Pressurized Cylindrical Shells Research Articles

Buckling of pressurized cylindrical shells using the Asymptotic Numerical Method

In this paper, we present a numerical analysis of the buckling of elastic thin structures by using Asymptotic Numerical Method (ANM) and Padé approximants. We consider the case of cylindrical shells submitted to external pressure and we show how the perturbation technique can be applied for conservative and non-conservative loadings. A shell formulation well adapted to thin structures and which uses the Enhanced Assumed Strain (EAS) concept and a three-dimensional constitutive law without condensation is considered in this study. Numerical examples are presented with comparison between conservative and non-conservative loading in term of critical pressure.

Research on the dynamic response of pressurized cylindrical shell structures subjected to a near-field underwater explosion

To study the dynamic response of a pressurized thin-walled circular tube structure subjected to a near-field underwater explosion, deformation and damage tests of a pressurized cylindrical tube shell with different internal pressures and wall thicknesses with the effects of an underwater explosion from 2 g of explosives at different stand-off distances were carried out in a water tank. LS-DYNA finite element software was used to carry out relevant numerical simulations to explore the anti-explosion mechanism of a pressurized cylindrical shell structure affected by factors including the initial internal pressure, the thickness of the cylindrical shell, and the stand-off distance. The simulation inputs are high-speed photography images and the damage results of the cylindrical shell. The simulation results highlight the bubble pulsation, action process deformation, and energy change of the cylindrical shell. The results indicate that an increase in the initial pressure of the cylindrical shell can effectively improve its anti-explosion ability, while the different stand-off distances of r = 12 cm and r = 9 cm correspond to the same initial internal pressure. Increasing the initial internal pressure also causes the deflection difference of the cylindrical shell to decrease. The modeling results also indicate that an increase in the wall thickness may weaken the anti-explosion ability of the cylindrical shell, which has an initial internal pressure of Pr = 0.7 MPa. After an underwater explosion, the maximum displacement difference of a cylindrical shell with thicknesses of h = 1 mm and h = 1.5 mm is less than the maximum rebound distance difference. With this decrease in the distance, the proportion of the high-pressure cylindrical shell subjected to a shock wave increases while the proportion of bubble pulsation decreases. Specifically, the maximum proportions of bubble pulsation are 30% and 92% at the stand-off distances of 3 and 12 cm, respectively.

Mechanical stress and deformation analyses of pressurized cylindrical shells based on a higher-order modeling

In this research, mechanical stress, static strain and deformation analyses of a cylindrical pressure vessel subjected to mechanical loads are presented. The kinematic relations are developed based on higher-order sinusoidal shear deformation theory. Thickness stretching formulation is accounted for more accurate analysis. The total transverse deflection is divided into bending, shear and thickness stretching parts in which the third term is responsible for change of deflection along the thickness direction. The axisymmetric formulations are derived through principle of virtual work. A parametric study is presented to investigate variation of stress and strain components along the thickness and longitudinal directions. To explore effect of thickness stretching model on the static results, a comparison between the present results with the available results of literature is presented. As an important output, effect of micro-scale parameter is studied on the static stress and strain distribution.

A hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress: I. Out-of-plane deformation

This is the first part of a two-part article on a hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress. We present the derivation of the new model, with focus on the mechanics of the out-of-plane deformation. Accounting for the out-of-plane normal stress distribution in the out-of-plane direction affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the shell. The improvement is beyond what we get from accounting for the out-of-plane deformation mapping. By accounting for the out-of-plane normal stress, the traction acting on the shell can be specified on the upper and lower surfaces separately. With that, the new model is free from the “midsurface” location in terms of specifying the traction. We also present derivations related to the variation of the kinetic energy and the form of specifying the traction and moment acting on the upper and lower surfaces and along the edges. We present test computations for unidirectional plate bending, plate saddle deformation, and pressurized cylindrical and spherical shells. We use the neo-Hookean and Fung’s material models, for the compressible- and incompressible-material cases, and with the out-of-plane normal stress and without, which is the plane-stress case.

Thermo-elastic creep analysis and life assessment of rotating thick pressurized cylindrical shells using third-order shear deformation theory

In the present study, time-dependent thermo-elastic creep behavior and life assessment of rotating thick-walled cylindrical shells made of 304L austenitic stainless steel (304L SS) are investigated based on the third-order shear deformation theory (TSDT). Loading is composed of a uniform internal pressure, distributed temperature field, and a centrifugal body force due to rotating speed. Norton’s law is utilized as the material creep constitutive model. Using the minimum total potential energy principle, a system of differential equations in terms of displacement and boundary conditions are derived. Then, the governing equations are solved with an analytical approach, which leads to an accurate solution. Subsequently, an iterative procedure is also proposed to determine the stresses and deformations at different creep times. Larson-Miller Parameter (LMP) and Robinson's linear life fraction damage rule are employed for assessing the creep damages and the remaining life of cylindrical shells. To the best of the researcher’s knowledge, in the previous studies, there is no study carried out into third-order shear deformation theory for thermo-elastic creep analysis of cylinders. To validate the accuracy of the suggested method based on TSDT, a comparison among analytical results and those of the finite element method (FEM) is performed and very good agreement is found. The results indicate that the present analysis is accurate and computationally efficient.

Assessing the axial buckling load of a pressurized orthotropic cylindrical shell through vibration correlation technique

Traditional buckling experiments of imperfection-sensitive structures like cylindrical shells can cause the permanent failure of the specimen. Nevertheless, an experimental campaign is crucial for validation of the design and numerical models. There is, therefore, interest in nondestructive methods to estimate the buckling load of such structures from the prebuckling stage. The vibration correlation technique allows determining the buckling load without reaching the instability point. Recently, a novel empirical vibration correlation technique based on the effects of initial imperfections on the first vibration mode demonstrated interesting results when applied to composite and metallic unstiffened cylindrical shells. In this context, this paper explores this novel approach for determining the axial buckling load of a metallic orthotropic skin-dominated cylindrical shell under internal pressure, which represents a simplified downscaled model of a launcher propellant tank. An experimental campaign consisting of buckling tests and noncontact vibration measurements for different axial load levels is conducted considering the specimen without and with three different internal pressure levels. The experimental results validate the above-mentioned vibration correlation technique for determining the axial buckling load of pressurized cylindrical shells. Moreover, finite element models are calibrated in order to evaluate the frequency variation within a broader and dense range of the axial loading leading to an assessment of the considered maximum load level and number of load steps as related to the deviation of the estimation. The results corroborate the applicability of the vibration correlation technique as a nondestructive experimental procedure to assess the axial buckling load of imperfection-sensitive orthotropic skin-dominated cylindrical shells under internal pressure.

Analytical estimates of the contact zone area for a pressurized flat-oval cylindrical shell placed between two parallel rigid plates

The paper presents an analytical estimate for an area of contact for a thin-walled noncircular cylindrical shell placed between two parallel rigid plates with an initial gap and then pressurized hydrostatically up to the contact appearance. The Euler–Bernoulli beam is used to model the shell deformation under the plane strain assumption. Such a simplification allows one to obtain the simplest closed-form estimate for the contact zone area. The first approximation is obtained neglecting the deformation of the curvilinear segments of the flat oval shell cross-section while the solution for the curved beam loaded by the homogeneous pressure is considered as a second approximation. The accuracy of the proposed analytical solutions as well as their usability in the preliminary design of thin-walled elements of various cooling systems is validated by the results of both numerical simulations and experimental tests.

Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping

We derive a hyperelastic shell formulation based on the Kirchhoff–Love shell theory and isogeometric discretization, where we take into account the out-of-plane deformation mapping. Accounting for that mapping affects the curvature term. It also affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the material. In fluid–structure interaction analysis, when the fluid is inside a shell structure, the shell midsurface is what it would know. We also propose, as an alternative, shifting the “midsurface” location in the shell analysis to the inner surface, which is the surface that the fluid should really see. Furthermore, in performing the integrations over the undeformed configuration, we take into account the curvature effects, and consequently integration volume does not change as we shift the “midsurface” location. We present test computations with pressurized cylindrical and spherical shells, with Neo-Hookean and Fung’s models, for the compressible- and incompressible-material cases, and for two different locations of the “midsurface.” We also present test computation with a pressurized Y-shaped tube, intended to be a simplified artery model and serving as an example of cases with somewhat more complex geometry.

Experimental/numerical investigation of mechanical behaviour of internally pressurized cylindrical shells with external longitudinal and circumferential semi-elliptical defects

This paper presents an experimental-numerical investigation on the mechanical behaviour of pressurized cylindrical shells with external longitudinal and circumferential cracks of semi-elliptical shape. The research is motivated by the need to develop advanced design methodologies for shell structures. For that purpose, strain gauges are utilized to monitor strain concentrations near the cracks, and finite element simulations are carried out to predict the corresponding stress intensity factor distributions. A good agreement between numerical simulations and experimental data is found. This confirms that virtual simulations/calculations provide a reliable approach to evaluating mechanical behaviour of pressurized cylindrical shells with crack defects.

Bulging factor of a longitudinal crack in pressurized cylindrical shell with a reinforcing layer

Bulging factor expressions for a longitudinal crack in a pressurized cylindrical shell with a reinforcing layer are developed. In this study, a parametric finite element model was constructed, validated (based on experimental data) and used to simulate various shell configurations. A Python script automates the execution, data collection and calculation of the bulging factor for 2592 configurations using the commercial code ABAQUS. Candidate expressions for the bulging factor are selected based on physical arguments and fitted using stress displacement data obtained previously; several expressions were found to be in good agreement with finite element data.

Incontrovertible proof that the “discrepancies” in thin-shell-buckling studies are in the classical theory, not the test data

It is shown here that the classical shell-buckling analyses have been fatally flawed since they were first derived. One reason cited is a failure to freeze the buckling stresses at the values at which buckling commenced, which resulted in consistent over estimates of the true buckling stresses by large factors. Another is the misinterpretation of the inextensibility criterion, which is customarily expressed in terms of the linear equations pertaining prior to buckling instead of the nonlinear equations that govern once buckling has commenced. The consequence of not acknowledging these errors is that, for many decades, it has been assumed incorrectly that the classical analyses for the various shell geometries are valid and that the major discrepancies can all be attributed to imperfections in the testing. It is shown here that this is not the case, by deriving different governing equations for shell buckling, starting from the geometrically nonlinear equilibrium equations for thin shells. These equilibrium equations are shown to include both the linear terms governing prior to buckling, with the remaining terms pertaining during buckling. This shows that buckling is resisted entirely by bending stresses alone, just as is known to be the case for flat-plate buckling, instead of by the combination of membrane and bending stresses. Specific equations are included for cylindrical shells, along with test data showing that the correct buckling stress for longitudinally compressed unpressurized cylinders is only half the classical prediction. Future papers will include full analyses of the buckling of spherical shells under external pressure at half the classical prediction, and of cylindrical shells under external pressure at one third of the classical prediction, as well as the buckling of pressurized and unpressurized cylindrical shells under longitudinal compression showing how, as the internal pressure is increased, the diamond-buckling stress increases from half the classical prediction for zero pressure to the classical ring-buckling stress for high pressure.

The Stress Analysis of Pressurized Cylindrical Shell with a Surface Crack under Laser Irradiation

For the structure failure of pressurized cylindrical shell under laser irradiation, studied with axial semi-elliptical surface crack of cylindrical shell under the combined action of laser radiation and pressure, analysis of its thermal force coupling of stress and material for the 30CrMnSiA steel. According to of static fracture toughness and based on theof estimated impact dynamic fracture toughness, the application of finite element method to study the fracture problem under dynamic load. Analyzing the crack initiation propagation and static dynamic initiation based on fracture criterion and dynamic fracture criterion for crack initiation propagation, provides a useful research of the analysis to a certain extent on the structure in thermal force coupling failure mechanism.

Experimental study of pressurized, foam reinforced, cracked cylindrical aluminum shells

Cracks in pressurized cylindrical shells are subject to stress fields peculiar to the shell geometry and loading conditions which makes them more critical than cracks in flat plates under similar conditions. In order to mitigate the stress field around the crack tips a foam layer is applied to the shell as reinforcement. The effect of this solution on crack behavior is evaluated experimentally. Pre-cracked cylindrical aluminum shells with layers of rigid foam applied to their inner side are tested by subjecting them to cyclic internal pressure. A test bench built especially for the purpose of cyclic testing is described as well as the testing procedure. Results indicate that crack growth rates are significantly reduced and fatigue life is extended by as much as 161%. The application of a foam layer to may help slow down the growth of existing cracks. This solution may prove useful especially in ageing aircraft fuselage structures.

An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part II: Design Method

A universal design method for pressurized cylindrical shells with attached nozzles subjected to external forces (moments) and internal pressure are presented, based on theoretical stress analysis. The applicable ranges of the presented design methods are extended to ρ0=d/D≤0.9 and λ=d/(DT)1/2≤12. As a first step of design, the required reinforcement thicknesses, both of the main shell and nozzle due to internal pressure, can be determined by the presented theoretical solutions. When the junction is subjected to external nozzle loads, the next step is to determine the absolute values of dimensionless longitudinal and circumferential, normal and shear, membrane and bending stresses in the shell at the junction subjected to internal pressure, and six external nozzle load components by reading out from a number of sets of curves calculated by the present theoretical method. Then the stress components at eight examination points are calculated and superimposed for the combined loads. Finally, the membrane and primary plus secondary stress intensities can be calculated, respectively, to meet the design criteria.

On the finite element modeling of fatigue crack growth in pressurized cylindrical shells

A methodology for the computational modeling of the fatigue crack growth in pressurized shell structures, based on the finite element method and concepts of Linear Elastic Fracture Mechanics, is presented. This methodology is based on that developed by Potyondy [Potyondy D, Wawrzynek PA, Ingraffea, AR. Discrete crack growth analysis methodology for through crack in pressurized fuselage structures. Int J Numer Methods Eng 1995;38:1633–1644], which consists of using four stress intensity factors, computed from the modified crack integral method, to predict the fatigue propagation life as well as the crack trajectory, which is computed as part of the numerical simulation. Some issues not presented in the study of Potyondy are investigated herein such as the influence of the crack increment size and the number of nodes per element (4 or 9 nodes) on the simulation results by means of a fatigue crack propagation simulation of a Boeing 737 airplane fuselage. The results of this simulation are compared with experimental results and those obtained by Potyondy [1].

Crack growth in cylindrical aluminum shells with inner reinforcing foam layer

The occurrence of cracks in aging aircraft fuselage is major problem in the airline industry. The remaining life of the aircraft is strongly dependent on the residual strength of its structure. Residual strength is affected by crack sizes and their growth rates. In the case of a longitudinal crack in a pressurized cylinder (as in the case of an aircraft fuselage), the geometry and loading conditions cause the edges of the crack to bulge out generating a complex stress field around the crack tips; this is known as the ‘bulging effect’. The geometry of the shell, crack size and pressure contribute to this phenomenon. A proposed solution to reduce the effect of bulging for this type of crack is to apply a layer of polyisocyanurate (PIR) foam to the inner side of the fuselage near the crack site. This layer will bond to the shell and has the effect of reducing the bulge and consequently, the Stress Intensity Factor (SIF) at the crack tips. PIR foam is a lightweight material that adheres well to the shell and provides additional stiffness around the crack area. In the present study the effect of applying a PIR foam layer to a longitudinal crack in a pressurized cylindrical shell is assessed. Nonlinear Finite Element Analysis (FEA) is used in conjunction with the Modified Crack Closure Integral technique (MCCI) in order to evaluate the effect of bulging on the crack’s SIF. Parameters considered in this study include shell radius, shell thickness, crack length, foam thickness and pressure. Numerical results are compared with existing experimental data and the effect of foam thickness for several shell configurations is presented. Results indicate that the bulge factor (BF) could be reduced by as much as 45% depending on shell configuration, foam thickness and pressure.

Modeling of ductile fracture: Application of the mechanism-based concepts

This paper summarizes our recent studies on modeling ductile fracture in structural materials using the mechanism-based concepts. We describe two numerical approaches to model the material failure process by void growth and coalescence. In the first approach, voids are considered explicitly and modeled using refined finite elements. In order to predict crack initiation and propagation, a void coalescence criterion is established by conducting a series of systematic finite element analyses of the void-containing, representative material volume (RMV) subjected to different macroscopic stress states and expressed as a function of the stress triaxiality ratio and the Lode angle. The discrete void approach provides a straightforward way for studying the effects of microstructure on fracture toughness. In the second approach, the void-containing material is considered as a homogenized continuum governed by porous plasticity models. This makes it possible to simulate large amount of crack extension because only one element is needed for a representative material volume. As an example, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a modified Gologanu–Leblond–Devaux model [Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Tech. 116, 290–297; Gologanu, M., Leblond, J.B., Perrin, G., Devaux, J., 1995. Recent extensions of Gurson’s model for porous ductile metals. In: Suquet, P. (Ed.) Continuum Micromechanics. Springer-Verlag, pp. 61–130] is used to describe the evolution of void shape and void volume fraction and the associated material softening, and the material failure criterion is calibrated using experimental data. The calibrated computational model successfully predicts crack extension in various fracture specimens, including the compact tension specimen, middle crack tension specimens, multi-site damage specimens and the pressurized cylindrical shell specimen.

Numerical simulation of fatigue crack growth in pressurized shells

This paper presents a procedure for numerical simulation of fatigue crack growth in pressurized cylindrical and spherical shells using the dual boundary element method. The simulations are performed using an incremental crack growth procedure, where stress intensity factors, fatigue life cycles and crack growth directions are calculated for every increment of the growth. The results obtained in this work are shown to be in good agreement with experimental results. Some examples are presented to demonstrate the robustness of the proposed method.

Buckling analysis for design of pressurized cylindrical shell panels

In contrast with the pressure buckling of a complete cylinder, even a perfect cylindrical shell panel displays a complex form of nonlinear snap buckling behaviour. The prebuckling nonlinearity has been understood to be induced by the total equivalent imperfections involving the potential-load-induced imperfection and the actual geometric imperfection. Based on this concept, an alternative estimation procedure of the elastic and elastoplastic buckling load-carrying capacities is proposed and the resulting simple equations and formulae for design are represented.

The failure analysis of a cylindrical shell with arbitrarily oriented through cracks

Using the strain energy density theory and the three-dimensional finite element method, the residual strength and fracture behavior of a pressurized cylindrical shell with an arbitrarily oriented through crack are predicted elastically and/or plastically. First, mode I elastic fracture analysis verifies the methodology, then the cases of the mixed mode crack problem are analyzed. The results show that the stress intensity factor increases as the crack length is shorter or the thickness of the shell is thinner. It is well known that cracks, in all cases, tend to propagate along the axis of principal stress direction of the shell. When the thickness-to-crack length ratio is increased, the triaxial stress-state in the vicinity of the crack front becomes prominent and any assumptions made in shell theory are incorrect. Finally, the emphasis is placed on how the crack tip plastic zone affects the failure behavior, and with this, an elastic-plastic finite element analysis on mode I is performed. When the dissipated energy around the crack tip is considered, the critical crack length is almost twice that obtained from the elastic analysis.