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]. (C) 2008 Elsevier Ltd. All rights reserved.

An exact series solution for the vibration analysis of cylindrical shells with arbitrary boundary conditions

In this paper, an exact series solution for the vibration analysis of circular cylindrical shells with arbitrary boundary conditions is obtained, using the elastic equations based on Flügge's theory. Each of the three displacements is represented by a Fourier series and auxiliary functions and sought in a strong form by letting the solution exactly satisfy both the governing differential equations and the boundary conditions on a point-wise basis. Since the series solution has to be truncated for numerical implementation, the term exactly satisfying should be understood as a satisfaction with arbitrary precision. One of the important advantages of this approach is that it can be universally applied to shells with a variety of different boundary conditions, without the need of making any corresponding modifications to the solution algorithms and implementation procedures as typically required in other techniques. Furthermore, the current method can be easily used to deal with more complicated boundary conditions such as point supports, partial supports, and non-uniform elastic restraints. Numerical examples are presented regarding the modal parameters of shells with various boundary conditions. The capacity and reliability of this solution method are demonstrated through these examples. © 2012 Elsevier Ltd. All rights reserved.

Vibrations of ring-stiffened cylindrical shells.

"AFSWP no. 873. Office of Naval Research. Contract no. Nonr-266 (08) Technical report no. 13. CU-13-55-ONR-266 (08)-CE."

Approximate determination of the frequencies of ring stiffened cylindrical shells.

"AFSWP no. 874. Office of Naval Research. Contract no. Nonr 266 (08) Technical report no. 14. CU-14-55-ONR-266 (08)-CE."

On the buckling of circular cylindrical shells under external pressure,

"Project no. 9782. Contract AF 49(638)-430... CU-23-62-AF-430-CE."

Dynamic behavior of cylindrical shells under initial stress,

"Project no. 9782. Contract AF 49 (638)-430 ... CU-11-60-AF-430-CE."

Investigations into vibration and sound transmission characteristics of cylindrical shells

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Investigations into responses of cylindrical shells to random acoustic excitation

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Practical calculations for uniform external pressure buckling in cylindrical shells with stepped walls

Metal cylindrical storage structures of significant size, such as silos and vertical-axis tanks, are almost always constructed from many short cylindrical shells of different thickness as the stress resultants on the wall progressively increase towards the base. The resulting increases in thickness are always made in step changes using metal sheets of uniform thickness because of the availability of such source materials. The result is a shell with a stepped wall with multiple discrete steps in thickness. Such shells are very susceptible to buckling under external pressure when empty or partially filled, but the buckling mode may involve only part of the shell height due to the changes in shell thickness. These changes must therefore be accounted for within the design process. A new method of determining the critical buckling resistance of such shells was recently developed, and although it has been shown to be valid, the methodology for its application in practical design has not been set out or shown. This paper therefore briefly describes the new method and demonstrates the manner in which it can be used to produce rapid, safe assessments of cylindrical shells with a wide range of patterns of wall thickness changes. The results are then suitable for direct introduction into such documents as the European standard on metal shells [1] and the ECCS Recommendations [2].

Analytical Investigations 0n Collapse of Cylindrical Submarine Shells

Submarine hull structure is a watertight envelope, under hydrostatic pressure when in operation. Stiffened cylindrical shells constitute the major portion of these submarine hulls and these thin shells under compression are susceptible to buckling failure. Normally loss of stability occurs at the limit point rather than at the bifurcation point and the stability analysis has to consider the change in geometry at each load step. Hence geometric nonlinear analysis of the shell forms becomes. a necessity. External hydrostatic pressure will follow the deformed configuration of the shell and hence follower force effect has to be accounted for. Computer codes have been developed based on all-cubic axisymmetric cylindrical shell finite element and discrete ring stiffener element for linear elastic, linear buckling and geometric nonIinear analysis of stiffened cylindrical shells. These analysis programs have the capability to treat hydrostatic pressure as a radial load and as a follower force. Analytical investigations are carried out on two attack submarine cylindrical hull models besides standard benchmark problems. In each case, the analysis has been carried out for interstiffener, interdeepframe and interbulkhead configurations. The shell stiffener attachment in each of this configuration has been represented by the simply supported-simply supported, clamped-clamped and fixed-fixed boundary conditions in this study. The results of the analytical investigations have been discussed and the observations and conclusions are described. Rotation restraint at the ends is influential for interstiffener and interbulkhead configurations and the significance of axial restraint becomes predominant in the interbulkhead configuration. The follower force effect of hydrostatic pressure is not significant in interstiffener and interdeepframe configurations where as it has very high detrimental effect on buckling pressure on interbulkhead configuration. The geometric nonlinear interbulkhead analysis incorporating follower force effect gives the critical value of buckling pressure and this analysis is recommended for the determination of collapse pressure of stiffened cylindrical submarine shells.

Static analysis of functionally graded cylindrical and conical shells or panels using the generalized unconstrained third order theory coupled with the stress recovery

A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded conical and cylindrical shells subjected to mechanical loadings. Several types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the conical or cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally conical and cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out.

Influence of imperfect interfaces on bending and vibration of laminated composite shells

This paper is devoted to modeling elastic behavior of laminated composite shells, with special emphasis on incorporating interfacial imperfection. The conditions of imposing traction continuity and displacement jump across each interface are used to model imperfect interfaces. Vanishing transverse shear stresses on two free surfaces of a shell eliminate the need for shear correction factors. A linear theory underlying elastostatics and kinetics of laminated composite shells in a general configuration is presented from Hamilton's principle. In the special case of vanishing interfacial parameters, this theory reduces to the conventional third-order zigzag theory for perfectly bonded laminated shells. Numerical results for bending and vibration problems of laminated circular cylindrical panels are tabulated and plotted to indicate the influence of the interfacial imperfection. (C) 2000 Elsevier Science Ltd. All rights reserved.

Scaling of structures subject to impact loads when using a power law constitutive equation

It is well known that structures subjected to dynamic loads do not follow the usual similarity laws when the material is strain rate sensitive. As a consequence, it is not possible to use a scaled model to predict the prototype behaviour. In the present study, this problem is overcome by changing the impact velocity so that the model behaves exactly as the prototype. This exact solution is generated thanks to the use of an exponential constitutive law to infer the dynamic flow stress. Furthermore, it is shown that the adopted procedure does not rely on any previous knowledge of the structure response. Three analytical models are used to analyze the performance of the technique. It is shown that perfect similarity is achieved, regardless of the magnitude of the scaling factor. For the class of material used, the solution outlined has long been sought, inasmuch as it allows perfect similarity for strain rate sensitive structures subject to impact loads. (C) 2009 Elsevier Ltd. All rights reserved.

Estudo do fenômeno de instabilidade de estruturas cilíndricas de paredes finas submetidas ao carregamento de pressão externa

Thin walled cylindrical shells are widely used in many areas of industry, including civil, mechanical, nuclear, marine, petroleum and aerospace engineering. The wide application of thin cylindrical shells and the importance of instability phenomenon are the motivation basis to this study, since these factors have a great importance in engineering projects. It is presented a detailed study about the instability of cylindrical shells based on theoretical calculation, which results are compared with finite elements method calculation. The loading and boundary conditions analyzed are based on the most common types verified in real engineering projects and refer respectively to lateral (external) pressure and cylinders with simply supported edges. The calculation based on the finite elements method was executed with ANSYS 13.0 software. The results obtained with this calculation are in good agreement with the analytical theory presented in the technical note NACA No 1341 (BATDORF, 1947) considering a wide range of applicability. On the other hand, the analytical method presented in the book Theory of Elastic Stability (TIMOSHENKO; GERE, 1936) has a very restrict applicability and has presented considerable deviations in a great sort of the analyzed cases

Predicting the behaviour of structures under impact loads using geometrically distorted scaled models

When a scaled structure (model or replica) is used to predict the response of a full-size compound (prototype), the model geometric dimensions should relate to the corresponding prototype dimensions by a single scaling factor. However, owing to manufacturing technical restrictions, this condition cannot be accomplished for some of the dimensions in real structures. Accordingly, the distorted geometry will not comply with the overall geometric scaling factor, infringing the Pi theorem requirements for complete dynamic similarity. In the present study, a method which takes geometrical distortions into account is introduced, leading to a model similar to the prototype. As a means to infer the performance of this method, three analytical problems of structures subjected to dynamic loads are analysed. It is shown that the replica developed applying this technique is able to accurately predict the full-size structure behaviour even when the studied models have some of their dimensions severely distorted. (C) 2012 Elsevier Ltd. All rights reserved.