Buckling of Composite and Homogeneous Isotropic Cylindrical Shells Under Axial and Radial Loading

1969 ◽  
Vol 36 (4) ◽  
pp. 791-798 ◽  
Author(s):  
M. M. Lei ◽  
Shun Cheng
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Circular Cylindrical Shell ◽  
Radial Pressure ◽  
Buckling Load ◽  
Simply Supported ◽  
Classical Boundary ◽  
Axial Compressive Stress ◽  
Radial Loading ◽  
Geometrical Dimensions

A theoretical analysis of the buckling of a multilayered thin orthotropic composite circular cylindrical shell of finite length, subjected to (a) uniform axial compression, and (b) axial compression combined with radial pressure, is presented. At each end of the shell, four boundary conditions are satisfied. Four combinations of boundary conditions for simply supported shells, and four combinations of boundary conditions for clamped shells, are treated. These boundary conditions are reduced to the vanishing of a fourth-order determinant. Buckling loads for boron-epoxy composite shells are determined and the results are shown in a series of diagrams. The effect of boundary conditions on the buckling load for various geometrical dimensions of composite cylinders is investigated. Details of the boundary conditions are shown to have strong influence on the buckling load of the shell. The minimum critical axial compression for a simply supported shell with boundary conditions SS1 is as low as 79 percent of the minimum critical axial compression for a shell with classical boundary conditions SS3. As a special case of a composite shell, the minimum critical axial compressive stress for a homogeneous, isotropic, simply supported shell with end conditions SS1 is found to be 43.7 percent of the classical critical stress.

Experiments on the Buckling of Simply-Supported Rectangular Plates

1969 ◽  
Vol 73 (703) ◽  
pp. 607-608 ◽  
Author(s):  
A. C. Mills
Keyword(s):  
Experimental Investigation ◽  
Theoretical Analysis ◽  
Boundary Conditions ◽  
Buckling Load ◽  
Theoretical Solution ◽  
Rectangular Plates ◽  
Uniform Load ◽  
Simply Supported

In ref. (1) Pope presents a theoretical analysis of the buckling of rectangular plates tapered in thickness under uniform load in the direction of taper. An experimental investigation into the end load buckling problem for a plate having simply-supported edges with the sides prevented from moving normally in the plane of the plate is described in ref. (2). For these boundary conditions the theoretical solution is exact. However, the compatability equation is not satisfied exactly when the sides are free to move in the plane of the plate. This experimental investigation demonstrates that the buckling load is nevertheless adequately predicted by the analysis in these circumstances.

The Effect of Shape, Thickness and Boundary Imperfections on Plastic Buckling of Cones

2011 ◽  
Author(s):  
O. Ifayefunmi ◽  
J. Błachut
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Wall Thickness ◽  
Thickness Distribution ◽  
Radial Pressure ◽  
External Pressure ◽  
Combined Loading ◽  
Small Radius ◽  
Worst Case ◽  
Buckling Strength

Three types of imperfections are analysed in the current paper, and they are: (i) Initial geometric imperfections, i.e., deviations from perfect geometry, (ii) Variations in the wall thickness distribution, and (iii) Imperfect boundary conditions. It is assumed that cones are subject to: (a) axial compression only, (b) radial pressure only, and (c) combined loading, i.e., axial compression and external pressure acting simultaneously. Buckling strength of imperfect cones is obtained for all of the cases above. It is shown that the buckling strength is differently affected by imperfections, when cones are subjected to axial compression or to radial external pressure. The response to imperfections along the combined stability envelope is also provided, and these results are first of this type. The finite element analysis, using the proprietary code is used as the numerical tool. Cones are assumed to be from mild steel and the material is modelled as elastic perfectly plastic. Geometrical imperfection profiles are affine to eigenshapes. A number of them are tried in calculations, as well as the effect of them being superimposed. The results indicate that imperfection amplitude and its shape strongly affect the load carrying capacity of conical shells. Also, it is shown that the buckling loads of analyzed cones are more sensitive when subjected to combined loading as compared to their sensitivity under single load conditions. At the next stage, uneven thickness distribution along the cone slant was considered. Variation of wall thickness was assumed to vary in a piece-wise constant fashion. This appears to have a large effect on the buckling strength of cones under axial compression only as compared with that of cones subjected to radial external pressure only. Finally, the effect of variability of boundary conditions on failure load of cones was investigated for two loading conditions, i.e., for axial compression and for radial pressure, only. Results indicate that change of boundary conditions influences the magnitude of buckling load. For axially compressed cones the loss of buckling strength can be large (about 64% for the worst case (beta = 30 deg, the cone not restrained at small radius end). Calculations for radial pressure indicate that the loss of buckling strength is not as acute — with 34% for the worst case (beta = 40 deg, relaxed boundary conditions at the larger radius end). This is an entirely numerical study but references to accompanying experimental programme are provided.

A Theorem on Buckling and Structural Stiffness

1965 ◽  
Vol 9 (02) ◽  
pp. 9-10
Author(s):  
William P. Vafakos
Keyword(s):  
Cylindrical Shell ◽  
Axial Compression ◽  
Circular Cylindrical Shell ◽  
Sufficient Conditions ◽  
Buckling Load ◽  
Structural Stiffness ◽  
Axisymmetric Buckling

Sufficient conditions are presented under which an increase (decrease) of the flexural, torsional, or extensional stiffness in any part of a structure cannot result in a decrease (increase) of the classical buckling load. A problem of axisymmetric buckling of a ringstiffened circular cylindrical shell under axial compression is considered for illustration.

scholarly journals Frequency Equations and Modes of Free Vibrations of Rectangular Plates with Various Edge Conditions

1994 ◽  
Vol 208 (5) ◽  
pp. 307-319 ◽  
Author(s):  
C W Bert ◽  
M Malik
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Free Vibrations ◽  
Edge Condition ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Edge Conditions ◽  
Classical Boundary ◽  
Free Edges

This paper considers linear free vibrations of thin isotropic rectangular plates with combinations of the classical boundary conditions of simply supported, clamped and free edges and the mathematically possible condition of guided edges. The total number of plate configurations with the classical boundary conditions are known to be twenty-one. The inclusion of the guided edge condition gives rise to an additional thirty-four plate configurations. Of these additional cases, twenty-one cases have exact solutions for which frequency equations in explicit or transcendental form may be obtained. The frequency equations of these cases are given and, for each case, results of the first nine mode frequencies are tabulated for a range of the plate aspect ratios.

Evaluation of Buckling Performance of Fibre Metal Rectangular Plates: Experimental and Numerical Investigation

2014 ◽  
Vol 575 ◽  
pp. 185-190
Author(s):  
M. Vasumathi ◽  
Murali Vela
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Buckling Load ◽  
Thin Layers ◽  
Maximum Deviation ◽  
Critical Buckling Load ◽  
Buckling Strength ◽  
Different Boundary Conditions ◽  
Simply Supported ◽  
Fibre Metal

Carbon reinforced aluminium laminate (CARAL) is a fibre metal laminate which consists of layers of carbon fibre and thin layers of aluminium. Buckling strength of CARAL under various support conditions is studied in this paper. Since CARAL is composed of fibre and metal, the pattern of failure of the laminate under compressive loads is truly imperative. The compressive buckling strength depends on geometrical parameters like length and width of the specimen and the sequence in which the layers are stacked. It also depends on the boundary condition. In this study, the critical buckling load is determined by varying the parameters such as aspect ratio (length/width), stacking sequence and boundary condition. Two different boundary conditions are considered, simply supported and fixed support condition. Numerical simulation analysis shows a maximum deviation of 16.72% from experimental results. The different failure modes executed by the laminate under compressive loading are also determined. The critical buckling load of CARAL constrained on all sides is evaluated numerically for different boundary conditions. Buckling load, in this case, takes maximum value when CARAL is clamped on all sides whereas it takes minimum value when the plate is simply supported on three sides keeping the fourth side fixed.

Vibration Characteristics of the Respiratory Branched Network-Comparative Study

2005 ◽  
Author(s):  
P. M. Au ◽  
A. M. Al-Jumaily
Keyword(s):  
Boundary Conditions ◽  
Comparative Study ◽  
Circular Cylindrical Shell ◽  
Vibration Characteristics ◽  
The Finite Element Method ◽  
Resonant Frequencies ◽  
Membrane Shell ◽  
Classical Boundary ◽  
Circular Cylindrical Shells ◽  
Shell Approximation

Determining the vibration characteristics of a realistic branched biological network, such as the respiratory system, faces many hurdles, which includes using the appropriate theory, specifying suitable boundary conditions and selecting accurate physical properties. Further, dichotomized or bifurcated structures beyond a simple circular cylindrical shell induce problems and difficulties in boundary matching between generations. This paper determines the natural frequencies using the Donnell-Mushtari formulation, membrane-shell approximation, a simplified limiting ring formula and the finite element method using COSMOS/Works™ for circular cylindrical shells with classical boundary conditions. Some experimental data are used for comparison and validation. Comparative study between the various methods sets the pros, cons, limitations of each method and the boundaries for the resonant frequencies of each individual generation of this system.

Buckling of Edge Damaged, Cylindrical Composite Shells

1989 ◽  
Vol 56 (1) ◽  
pp. 121-126 ◽  
Author(s):  
M. Sabag ◽  
Y. Stavsky ◽  
J. B. Greenberg
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
Buckling Load ◽  
Composite Shells ◽  
Gradual Reduction ◽  
Critical Buckling Load ◽  
Anisotropic Composite ◽  
The Stability ◽  
Edge Damage

The stability of thin composite layered anisotropic cylindrical shells under axial compression is considered for the case of nonuniform boundary conditions. Such conditions are employed to model the situation where there is edge damage to the shell. The influence of weakening or a crack at an edge on the critical buckling load of a variety of single and multilayered shells is investigated. Results indicate that isotropic shells exhibit a rather sudden steep reduction in the critical buckling load for relatively small edge damage. However, some anisotropic composite shells may not be so sensitive and, in contrast, only a gradual reduction may be brought about by the edge damage. The degree of sensitivity to edge damage appears to be dependent, in some complex fashion, on the various geometric and physical shell parameters.

scholarly journals DIAGRAMS FOR STRESS AND DEFLECTION PREDICTION IN CROSS-LAMINATED TIMBER (CLT) PANELS WITH NON-CLASSICAL BOUNDARY CONDITIONS

2020 ◽  
Vol 14 (1) ◽  
Author(s):  
Nikola Obradović ◽  
Marija Todorović ◽  
Miroslav Marjanović ◽  
Emilija Damnjanović
Keyword(s):  
Boundary Conditions ◽  
Engineering Practice ◽  
Design Codes ◽  
Detailed Design ◽  
Cross Laminated Timber ◽  
Simply Supported ◽  
Laminar Composites ◽  
Different Types ◽  
Practical Engineering ◽  
Classical Boundary

Invention of cross-laminated timber (CLT) was a big milestone for building with wood. Due tonovelty of CLT and timber’s complex mechanical behavior, the existing design codes cover onlyrectangular CLT panels, simply supported along 2 parallel or all 4 edges, making numerical methodsnecessary in other cases. This paper presents a practical engineering tool for stress and deflectionprediction of CLT panels with non-classical boundary conditions, based on the software for thecomputational analysis of laminar composites, previously developed by the authors. Diagramsapplicable in engineering practice are developed for some common cases. The presentedmethodology could be a basis for more detailed design handbooks and guidelines for various layoutsof CLT panels and different types of loadings.

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