Ring-stiffened Cylindrical Shells Research Articles

Implosion mechanisms of underwater ring-stiffened metallic cylindrical shells

Underwater cylindrical shells are prone to implosion due to the surrounding high hydrostatic pressure, and introducing ring-rib is a promising approach to reduce the risk. However, the influences of the ring-rib on the deformation mode and the fluid-structure interaction mechanism are still unclear. This paper investigates the dynamic response of ring-stiffened cylindrical shells during the implosion process. The finite element model is firstly established and the numerical simulation is verified by the existing experiment. Then, the numerical method is used to simulate the implosion of ring-stiffened cylindrical shells with various geometrical parameters. The fluid motion, induced pressure and deformation features are investigated and the relationship between them is clarified. Finally, pure and ring-stiffened cylindrical shell implosions are compared and parametric analyses are performed by varying the number and thickness of ring-ribs. Results show that ring-stiffened cylindrical shells with higher collapse resistance deform asymmetrically and the flow field response changes depending on the deformation mode. Introduction of ring-ribs can significantly increase the critical pressure and reduce the percentage of induced pressure. As the number and thickness of ribs increased, the critical and peak implosion pressures of the ring-stiffened cylindrical shells increased by 153% and 146%, respectively.

Deformation characteristics of a ring-stiffened cylindrical shell induced by shock waves and coalesced bubbles in double-charge underwater explosions

This study investigates the deformation characteristics of a ring-stiffened cylindrical shell induced by shock waves and coalesced bubbles in double-charge underwater explosions. A numerical model for coupling underwater multi-point explosion loads with the cylindrical shell is established by the Arbitrary Lagrange Euler method, and underwater explosion experiments with double charges are also conducted. The numerical model's effectiveness is validated by comparing shock wave superposition characteristics, bubble coalescence processes, and bubble pulsation periods with the experimental results. Based on the numerical model, the influences of detonation intervals and layout angles of charge on shock wave superposition effects, temporal and spatial distribution characteristics of shock waves, and the evolution process of coalesced bubbles in underwater explosions with double charges are explored. Additionally, the deformation characteristics of cylindrical shells induced by shock waves and coalesced bubbles for double charges with different detonation intervals and layout angles of charge are analyzed. The results indicate that double charges can induce more substantial deformation on the cylindrical shell at a specific detonation interval than a single charge with equal total mass. During the shock wave phase, the cylindrical shell's deformation decreases nonlinearly with an increased layout angle. Conversely, during the bubble load phase, the deformation of the cylindrical shell shows an approximately linear decrease with an increase in layout angle. A critical angle exists, below which the impact of double charges on the cylindrical shell is more substantial when detonated with an interval than simultaneous detonation.

Buckling and strength failure for unstiffened and ring-stiffened composite shells

An experimental method was applied to study the buckling pressure and failure strength for the unstiffened and ring-stiffened fiber reinforced composite cylindrical shells under the external hydrostatic pressure. Both the strain and pressure data are collected and discussed. The FE simulation models are also analyzed as comparison to investigate the relation among the critical buckling pressure, failure strength and the final structure failure strength. The results indicate that the ring-stiffened structure can improve the buckling pressure more significantly than increasing the failure pressure. The experimental burst pressure of the ring-stiffened cylindrical shell is increased by 23.2%. The buckling mode is changed and the buckling behavior can be improved and eliminated by the ring-stiffened structure before the cylinder bursts under the hydrostatic pressure load.

Influence of allowable stress on structural design of ring-stiffened cylindrical shells

Influence of allowable stress on structural design of ring-stiffened cylindrical shells

Analysis of residual stresses and distortions of a titanium alloy ring-stiffened cylindrical shell

Abstract Ring-stiffened cylindrical shell is the main pressure structure of underwater carrier equipment, and the residual stress and deformation introduced by welding of ring-ribbed frame and cylinder body pose a great threat to the performance and safety of the structure. In this paper, finite element software is used to numerically simulate the residual stress and deformation caused by fillet welding. The influence of welding position, constraint tooling and post-weld heat treatment PWHT on the residual stress and deformation is analyzed systematically. The results show that the gravity has little effect on the welding residual stress and deformation, but it has a significant impact on deformation uniformity. Under the action of restraint, the welding distortion is effectively controlled, but it will lead to the increase of the overall stress level of the structure simultaneously. Heat treatment can dramatically diminish the welding residual stress at the expense of deformation, which may result in structural maladjustment.

Effect prediction of stiffened-ring cylindrical shells subjected to drop mass impact

This study focuses on the effect of lateral mass impact on ring-stiffened thin-walled cylindrical shell. Cylindrical shells were fabricated to validate the numerical modeling and analytical techniques, and drop tests were performed using a rigid spherical indenter. Next, stiffened-ring cylindrical shells with various structural size parameters were simulated using ABAQUS software. The relationships between the impact force, deformation displacement, and rebound velocity were established, on the basis of impact mechanics theory and simulation results. It derived fitting functions to analyse the relationship between the maximum load and maximum displacement of ring-stiffened cylindrical shell under dynamic mass impact. Based on the validation of the simulation model, the fitting function data were compared with the simulation results, and the functions showed a good accuracy. Besides, the parameters, mass ratio and stiffened-ring mass ratio were used to reflect the effect of the mass change in the ring-stiffened cylindrical shell. Furthermore, parametric studies on ring-stiffened cylindrical shell models were conducted to analyse the progressive impact responses.

Buckling of ring-stiffened cylindrical shell under axial compression: Experiment and numerical simulation

Tanks and silos are often designed as ring-stiffened cylindrical shells. Nowadays, the load-increasing effect of closely spaced ring stiffeners under axial compression has received limited attention in research and practice. Considering the structural safety, the ring-stiffened shell needs to be estimated on the conservative side in practice. This is not desirable in terms of modern lightweight steel structures. However, material efficiency is achieved by combining thin plates with ring-stiffeners. In this paper, small specimen experimental series are carried out to calibrate numerical models, which are subsequently used in parameter studies, because the large-scale experiments are cost-intensive and therefore difficult to carry out in the laboratory. The small cylindrical shells are manufactured by welding of two half-cylindrical shells and the ring stiffeners are spot-welded to the cylindrical shell. Geometric dimension of shell specimens is measured by 3D scanning technology. The measured geometric imperfection information is directly imported into the numerical model based on a mapping relationship and the buckling tests are recalculated by means of geometrically and materially nonlinear analysis with imperfection. The results indicate that the buckling resistance calculated by the Finite Element analysis is very close to that of the test results. The initial geometric imperfection is discussed with reference to the Eurocodes design standard. Furthermore, influence of the ring-stiffener parameter, including imperfection amplitude, radius over thickness ratio, geometry of ring stiffener etc., on the buckling load and knockdown factor is discussed based on a large number of parameter study.

A semi-analytical method for vibro-acoustic analysis of submerged ring-stiffened cylindrical shells coupled with arbitrary inner structures

A semi-analytical method is developed for vibration and acoustic analysis of a submerged ring-stiffened cylindrical shell coupled with arbitrary inner structures. The whole structure is firstly disassembled into the stiffened cylindrical shell and inner structures, which are respectively analyzed through analytical substructure method and numerical approach. For the analytical substructure method, the cylindrical shell is decomposed into several shell segments according to positions of stiffeners and external forces, including exciting forces and coupling forces. These shell segments are described by Flügge shell theory and the ribs are governed by the annular plate equations. The solutions for cylindrical shell segments and rings are expanded as wave functions and Bessel functions. For the inner structures with arbitrary irregular shapes, finite element method (FEM) is utilized to establish their motion equations. At each coupling node, an artificial spring is adopted to connect the shell and inner structures, so rigid and elastic coupling conditions can be easily simulated by setting different stiffenesses to these springs. For external fluid field, an axisymmetric boundary element method (BEM) is employed to calculate the acoustic pressure. Combining the displacement continuity and force balance conditions at the joints of adjacent shell segments and introducing the coupling forces derived from inner structures and the fluid loading, the vibro-acoustic equations of the coupled system are obtained. To verify the validity of the present approach, vibro-acoustic responses of the semi-analytical method are compared with the ones calculated through FEM/BEM. Furthermore, effects of the coupling stiffness between the shell and inner structures and external fluid loading on vibro-acoustic responses are also evaluated.

Donaldson Co Inc, USA

A semi-analytical method is developed for vibration and acoustic analysis of a submerged ring-stiffened cylindrical shell coupled with arbitrary inner structures. The whole structure is firstly disassembled into the stiffened cylindrical shell and inner structures, which are respectively analyzed through analytical substructure method and numerical approach. For the analytical substructure method, the cylindrical shell is decomposed into several shell segments according to positions of stiffeners and external forces, including exciting forces and coupling forces. These shell segments are described by Flügge shell theory and the ribs are governed by the annular plate equations. The solutions for cylindrical shell segments and rings are expanded as wave functions and Bessel functions. For the inner structures with arbitrary irregular shapes, finite element method (FEM) is utilized to establish their motion equations. At each coupling node, an artificial spring is adopted to connect the shell and inner structures, so rigid and elastic coupling conditions can be easily simulated by setting different stiffenesses to these springs. For external fluid field, an axisymmetric boundary element method (BEM) is employed to calculate the acoustic pressure. Combining the displacement continuity and force balance conditions at the joints of adjacent shell segments and introducing the coupling forces derived from inner structures and the fluid loading, the vibro-acoustic equations of the coupled system are obtained. To verify the validity of the present approach, vibro-acoustic responses of the semi-analytical method are compared with the ones calculated through FEM/BEM. Furthermore, effects of the coupling stiffness between the shell and inner structures and external fluid loading on vibro-acoustic responses are also evaluated.

Estimation of ultimate strength of ring-stiffened cylindrical shells under external pressure with local shell buckling or torsional buckling of stiffeners

This study discusses the ultimate strength and collapse behavior of ring-stiffened cylindrical shells under external pressure with local shell buckling or torsional buckling of stiffeners. In past studies, the effect of initial deflection shape on the ultimate strength has not been completely elucidated. Additionally, a clarification of the collapse behavior and theoretical formulation based on it has not yet been reached. Therefore, in this study, the influence of the initial deflection shape is investigated using eigenmodes obtained from the elastic buckling eigenvalue analysis and the hungry-horse mode described by a simple equation. Then, the ultimate strength analyses of 432 models of ring-stiffened cylindrical shells with various dimensions are carried out using the nonlinear finite element method. From the analysis, the collapse modes are classified into five categories, namely, the shell buckling (SB) collapse (localized mode SB-1 and uniform deformation mode SB-2), the torsional buckling (TB) collapse (localized mode TB-1 and uniform deformation mode TB-2), and the combined shell-torsional buckling collapse. A new slenderness ratio is proposed using the formula for strength when the circumferential stress reaches yield stress, and the formula for the elastic buckling strength developed previously by the authors. Then, theoretical formulas for the ultimate strength are developed using the slenderness ratio, which can rationally estimate the strength.

A semi-analytical analysis of strength and critical buckling behavior of underwater ring-stiffened cylindrical shells

In this paper, strength and buckling behavior analysis of a ring-stiffened cylindrical shell for the sightseeing submersible subjected to mechanical and thermal loads are studied. Based on the Donnell’s assumption and classical shell theory, the governing equations of strength analysis for the ring-stiffened cylindrical shell are established, and the problems are solved by finite difference method (FDM) and Newmark-β method. Meanwhile, the governing equations of buckling behavior for the ring-stiffened cylindrical shell are set up in view of the energy method, which are resolved by the Ritz method. The research shows that the external load has the most significant influence on the strength of ring-stiffened cylindrical shell. Moreover, compared with other factors, the external load has a great influence on its strength, and the effect of shell thickness on the buckling load of ring-stiffened cylindrical shell is most obvious. The research work can provide theoretical basis for the design and optimizing of underwater equipment such as tourist submarines.

Study on the Coupling Frequency of Double-Sided Submerged Ring-Stiffened Cylindrical Shells

Based on the Flügge theory and orthotropic theory, the acoustic vibration coupling model of ring-stiffened cylindrical shell is established by using the wave propagation method and virtual source method. And the effects of water immersion on both sides, free surface, and hydrostatic pressure on the cylindrical shell are considered in the coupling model. Muller three-point iterative method is used to solve the coupling frequency. The calculation results of degradation theory are compared with COMSOL’s calculation results and experimental results, respectively, which verifies the reliability of the theoretical method. Finally, the influence of fluid load, ring rib parameters, boundary conditions, hydrostatic pressure, and free surface on the coupled vibration of ring-stiffened cylindrical shell is analyzed by an example.

Acoustic radiation efficiency of a submerged periodic ring-stiffened cylindrical shell with finite vibration loading

The acoustic radiation efficiency of a cylindrical shell is an important parameter in estimating the sound radiation emitted by a structure. However, many of the relevant previous studies have approached acoustic radiation problem by employing numerical methods, requiring large computational resources. In this study, an analytical method is developed to calculate the acoustic radiation efficiency of a finite-length, submerged, periodically stiffened cylindrical shell excited by a radial line force. Using the Flügge shell equations and Helmholtz equation, the motions of the shell wall and the acoustic pressure field in the outer fluid can be expressed analytically. Furthermore, to investigate the effects of finite length on the acoustic radiation efficiency, a stiffened cylindrical shell of infinite length is assumed to have a finite-length vibration distribution and to be constrained by simply supported boundary conditions. Numerical simulations are performed to investigate the acoustic radiation efficiency’s dependency on the finite-length vibration and the presence of stiffeners.

Optimisation of the design of a steel-welded pressure hull structure based on interactive nonlinear collapse strength analyses

ABSTRACT In this study, the genetic algorithm (GA) was implemented for the multi-objective optimization of the structural design of a pressure hull. The objective functions sought the maximum ultimate strength of the ring-stiffened cylindrical shell structure with minimum structural weight and maximum volume of the configured structural member. First, the evaluation models of several design variables of submarine structures were studied. Subsequently, a multi-objective GA algorithm was introduced. To improve the quality of the new population, several design constraints are applied. The final candidate structures were recomputed by non-linear finite element analysis (FEA) to observe the failure modes and compared with the initial design model. The results suggest that a lightweight construction would be achieved when a material with higher strength is used, especially for greater design depths

Influence of the Position of Artificial Boundary on Computation Accuracy of Conjugated Infinite Element for a Finite Length Cylindrical Shell

Structural finite element coupled with the conjugated infinite element method is an efficient numerical technique for solving the acoustic radiation problem due to the vibration of underwater objects. However, for large complex structures, the total acoustic mesh would become very large if the artificial boundary is too far away from the structural wetted surface. Thus, the calculation time can become too long to confine the application of the conjugated infinite element method. On the other hand, if the artificial boundary is close to the structural wetted surface, it will lead to computation accuracy losing due to the near-field effects. Consequently, it is essential to present some guidelines based on the physical mechanism of structural acoustics to choose a suitable artificial boundary that optimizes calculation accuracy and efficiency. In present work, the evanescent wave theory of an infinite length cylindrical shell is adopted to theoretically analyze the decay characteristic of evanescent waves in near field. Then, the effect of the position of artificial boundary on computation accuracy of conjugated infinite element for a finite length ring-stiffened cylindrical shell is numerically investigated. Results suggested that for the cylindrical shell mentioned in this study, the artificial boundary can be placed at least 0.4 times the acoustic wavelength away from the structural wetted surface. What’s more, for high frequencies or large-scale structures, the required non-dimensional distance between the artificial boundary and the structural wetted surface increases.

Vibro-acoustic analysis of submerged ring-stiffened cylindrical shells based on a symplectic wave-based method

A symplectic wave-based method is applied to the vibro-acoustic problems of submerged ring-stiffened cylindrical shells, accounting for the effects of hydrostatic pressure and acoustic-structure interaction. The symplectic wave-based method combines the symplectic state space theory with the traditional wave propagation approach, and shows the characteristics of high precision and high numerical stability. However, this method is only applied to the vibration analysis of relatively simple and geometrically regular structures before. In this paper, the method is extended to the acoustic vibration analysis of general ring-stiffened cylindrical shells, in which numerical integration strategies are adopted to deal with unknown acoustic-structure coupling terms, finally a complete coupled vibro-acoustic analysis is realized. A further quantitative investigation clearly reveals the effects of hydrostatic pressure on the vibration and acoustic responses. Compared with the existing methods, the present method shows better convergence and accuracy properties, especially when the stiffening rings are dense. It is also shown that hydrostatic pressure cannot be ignored in the acoustic radiation analysis if the low-frequency near-field acoustic pressure is concerned, otherwise, it can be ignored.

Elastic local shell and stiffener-tripping buckling strength of ring-stiffened cylindrical shells under external pressure

Abstract Ring-stiffened cylindrical shells are often used in offshore and submergible structures, it is important for the structural safety to estimate the buckling strength of those under extremely high water pressure. Although the buckling strength can be accurately calculated using the finite element analysis (FEA), the estimation by more easy way is required at an initial stage of the structural design. This paper proposes two formulas for the local shell and stiffener-tripping buckling strength of the ring-stiffened cylindrical shells under external pressure. One can estimate the tripping buckling strength only and is derived assuming the tripping buckling as buckling of only the flange-beam supported by springs and considering effects of the cylindrical shape and torsional stiffness which are not included in a conventional formula. The other can estimate both the shell and tripping buckling strength and is considered interaction of buckling deflection between a cylindrical shell and ring-stiffeners and influence of stresses acting on the web which are not included in conventional formulas. Based on the principle of minimum potential energy, the formula is derived using the functions to express the buckling deformation in the cylindrical shell and ring-stiffeners. The buckling strength estimated by the two proposed formulas is compared with that by existing conventional formulas and the finite element analysis, and this study discusses the influence of new considerations on the shell and tripping buckling strength. From the results, it is found that the second formula can deal with any buckling mode and has greatly high accuracy compared with other conventional formulas.

Acoustic scattering from a stiffened finite cylindrical shell with external rings

Studying the interaction of sound with cylindrical shells immersed in water is essential and helpful to improving underwater target detection and classification algorithms. Elastic cylindrical shells often occur as part of double-layered shell and have been widely used in marine and aerospace area. Acoustic waves are easy to be transmitted through the outer shell to the interior especially at low frequencies, thus directly being scattered by the inner shell and the rings in water between double-layered shells. Therefore, the externally ring-stiffened cylindrical shell is investigated in this paper. An experiment was conducted that measured the acoustic scattering. A hybrid 2-D/3-D finite-element modelling technique is employed to numerically calculate the scattering characteristics. Good qualitative agreement is found between numerical calculations and experimental measurement. An approximate analytical expression is given explicitly to identify the Bragg wave trajectories in the frequency-angle spectrum. It also has been shown that the rings not only affect the dynamic response of shell and indirectly influence the exterior scattered field, but also become direct acoustic scatterers in water and increase the target cross section especially at oblique incidence.

Experiment and modeling of vibro-acoustic response of a stiffened submerged cylindrical shell with force and acoustic excitation

Abstract Taken a submerged ring-stiffened cylindrical shell as an experimental model, the experimental studies was investigated to study the effects of force and acoustic excitation on the vibro-acoustic response of the cylindrical shell. A precise transfer matrix method (PTMM) was presented to compare the shell vibration and sound radiation of the submerged stiffened cylindrical shell with the experimental results. The result shows that results from PTMM are in good agreement with the experimental results. It shows that the PTMM is reliable and the result from PTMM is credible. The vibration acceleration response of the water case has less peak numbers and the value is less than that of the air case. The peak value of sound pressure in the force excitation case is relate to structural natural frequency. The peak value of sound pressure in the acoustic excitation case is relate to structural natural frequency and internal cavity natural frequency.

A Mixed Analytical-Numerical Method for the Vibro-Acoustic Analysis of an Underwater Ring-Stiffened Cylindrical Shell Containing Substructures

A new sono-elastic substructure method is proposed in this paper to improve the computational efficiency of the hull-substructure coupled and fluid-structure interacted vibration and acoustic radiation of a submerged cylindrical-shell-type vehicle. The typical part of the vehicle structure is divided into the main hull and the internal substructures. The fluid-structure interaction problem of the main hull is solved by an analytical method based on the simplified model of a single-hull ring-stiffened cylindrical shell simply supported at both ends. Meanwhile, the substructures are numerically modeled through the Finite Element Method, with the condensed dynamic stiffness matrices of them obtained via the Superelement Method of Modal Synthesis. The main hull and the internal substructures are then integrated according to the boundary compatibility conditions at the connecting parts. Thus, a Mixed Analytical-Numerical Substructure (MANS) method is formulated. The applicability of this method is validated by two numerical examples as well as the test results of a large-scale submerged structural model. It is shown that the MANS method is suitable for the prediction of vibration and acoustic radiation of typical cylindrical-shell-type submerged structures in the medium frequency region.