Ring-stiffened Conical Shells Research Articles

Numerical modeling and analysis of fluid-filled truncated conical shells with ring stiffeners

This study uses a hybrid finite element method to predict dynamic behavior of truncated conical shells with ring stiffeners under fluid loading. The proposed approach combines classical shell theory and the finite element method, making use of displacement functions derived from exact solutions of Sanders’ shell equilibrium equations for conical shells. The analysis of the shell-fluid interface involves leveraging the velocity potential, Bernoulli’s equation, and impermeability conditions to determine an explicit expression for fluid pressure. To the best of our knowledge, this paper is the first to compare the methods applied to ring-stiffened shells against other numerical and experimental findings. Our results on conical shells in various conditions, with and without ring stiffeners, are largely consistent with previous findings. This study also explores the influence of geometric parameters, stiffener quantity, cone angle, and applied boundary conditions on the natural frequency of fluid-loaded ring-stiffened conical shells. The paper concludes with a discussion of several useful implications for further research.

Analysis of Viscoelastic Damping Effect on the Underwater Acoustic Radiation of a Ring-Stiffened Conical Shell

Hydroacoustic radiation from submarine power compartments has been the focus of research for many years. In this work, a ring-stiffened conical shell with bases is employed as the target model. The self-factors of viscoelastic damping, such as the damping thickness and damping location, are selected to study their effect on the underwater acoustic radiation, which will give a better understanding of the optimal scheme for applying damping. Firstly, based on a combination of finite element method (FEM) and boundary element method (BEM), the underwater vibration and acoustic radiation of the whole structure are analyzed. Secondly, taking a clamped-free sandwich beam as an example, through comparison with the published numerical data, the present damping application method and mesh density are verified. Finally, the influence of viscoelastic damping parameters on acoustic radiation is studied. The results show that the viscoelastic damping thickness has a significant influence on the amplitude of radiated noise but does not change the distribution of the acoustic field. Furthermore, the damping on the web may achieve the best vibration damping effect in this work.

Structure-Acoustic Coupling Analysis of Vibration and Underwater Acoustic Radiation of a Ring-Stiffened Conical Shell

The underwater acoustic radiation of the submarine power cabin has recently become a hot topic in the industry and also in the academia. In this article, the vibration and underwater acoustic radiation of a ring-stiffened conical shell with bases are investigated numerically by means of the combination of the finite element method and boundary element method. The acoustic radiation field is obtained by the traditional acoustic field model and ISO acoustic field model, respectively. A series of numerical examples are given, and the results are compared. Besides, the sound pressure at different positions with frequency is further studied. It is shown that the sound radiated by the structure mainly propagates to the side directions of the shell and propagates relatively less to the front side and the rear side.

Experimental study on ultimate strength of steel-welded ring-stiffened conical shell under external hydrostatic pressure

This paper reports experimental and numerical investigations on the ultimate strength responses of steel-welded, ring-stiffened conical shells when subjected to external hydrostatic pressure. Four small-scale shell models were fabricated from general structural steel by cold bending and arc welding. First, hydrostatic pressure tests were performed to investigate the collapse behaviour of the models. The influences of different parameters were also studied experimentally. Before the experiments, quasi-static tensile tests were performed to obtain detailed characterisation of the test model material. In addition, the initial imperfection of the shell and other as-built geometry parameters were carefully measured. The test was conducted using compressed water in a small-sized chamber and loaded to collapse. Three models with heavy stiffeners were failed by local buckling at the shell between the ring frames. Another model failed by the overall buckling of the adjacent frames together with the shell. The numerical computations were performed on the finite element code of ABAQUS FEA. The imperfection due to fabrication, such as initial out-of-circularity, and residual stresses due to welding are simulated. The quasi-static response was compared with the experimental load and plastic deformation curves. The numerical results revealed a close agreement between the collapse pressure prediction and failure modes of the simulation and the experiment.

Free and forced vibration of submerged ring-stiffened conical shells with arbitrary boundary conditions

An analytic approach is presented to analyze free and forced vibration of submerged ring-stiffened conical shell with arbitrary boundary conditions at low frequencies. According to the junctions of shell-stiffener, the shell is firstly divided into multiple substructures, e.g. conical segments and stiffeners. To take into account fluid loading, conical segments are divided into more narrow strips and those strips are approximately considered as local cylindrical shells. Then, Flügge theory is used to describe the motion of conical strips and displacement functions are expressed as power series. Instead of utilizing smeared out method, ring stiffeners are treated as discrete members and the equations of motion of annular plate, rather than curve beam, are adopted to describe the motion of stiffeners with rectangular cross-section. Lastly, boundary conditions and continuity conditions of adjacent substructures are used to assemble the final governing equation. Comparisons of free and forced vibration results of present method and those in literature and/or calculated by finite element method show the validity of present method. The effects of boundary conditions, ring stiffeners and fluid loading on free vibration are studied. The effects of external point force and fluid loading on forced vibration are also discussed.

Dynamic instability of ring-stiffened conical thin-walled rocket fairing in supersonic gas stream

The assumed-modes method is applied to obtain the dynamical model of the ring-stiffened conical shells in a supersonic gas stream. The pressure acting on the shell is described by the piston theory. The displacements of the rings are functions of the shell displacements. The kinetic and the potential energies of the structure are obtained as the functions of the shell displacements. It is suggested the approach to calculate the shell spatial mode, when the shell dynamic stability is lost. The free vibrations of the structures with different numbers of the rings are analyzed. The loss of the structure dynamic stability is investigated.

Free Vibration of a Fluid Loaded Ring-Stiffened Conical Shell With Variable Thickness

An analytical method is presented for the free vibration of a fluid loaded (submerged) ring-stiffened conical shell with variable thickness in the low frequency range. Based on the Flügge theory and equivalent method of ring-stiffeners, the governing equations of vibration of a ring-stiffened conical shell are developed in the form of a coupled set of the first order differential equations. Fluid loading is taken into account by dividing the shell into narrow strips which are considered to be locally cylindrical. Analytical solutions are presented by using the transfer matrix method, which is suitable for structures broken into a sequence of subsystems that interact only with adjacent subsystems. By comparing the results from the present method and the finite element model, good agreement are obtained. The effects of the spacing of the stiffeners, the shell thickness, the shell thickness ratio, the ring's height, and the boundary conditions on the natural frequencies of the fluid loaded ring-stiffened conical shell with variable thickness are discussed.

A semi-analytical method of free vibration of fluid loaded ring-stiffened stepped conical shell

The motion differential equation of fluid loaded ring-stiffened stepped conical shell is derived by using Flügge classical thin shell theory and equivalent method of ring stiffeners, in which force and moment of a ring stiffener is apportioned in the spacing. In the analysis, the conical shell is divided into many narrow cylindrical strips, the fluid loading of which are available, to consider fluid loading of conical shell approximately. The semi-analytical solution in terms of power series to the equation is then obtained. The free vibration frequencies of a ring-stiffened stepped conical shell in air and in water are respectively solved using the proposed method. The results are compared with the ones obtained from the finite element software ANSYS and they are well agreed.

Non-linear general instability of ring-stiffened conical shells under external hydrostatic pressure

The paper presents the experimental results for 15 ring-stiffened circular steel conical shells, which failed by non-linear general instability. The results of these investigations were compared with various theoretical analyses, including an ANSYS eigen buckling analysis and another ANSYS analysis; which involved a step-by-step method until collapse; where both material & geometrical nonlinearity were considered. The investigation also involved an analysis using BS5500 (PD 5500), together with the method of Ross of the University of Portsmouth. The ANSYS eigen buckling analysis tended to overestimate the predicted buckling pressures; whereas the ANSYS nonlinear results compared favourably with the experimental results. The PD5500 analysis was very time consuming and tended to grossly underestimate the experimental buckling pressures and in some cases, overestimate them. In contrast to PD5500 & ANSYS, the design charts of Ross of the University of Portsmouth were the easiest of all these methods to use and generally only slightly underestimated the experimental collapse pressures. The ANSYS analyses gave some excellent graphical displays.

Plastic General Instability of Ring-Stiffened Conical Shells under External Pressure

The paper describes experimental tests carried out on three ring-stiffened circular conical shells that suffered plastic general instability under uniform external pressure. The cones were carefully machined from EN1A mild steel to a very high degree of precision. The end diameters of the cones, together with their thicknesses were the same, but the size of their ring stiffeners was different for each of the three vessels. In the general instability mode of collapse, the entire ring-shell combination buckles bodily in its flank. The paper also provides three design charts using the results obtained from these three vessels, together with the results obtained for twelve other vessels from other tests. All 15 vessels failed by general instability. One of these design charts was based on conical shell theory and two of the design charts were based on the general instability of ring-stiffened circular cylindrical shells, using Kendrick’s theory, which were made equivalent to ring-stiffened circular conical shells suffering from general instability under uniform external pressure. The design charts allowed the possibility of obtaining plastic knockdown factors, so that the theoretical elastic buckling pressures, for perfect vessels, could be divided by the appropriate plastic knockdown factor, to give the predicted buckling pressure. The theoretical work is based on the solutions of Kendrick, together with the finite element program of Ross, namely RCONEBUR and the commercial finite element package ANSYS. This method can also be used for the design of full-scale vessels.

Cost Minimization of a Ring-Stiffened Conical Shell Loaded by External Pressure

A ring-stiffened slightly conical shell is optimized for external pressure according to the design rules of Det Norske Veritas. The whole length and the different two end radii are given. The shell is divided into n equidistant segments with one stiffener in each segment. Each segment has a different shell thickness determined using a buckling constraint, and each ring-stiffener of welded square box section is designed by means of the required moment of inertia. The optimal number of shell segments (nopt) is determined by means of costs calculated for a series of n. The cost function includes the material, fabrication and painting costs. The shell normal stresses are determined also by finite element method.

Design charts for the general instability of ring-stiffened conical shells under external hydrostatic pressure

The paper describes experimental tests carried out on three ring-stiffened circular conical shells that suffered plastic general instability under uniform external hydrostatic pressure. In this mode of failure, the entire ring–shell combination buckles bodily in its flank. The cones were carefully machined from EN1A mild steel to a very high degree of precision. Using the results obtained from these three vessels, together with the results obtained from elsewhere, the paper also provides two-design charts, which are much easier to use than older design charts. The design charts allow the possibility of obtaining a plastic knockdown factor, so that the theoretical elastic buckling pressures for perfect vessels, can be divided by the plastic knockdown factor, to give the predicted buckling pressures. Although similar design charts have been produced in the past, the design charts presented here are based on using the simpler ring-stiffened circular cylinder, which has been made equivalent to the much more complex ring-stiffened circular conical shell. The advantage of using this method is that it is simpler and the design time is reduced by a factor of about 10 with little loss of precision. This method can also be used for the design of full-scale vessels.

Plastic buckling of ring-stiffened conical shells under external hydrostatic pressure

The paper describes experimental tests carried out on three ring-stiffened cones that were tested to destruction under external hydrostatic pressure. The cones were carefully machined from EN1A Steel. All three cones failed by plastic non-symmetric bifurcation buckling in a mode commonly known as general instability. In this mode the entire ring-shell combination buckles bodily. The paper also provides a design chart using the results obtained from these three vessels, together with the results of six other vessels obtained from other tests. The design chart allows the possibility of obtaining a plastic knock down factor, so that the theoretical buckling pressures, based on elastic theory, can be divided by the plastic knockdown factor, to give the predicted buckling pressure. This method can also be used for the design of full-scale vessels.

The Vibration of Ring-Stiffened Cones Under External Water Pressure

This paper describes a theoretical and an experimental investigation into the vibration of three ring-stiffened thin-walled conical shells, under external water pressure. The theoretical investigation was via the finite element method for both the shell structure and the surrounding water. Various fluid meshes were chosen, and a relatively simple one showed good agreement between experiment and theory.

Effects of ring reinforcement on the pulsed-load stability of a conical shell

Ring-stiffened conical shells are considered. It is assumed that the sections between the ribs represent medium-length shells. It is found that such reinforcement does not raise the critical pressure pulse but may actually reduce it.

Buckling experiments on stiffened cast-epoxy conical shells

This paper describes a casting technique for fabricating high-quality plastic structural models and presents results on the use of such specimens to parametrically study the effect of base-ring stiffness on the critical buckling pressure of a ring-stiffened conical shell. The fabrication technique involves machining a metal mold to the desired configuration and vacuum drawing the plastic material into the mold. A room-temperature-curing translucent thermoset epoxy was the casting material selected. The casting technique allows many high-quality specimens to be produced and each specimen is capable of being repeatedly tested without failure. The conical shell was modified for successive tests by machining the epoxy base-ring configuration to reduce its stiffness. A shell-of-revolution computer program which uses a nonlinear axisymmetric prebuckling strain field to obtain a bifurcation-buckling solution was used to guide the selection of configurations tested. The shell experimentally exhibited asymmetric collapse behavior and the ultimate load was considerably higher than the analyticalbifurcation prediction. The asymmetric buckling-mode shape, however, initially appeared at a pressure near the analysis-bifurcation solution. Comparison of experimental and analytical prebuckling strains at pressure magnitudes below the initiation of asymmetric collapse showed good agreement.

Experimental studies on buckling of ring-stiffened conical shells under axial compression

The buckling of integrally external ringstiffened conical shells under axial compression was investigated experimentally. Experimental results were compared with theory to find the effect of the stiffener parameters (e 2 /h), (A 2 /a 0 h) and (I 22 /a 0 h 3 ) as well as of shell geometry. Agreement between classical linear theory and experiments was found to be governed primarily by the area parameter (A 2 /a 0 h), and correlation with theory was significantly affected in the range 0.1<(A 2 /a 0 h)<0.5 of that parameter. Beyond this region there is practically no improvement with increase in ring area, whereas the weight of the shell continues to increase linearly.

Structural dynamics aspects of the Gemini program.

The Gemini Program has proceeded well into its flight phase. This advanced state of development permits a review of the adequacy of the structural dynamics analyses and tests performed. The areas covered include: 1) environmental prediction techniques based on flight data combined with wind-tunnel oscillatory pressure data, trajectory information, and ground test data; 2) the tests of individual components, modules, and ultimately the entire spacecraft to these environments; 3) the response of ring-stiffened conical shell structure to a nonuniform aerodynamic forcing function, based on ground vibration tests and wind-tunnel data with pressure correlation; 4) docking system development by analysis and |-scale model testing utilizing a zero spring rate support for six-degree-of-freedom motion; 5) stability of moored vehicles under thrust; 6) pyrotechnic shock transmitted through structure for separation devices; and 7) flutter. Where applicable, the analyses are compared with ground test results and available flight data.

Free vibrations of ring-stiffened conical shells

Linear shell theory was used to develop an analysis for predicting the natural frequencies of ring-stiffened simply supported conical shells. An experimental investigation was performed in conjunction with this analysis. In the analysis, the longitudinal, circumferential, and rotatory inertia forces were assumed to be small in comparison with the radial inertia force. The previous assumption simplified the uncoupling of the equilibrium equations. A linear Donnell-type vibration equation was obtained for orthotropic conical shells. By finding an equivalent orthotropic shell, the free vibration characteristics of a ring-stiffened conical shell were determined. Application of the Galerkin method reduced the shell equations to the form of frequency determinant. Digital computer techniques were used to solve the resulting frequency determinant.

Buckling of Orthotropic Conical Shells under External Pressure

SummaryDonnell type stability equations for thin circular orthotropic conical shells are presented and solved for external pressure loading. The solution is likewise applied to stiffened conical shells by consideration of equivalent orthotropic shells. Typical cases are computed and compared with corresponding isotropic shells. Correlation with equivalent cylindrical shells then yields a simple approximate stability analysis for orthotropic or ring-stiffened conical shells under hydrostatic pressure.