Buckling of Externally Pressurized Toroidal Shell With Stiffened Ribs

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Yongmei Zhu ◽  
Bo Zhao ◽  
Binbin Chen ◽  
Xilu Zhao ◽  
Wenxian Tang ◽  
...  
Keyword(s):  
Cross Sections ◽  
Shell Thickness ◽  
External Pressure ◽  
Toroidal Shell ◽  
Single Wire ◽  
Test Models ◽  
Buckling Behavior ◽  
Practical Engineering ◽  
Discrete Ribs ◽  
Toroidal Shells

Abstract The buckling characteristics of toroidal shells with closed circular cross sections loaded with a static external pressure were investigated. Eight toroidal shell test models were developed: two ribless, two semicircular discrete ribs, two rectangular discrete ribs, and two rectangular continuous ribs. The geometry, toroidal shell thickness, buckling load, and failure of each model were measured and compared. The effects of different ribbing methods (discrete, continuous unidirectional single-wire, continuous unidirectional multiwire wound, and continuous bidirectional wound ribs) on the buckling behavior of a ribbed toroidal shell were investigated, and the results provide guidance for practical engineering.

A Finite Strip for the Vibration Analysis of Rotating Toroidal Shell Under Internal Pressure

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Ivo Senjanović ◽  
Ivan Áatipović ◽  
Neven Alujević ◽  
Damjan Čakmak ◽  
Nikola Vladimir
Keyword(s):  
Internal Pressure ◽  
Cross Sections ◽  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Toroidal Shell ◽  
Beam Shape ◽  
Finite Strip ◽  
Finite Strip Method ◽  
Toroidal Shells

In this paper, a finite strip for vibration analysis of rotating toroidal shells subjected to internal pressure is developed. The expressions for strain and kinetic energies are formulated in a previous paper in which vibrations of a toroidal shell with a closed cross section are analyzed using the Rayleigh–Ritz method (RRM) and Fourier series. In this paper, however, the variation of displacements u, v, and w with the meridional coordinate is modeled through a discretization with a number of finite strips. The variation of the displacements with the circumferential coordinate is taken into account exactly by using simple sine and cosine functions of the circumferential coordinate. A unique argument nφ+ω t is used in order to be able to capture traveling modes due to the shell rotation. The finite strip properties, i.e., the stiffness matrix, the geometric stiffness matrix, and the mass matrices, are defined by employing bar and beam shape functions, and by minimizing the strain and kinetic energies. In order to improve the convergence of the results, also a strip of a higher-order is developed. The application of the finite strip method is illustrated in cases of toroidal shells with closed and open cross sections. The obtained results are compared with those determined by the RRM and the finite element method (FEM).

Buckling Analysis of an Orthotropic Elliptical Toroidal Shell

2009 ◽  
Author(s):  
D. Redekop
Keyword(s):  
Differential Quadrature Method ◽  
External Pressure ◽  
Buckling Analysis ◽  
Toroidal Shell ◽  
Shells Of Revolution ◽  
Good Correspondence ◽  
Elliptical Cross ◽  
Wide Range ◽  
Orthotropic Shells ◽  
Toroidal Shells

A theoretical solution is given for the linearized buckling problem of an orthotropic toroidal shell with an elliptical cross-section under external pressure loading. The solution is based on the Sanders-Budiansky shell theory, and makes use of the harmonic differential quadrature method. Theory developed earlier for the buckling of orthotropic shells of revolution, and the vibration of orthotropic elliptical toroidal shells, is incorporated in the present work. Numerical results obtained from the solution are compared with results given in the literature, and good correspondence is generally observed. A parametric study is then conducted, covering a wide range of material and geometric parameters. Regression formulas are derived, indicating the variation of the buckling pressure with the degree of orthotropy of the material. Overall, the study introduces a new tool for the buckling analysis of elliptical toroidal shells, and extends the information available for orthotropic toroidal shells.

Stresses and Deformations of Toroidal Shells of Elliptical Cross Section: With Applications to the Problems of Bending of Curved Tubes and of the Bourdon Gage

1952 ◽  
Vol 19 (1) ◽  
pp. 37-48
Author(s):  
R. A. Clark ◽  
T. I. Gilroy ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Closed Shell ◽  
Open Shell ◽  
Elliptical Cross Section ◽  
Axially Symmetric ◽  
Elliptical Cross ◽  
Two Parameters ◽  
Toroidal Shells

Abstract This paper is concerned with the application of the theory of thin shells to several problems for toroidal shells with elliptical cross section. These problems are as follows: (a) Closed shell subjected to uniform normal wall pressure. (b) Open shell subjected to end bending moments. (c) Combination of the results for the first and second problems in such a way as to obtain results for the stresses and deformations in Bourdon tubes. In all three problems the distribution of stresses is axially symmetric but only in the first problem are the displacements axially symmetric. The magnitude of stresses and deformations for given loads depends in all three problems on the magnitude of the two parameters bc/ah and b/c where b and c are the semiaxes of the elliptical section, a is the distance of the center of the section from the axis of revolution, and h is the thickness of the wall of the shell. For sufficiently small values of bc/ah trigonometric series solutions are obtained. For sufficiently large values of bc/ah asymptotic solutions are obtained. Numerical results are given for various quantities of practical interest as a function of bc/ah for the values 2, 1, 1/2, 1/4 of the semiaxes ratio b/c. It is suggested that the analysis be extended to still smaller values of b/c and to cross sections other than elliptical.

scholarly journals Buckling behavior of cold-formed steel columns at both ambient temperature and simulated fire conditions

Fire Research ◽  
2016 ◽  
Author(s):  
Hélder D. Craveiro ◽  
João Paulo C. Rodrigues ◽  
Luís M. Laím
Keyword(s):  
Experimental Investigation ◽  
Ambient Temperature ◽  
Cross Sections ◽  
Failure Modes ◽  
Steel Columns ◽  
Buckling Behavior ◽  
Wide Range ◽  
Cold Formed Steel ◽  
Simulated Fire ◽  
Fire Conditions

Cold-formed steel (CFS) profiles with a wide range of cross-section shapes are commonly used in building construction industry. Nowadays several cross-sections can be built using the available standard single sections (C, U, Σ, etc.), namely open built-up and closed built-up cross-sections. This paper reports an extensive experimental investigation on the behavior of single and built-up cold-formed steel columns at both ambient and simulated fire conditions considering the effect of restraint to thermal elongation. The buckling behavior, ultimate loads and failure modes, of different types of CFS columns at both ambient and simulated fire conditions with restraint to thermal elongation, are presented and compared. Regarding the buckling tests at ambient temperature it was observed that the use of built-up cross-sections ensures significantly higher values of buckling loads. Especially for the built-up cross-sections the failure modes were characterized by the interaction of individual buckling modes, namely flexural about the minor axis, distortional and local buckling. Regarding the fire tests, it is clear that the same levels of restraint used in the experimental investigation induce different rates in the generated restraining forces due to thermal elongation of the columns. Another conclusion that can be drawn from the results is that by increasing the level of restraint to thermal elongation the failure of the columns is controlled by the generated restraining forces, whereas for lower levels of restraint the temperature plays a more important role. Hence, higher levels of imposed restraint to thermal elongation will lead to higher values of generated restraining forces and eventually to lower values of critical temperature and time.

scholarly journals Hydrodynamic Interactions between Bracket and Propeller of Podded Propulsor Based on Particle Image Velocimetry Test

Water ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1142
Author(s):  
Dagang Zhao ◽  
Chunyu Guo ◽  
Tiecheng Wu ◽  
Wei Wang ◽  
Xunbin Yin
Keyword(s):  
Particle Image Velocimetry ◽  
Flow Field ◽  
Working Conditions ◽  
Cross Sections ◽  
Particle Image ◽  
Podded Propulsor ◽  
Image Velocimetry ◽  
Theoretical Significance ◽  
Practical Engineering ◽  
Flow Field Characteristics

In this study, particle image velocimetry was used to measure the fine flow-field characteristics of an L-type podded propulsor in various working conditions. The flow-field details at different cross-sections between the propeller and the inclined bracket were compared and analyzed, allowing for more intuitive comparison of the flow-field characteristics of L-type podded propulsors. The interference mechanisms among the propeller, pod, and bracket of the L-type podded propulsors at different advance coefficients, deflection angles, and deflection directions were investigated in depth. The results of this study can serve as reference material and provide technical support for the design and practical shipbuilding application of L-type podded propulsors. Therefore, the results have theoretical significance and practical engineering value.

Influence of Crack on the Instability of GFRP Composite Cylindrical Shells under Combined Loading

2018 ◽  
Vol 877 ◽  
pp. 453-459
Author(s):  
B. Angelina Catherine ◽  
R.S. Priyadarsini
Keyword(s):  
Structural Integrity ◽  
Cylindrical Shells ◽  
Laminated Composite ◽  
External Pressure ◽  
Industrial Applications ◽  
Combined Loading ◽  
Finite Element Software ◽  
Buckling Behavior ◽  
Thin Walled ◽  
Composite Cylindrical Shells

Buckling is a prominent condition of instability caused to a shell structure as a result of axial loadings. The process of buckling becomes more complex while analyzing thin walled structures like shells. Today such thin walled laminated composite shells are gaining more importance in many defense and industrial applications since they have greater structural efficiency and performance in relation to isotropic structures. Comprehensive understanding of the buckling response of shell structures is necessary to assure the integrity of these shells during their service life. The presence of defects, such as cracks, may severely compromise their buckling behavior and jeopardize the structural integrity. This work aims in conducting numerical analysis of cracked GFRP (Glass fibre-reinforced polymer) composite cylindrical shells under combined loading to study the effect of crack size on the buckling behavior of laminated composite cylindrical shells with different lay-up sequences. The numerical analyses were carried out using the finite element software, ABAQUS in order to predict the buckling behaviour of cracked laminated composite cylinders subject to different combinations of axial compression, torsion, internal pressure and external pressure from the interaction buckling curves.

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