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A comparison of techniques for computing the buckling loads of stiffened shells
Computers & Structures, 1993
Abatraet-Three different methods are employed to estimate the buckling loads of several ring stiffened and orthotropic cylindrical shells using finite elements. The methods used are a nonlinear bifurcation analysis and two linearized buckling analyses, one that ignores the initial displacement stiffness matrix, and one that includes it. Large differences are observed between the predictions made by the two linearized buckling analyses for a range of shell geometries. Detailed studies of a shell with six stiffeners demonstrate that them differences am caused by different versions of the linearized eigenvalue problem, rather than by the use of different numerical formations. These diserepaneies are also observed for orthotropic shells when L/R is small (< 1) and the degree of orthotropy (EJE,) is high (2 10). Investigations of the prebuckling behavior of some of the cylinders show that the problem is caused by significant nonlinear pmbuckling deformations. This means that a nonlinear bifurcation analysis must sometimes be used to accurately estimate the buckling load of stiffened shells.
Computers & Structures, 1988
The effects of physical and geometrical non-linearities on the buckling and post-buckling behaviour of reticulated shells are analysed, paying particular attention to the influence of imperfections. Two types of random imperfections are considered: joint imperfections, which are often caused by the technical assemblying of the elements, and geometry (or scheme's) imperfections, which occur when the real configuration of the shell does not respect the designed one. The static analysis consists firstly of modelling the material non-linearity of a tubular element under eccentrical normal load and secondly of developing the iterative incremental procedure to solve the non-linear equilibrium conditions. Finally, the problem of tracing secondary equilibrium paths is faced, by means of a non-linear stability analysis. The results obtained by a test structure hexagonal in plan are compared in the final section for the perfect and imperfect cases.
Comments on effective use of numerical modelling and extended classical shell buckling theory
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 2023
2. Extended classical shell buckling theory A number of reviews [31-34] have covered some of the background and important applications of the RS extension to classical shell buckling theory. These have demonstrated that for wide ranges of shell forms and loading conditions, the lower limits to the reductions in buckling loads caused by increasing levels of geometric (and loading) imperfections are provided by RS analysis, including the treatment of the development of material failure [6,31-33]. The philosophical basis of the RS method can be formulated [34] in terms of the following lemmas: Lemma 2.1. Significant geometric nonlinearity in structural behaviour results from changes in incremental membrane energy (or equivalently membrane stiffness). Corollary 2.2. Significant nonlinearity in the buckling of shell and plate structures derives from changes in incremental membrane energy. Corollary 2.3. Nonlinearity arising from changes of incremental bending energy is practically negligible. Lemma 2.4. Loss of stiffness (or load carrying capacity) in the buckling 1 and postbuckling (see footnote 1) of shells is the result of loss of incremental membrane energy. Corollary 2.5. Loss of stiffness (or load carrying capacity) in the postbuckling of shells can only occur if the initial buckling mode (critical bifurcation mode) contains membrane energy. Corollary 2.6. Loss of stiffness (or load carrying capacity) resulting from changes of incremental bending energy in the postbuckling of shells is practically negligible.
The Bulletin of the Polytechnic Institute of Jassy, Construction. Architecture Section, 2012
The problem of dynamic stability is substantially more complex than the buckling analysis of a shell subjected to static loads. The fundamental aim of this paper is to present criteria for determining the critical load of dynamic buckling of thin shell. Another purpose of establishing such criteria is to guide engineers scientists and researchers dealing with such problems, for a better comparison verification and a validation of their experimental or numerical results. To illustrate the application of these criteria, two examples have been studied.
BUCKLING ANALYSIS OF SHELLS SUBJECTED TO COMBINTED LOADS
IAEME Publication, 2014
A semi-analytical isoparametric finite element with three nodes per element and five degrees of freedom per node has been used for the solution. Moderately thick shell theory has been used for the analysis. Second order strains with the in plane and transverse non-linear terms are used for the derivation of geometric matrix. Full Fourier expansion is used in the circumferential direction to overcome the coupling that arises due to material anisotropy and torque prestress. Comparison of the results obtained due to finite element is made with simplified solutions using two thin shell theories with and without shear deformation. The effects of combined load (axial compression and external pressure) on pre-buckling characteristics of composite circular cylindrical and conical shells of various geometric properties have been presented.
Buckling and Sensitivity to Imperfection of Conical Shells Under Dynamic Step-Loading
Journal of Applied Mechanics-transactions of The Asme, 2007
A general nonlinear dynamic analysis, based on Donnell's shell-type theory, is developed for an arbitrary imperfect isotropic conical shell. It is used for studying dynamic stability and imperfection sensitivity under dynamic step loading. The nonlinear dynamic time history and the sensitivity behavior are examined in parametric terms over a wide range of aspect ratios. A general symbolic code (using the MAPLE compiler) was programmed to create the differential operators. By this means the Newmark discretization, Galerkin procedure, Newton-Raphson iteration, and finite difference scheme are applied for automatic development of an efficient FORTRAN code for the parametric study, and for examining the correlation of the sensitivity behavior between two different dynamic stability criteria. An extensive parametric study of the effect of the cone semi-vertex angle on the stability and sensitivity to imperfection under dynamic step loading was carried out. It was found that the dynamic buckling can indeed be derived from the nonlinear static solution.
On Introducing Imperfection in the Non-Linear Analysis of Buckling of Thin Shell Structures
This master thesis details the investigation of the effect of geometrical imperfection on thin shell structures using general FEM software packages. The author proposes a finite element based method for the analysis and design of thin shell structures, and describes the implementation of such a procedure on four FEM packages. The procedure involves assessing structural imperfection sensitivity, and imposing geometrical imperfection prior to a physical and geometrical non-linear analysis.
Towards a rationally based elastic-plastic shell buckling design methodology
Thin-Walled Structures, 1995
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.
On load interaction in the non linear buckling analysis of cylindrical shells
Advances in Engineering Software, 1991
The elastic stability of shells or shell-like structures under two independent load parameters is considered. One of the loads is associated to a limit point form of buckling, whereas the second is a bifurcation. A simple one degree of freedom mechanical system is first investigated, for which an analytical solution is possible. Next, a cylindrical shell under the combined action of axial load and localised lateral pressure is studied via a non linear, two-dimensional, finite ele ment discretization. It is shown that both problems display the same general behaviour, with a stability boundary in the load space which is convex towards the region of stability. The results show the need of performing a full non-linear analysis to evaluate the stability boundary for the class of interaction prob lems considered.