scholarly journals Buckling of the cylindrical shell joint with annular plates under external pressure

2021 ◽  
Vol 8 (2) ◽  
pp. 282-294
Author(s):  
Sergei B. Filippov ◽  
Keyword(s):  
Cylindrical Shell ◽  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Critical Pressure ◽  
External Pressure ◽  
Zero Approximation ◽  
Beam Model ◽  
Annular Plates ◽  
Circular Beam ◽  
Narrow Plate

By means of an asymptotic method the buckling under the uniform external pressure of the thin cylindrical shell supported by identical annular plates is analyzed. Boundary conditions on an internal parallel of the shell joined to a thin plate are obtained. At the edges of the shell the free support conditions are introduced. We seek the approximate solutions of the eigenvalue problem as a sum of slowly varying functions and edge effect integrals. On a parallel, where the plate joint with the shell, the main boundary conditions for the formulation of an eigenvalue problem of zero approximation are obtained. This problem describes also vibrations of a simply supported beam stiffened by springs. Its solution we seek as linear combinations of Krylov’s functions. It is shown, that in zero approximation it is possible to replace a narrow plate with a circular beam. At increase in width of a plate stiffness of the corresponding spring tend to a constant. It occurs because of localization plate deformations near to the internal edge of a plate. As an example the dimensionless critical pressure for the case when the shell is supported by one plate is found. The replacement of a narrow plate with a circular beam does not lead to appreciable change of the critical pressure, however for a wide plate the beam model gives the overestimated value of critical pressure.

scholarly journals Experimental and Numerical Determination of Critical Buckling Pressure of thin Cylindrical Shells Subjected To External Pressure

2020 ◽  
Vol 8 (6) ◽  
pp. 4362-4366
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Measurement System ◽  
Pressure Measurement ◽  
Thin Shell ◽  
External Pressure ◽  
Shell Structures ◽  
Test Rig ◽  
Critical Buckling Pressure ◽  
Pressure Measurement System

Thin shell structures have very high load bearing capacity, hence find wide applications in the field of mechanical engineering, structural engineering, sea shore structures, aerospace industries and nuclear engineering structures. The major failure of thin shell structures is buckling. Oil carrying pipelines, hull structures, oil tankers are few examples in which thin cylindrical shell structures fails by buckling under external pressure loading. In order to avoid the buckling failure, prediction of critical buckling pressure is important in thin shell structures under external pressure. But this critical buckling pressure depends on boundary conditions, imperfections, thickness variation of shells etc. To estimate the effects of these parameters on Critical Buckling Pressure (CBP) require a reliable experimental test rig. Hence in our proposed work, efforts are taken to develop a simple cost-effective reliable test rig to determine the effects of these parameter variations on the critical buckling pressure. For developing the test rig two important components to be designed properly namely, external cover cylinder and online pressure measurement system. The external cover cylinder with lid which contains test cylindrical shell inside should be designed in such a way that it should be leak proof and rigid so as to withstand the internal working pressure with negligible deformations. Hence, a ring and stinger stiffened cylindrical shell is taken as external cylindrical shell. The pressure variation in the test rig should be recorded online so as to predict the critical buckling pressure accurately. Hence, PC interfaced microcontroller-based pressure measurement system is developed in our proposed work. The test cylinder considered for this work is made of mild steel of size diameter 456 mm, length 456 mm and thickness 1 mm. The classical (simply supported) boundary conditions are assumed and simulated on both sides of the test cylinders. The experimental critical buckling pressures are compared with the FE results and both the results have good agreement

scholarly journals Axisymmetric Natural Frequencies of Statically Loaded Annular Plates

2003 ◽  
Vol 10 (5-6) ◽  
pp. 301-312 ◽  
Author(s):  
Eihab M. Abdel-Rahman ◽  
Waleed F. Faris ◽  
Ali H. Nayfeh
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Shooting Method ◽  
Large Deformations ◽  
Natural Frequencies ◽  
Numerical Procedure ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Plate Model ◽  
Annular Plates

We present a numerical procedure to solve the axisymmetric vibration problem of statically loaded annular plates. We use the von Kármán nonlinear plate model to account for large deformations and study the effect of static deflections on the natural frequencies and mode shapes for six combinations of boundary conditions. The shooting method is used to solve the resulting eigenvalue problem. Our results show that static deformations have a significant effect on the natural frequencies and small effect on the mode shapes of the plate. Further, the results show that the presence of in-plane stresses has a significant effect on the natural frequencies.

Case Study of Buckling Failure of a Large Liquid Storage Tank

2005 ◽  
Author(s):  
Enayat Mahajerin ◽  
Gary Burgess
Keyword(s):  
Cylindrical Shell ◽  
Human Error ◽  
Critical Pressure ◽  
Radial Pressure ◽  
External Pressure ◽  
Hot Water ◽  
Aspect Ratios ◽  
Buckling Failure ◽  
Cylindrical Tanks

Large cylindrical tanks are often used to store liquids like milk and chemicals for distribution. These structures are considered thin shells because of their geometry, dimensions, and aspect ratios. In this paper, an actual failure of a large vertical tank is investigated. The tank contained milk and buckled as a result of an internal vacuum caused by human error. Inspection done after failure revealed that an internal vacuum could have been created by a large drop in the inside air temperature. Such tanks are usually washed using extremely hot water. If the water temperature exceeded the manufacturer’s recommendations and the tank is not vented during the cool-down cycle, the contracting air would have drawn a vacuum. Another possibility is that the tank may have been drained without venting the headspace above the milk. This would cause the fixed mass of air above the milk to expand and draw a vacuum. To investigate these scenarios we consider stability of a vertical cylindrical shell under external pressure. The critical pressure differential for buckling of a vertical cylindrical shell with closed ends subjected to uniform axial and radial pressure is known from basic theories of buckling. These equations are used to determine the critical pressure for lobar buckling. The results show that each of these scenarios could have caused failure of the tank. Recommendations to prevent future failures in such storage tanks and design considerations for tanks having arbitrary dimensions and aspect ratios are presented in the paper.

scholarly journals On the elastoplastic stability problem of the thin round cylindrical shells subjected to complex loading processes with the various kinematic boundary conditions

2004 ◽  
Vol 26 (1) ◽  
pp. 11-22
Author(s):  
Dao Van Dung
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Stability Problem ◽  
Cylindrical Shells ◽  
Complex Loading ◽  
External Pressure ◽  
Sufficient Condition ◽  
Compression Force ◽  
Simply Supported ◽  
Long Cylindrical Shell

In this paper, the elastoplastic stability of cylindrical shells simultaneously subjected to compression force along the generatrix and external pressure has been presented. Two types of considered kinematic boundary conditions are simply supported and clamped at the butt-ends. The expressions for determining the critical forces by using the Bubnov-Galerkin method [3] have been established. The sufficient condition of extremum for a long cylindrical shell also is considered. Some results of numerical calculation have been also given and discussed.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

Stability and Natural Characteristics of a Supported Beam

2011 ◽  
Vol 338 ◽  
pp. 467-472 ◽  
Author(s):  
Ji Duo Jin ◽  
Xiao Dong Yang ◽  
Yu Fei Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Axial Force ◽  
Critical Values ◽  
Rotational Spring ◽  
Analytical Expression ◽  
The Stability ◽  
Spring Constants ◽  
Critical Axial Force ◽  
Natural Characteristics

The stability, natural characteristics and critical axial force of a supported beam are analyzed. The both ends of the beam are held by the pinned supports with rotational spring constraints. The eigenvalue problem of the beam with these boundary conditions is investigated firstly, and then, the stability of the beam is analyzed using the derived eigenfuntions. According to the analytical expression obtained, the effect of the spring constants on the critical values of the axial force is discussed.

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

2021 ◽  
pp. 109963622110204
Author(s):  
Xue-Yang Miao ◽  
Chao-Feng Li ◽  
Yu-Lin Jiang ◽  
Zi-Xuan Zhang
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Ritz Method ◽  
Admissible Function ◽  
Free Vibration Analysis ◽  
Middle Layer ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

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