Criterion analysis of the fracture of cylindrical shell structures loaded by internal pressure induced by localized thermal impacts

We present experimental results of the investigation of the strength of cylindrical shells loaded by internal pressure formed as a result of a localized thermal impact caused by laser radiation. The types of fracture of shells recorded in the experiments are characterized either by the loss of gas-tightness as a result of the formation of cracks (or holes) or by the total fracture of a shell. We performed the criterion analysis of the experimental results by using the methods of the theory of similarity. The amount of conveyed radiant energy and the level of excess internal pressure are the main factors responsible for the fracture of shells. We suggest a formula which establishes a relationship between these factors and which can be regarded as a helpful criterion in comparing the results of testing of various models under different loading modes and application of these results to actual objects. Translated from Problemy Prochnosti, No. 5, pp. 51–57, September–October, 1997.     

Ductile failure of cylindrical bodies with axial cracks loaded by internal pressure

The article considers problems of finding the limit pressure leading to ductile failure of a cylinder with an axial crack. Actual formulas are obtained for a thin-walled shell and for cylinders with considerable thickness. The article shows their satisfactory agreement with the results of full-scale tests.Translated from Problemy Prochnosti, No. 2, pp. 16–20, February, 1990.     

A longitudinal crack in a cylindrical shell under internal pressure

The study relates to the strength of a cracked shell. Linear thin shell theory is employed to obtain solutions for internal pressure and uniform circumferential bending. A shallow shell approximation is used, and shown valid providing crack length and shell thickness are small enough in comparison with shell radius. Initial formulation as a boundary value problem is shown equivalent to two coupled singular integral equations. These were solved numerically using a computer. Stresses are found to display singularities as inverse square-root of distance from a crack tip, as with the flat plate. The main results are graphs of normal and bending stress singularity strengths against a curvature/crack-length dimensionless parameter.

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Zusammenfassung Diese Arbeit behandelt die Stärke von einer gerissenen Schale. Die lineare Theorie dünner Schalen ist benutzt um dieses Problem für den Innendruck und gleichmäßige Umkreis-biegung zu lösen. Die Annäherungen der mäßig gekrümte Schalen sind benutzt welche zulassig sind nur wenn die Rißlänge und die Dicke der Schale klein sind im Vergleich zu dem Schalradius. Die anfängliche Formelierung als ein Randwertproblem ergibt sich als gleichwertig zwei gekuppelten singulären Integralgleichungen. Diese sind numerisch gelöst mit Hilfe einer Rechenautomat. Die Spannungen zeigen, in Übereinstimmung mit der flachen Platte, umgekehrte Quadratwurzelsingularitäten. Die Resultaten der Stärke der Normal- und Biegung-spannungsingularitäten sind graphisch als Funktion eines dimensionslosen Krümmungs-Rißlängeparameter gegeben.

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Résumé Cette étude est sur la résistance d'une monocque fêlée longitudinalement. À l'aide de la théorie linéare des toques minces élastiques l'on obtient la solution de deux cas: 1) coque sous pression intérieure et 2) flexion circonférentielle uniforme. On fait l'approximation que la coque est de faible profondeur et l'on démontre que les solutions sont valables pourvu que la longeur de la fêlure et l'épaisseur de la coque soient assez petites comparées au rayon de la coque. On formule d'abord un système elliptique des équations aux dérivées partielles, qui se transforme en deux équations intégrales simultanées. Celles-ci sent résolues numériquement à l'aide d'un ordinateur. On trouve que la contrainte possède des singularités proportionelles à l'inverse de la racine carrée de la distance d'une extrémité de la fêlure: ce résultat est identique à celui qui existe pour une plaque. Les résultats principaux que l'on présente sont des courbes de l'amplitude de ces singularités en fonction d'un paramètre charactéristique de la grandeur de la fêlure et du rayon de la coque.

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Notation c half crack length, inch - E Young's modulus of elasticity, psi - h thickness of shell, inch - M _t twisting moment resultant - M circumferential bending moment resultant far from crack - M _x , M _y , M _xy bending and twisting moment resultants - N _x , N _y , N _xy normal and shear stress resultants - p _i internal pressure, psi - p ₀ reference pressure, psi - Q, Q _x , Q _y transverse shear stress resultants - R radius of shell, inch - x, y Cartesian coordinates for shallow shell formulation, inch - w outward radial displacement of cylindrical shell, inch - Euler constant (0.5772...) - dimensionless parameter, ²=[3(1–v ²)/4]^1/2(c ²/Rh) - v Poisson's ratio This work was supported in part by the Office of Naval Research under Contract Nonr 1866(02), in part by the National Aeronautics and Space Administration under Grant NsG-559, and by the Division of Engineering and Applied Physics, Harvard University.     

A multilayered thick cylindrical shell under internal pressure and thermal loads applicable to solid propellant rocket motors

A solid propellant rocket motor can be considered to be made of various circumferential layers of different properties. A simple procedure is described here to obtain an analytical solution for the general case of multilayered thick cyclindrical shell for internal pressure and thermal loads. This analytical procedure is useful in the preliminary design analysis of solid propellant rocket motors. Since solid propellant material is of viscoelastic behaviour an approximate viscoelastic solution methodology for the multilayered shell is described for estimation of time dependent solutions of propellant grain in a rocket motor. The analytical solution for a two layer reinforced thick cylindrical shell available in the literature is shown to be a special case of the present analytical solution. The results from the present analytical solution for multilayers is found to be in good agreement with FEA results.     

热环境下功能梯度圆柱壳振动特性分析

应用谱几何法研究了热环境下功能梯度圆柱壳自由振动和瞬态振动特性。采用边界弹簧技术模拟圆柱壳结构的任意经典或者弹性边界约束条件,并结合一阶剪切变形理论建立了考虑温度场作用的功能梯度圆柱壳结构能量泛函。采用谱几何法与周向傅里叶谐波函数乘积和的形式描述圆柱壳的位移容许函数,以克服不同边界条件下壳体位移函数微分在边界上存在的不连续问题。在此基础上,将位移容许函数代入至结构能量泛函,并采用 Ritz 法获得结构振动分析模型。数值分析结果表明,所构建分析模型能够快速准确预测功能梯度圆柱壳结构的振动特性。研究了幂律指数、温度、载荷等参数对功能梯度圆柱壳振动特性的影响规律,为其他数值分析方法研究提供参考。     

Looping post-buckling paths of an axially loaded elastic cylindrical shell

We present first-order and second-order iteration solutions to the Donnell cylinder equations for the post-buckling response of an axially loaded elastic cylindrical shell. Both solutions possess looping equilibrium paths with a remote bifurcation point, a feature inaccessible to standard linear perturbation analysis. The implication of this result for linear perturbation theory is discussed.     

Dilatation of double-layered cylindrical shell under internal explosive loading

To study the influence of the layered structure of a shell on the dynamics of its dilatation and rupture, the problem of the motion of an elastoplastic double-layered shell under the effect of the internal pressure of detonation products was posed. The solution of the problem reduced to the integration of a linear differential equation. Test examples showed the research possibilities of the suggested statement, and also special traits of the rupture of double-layered shells with different physicomechanical properties of the materials of the layers.Translated from Problemy Prochnosti, No. 6, pp. 49–56, November–December, 1996.The work was carried out with the support of the Humanitarian Fund of Soros and in cooperation with the American Physical Society. Grand UG225.     

Integrity of pressurized components with localized corrosion under internal pressure and transient thermal loading

This paper is devoted to the modelling and analysis of the problem of the safety and residual lifetime of pressurized components (e.g. pressure vessels, apparatus, pipelines) with zones of local corrosion damage. Corrosion damage is the most common form of structural material degradation in service conditions, in particular, in the chemical and gas, and oil industries. Attention is paid to nonstationary regimes of the component operation, e.g., start‐stop regimes. It is shown that the critical parameters calculated taking into account the nonstationary loading can be lower compared with ones determined for the stationary regimes, e.g., on the basis of the ASME Code B31G.     

Stress in an elastic wedge or notch loaded by a localized internal source

A study is presented of the stress inside a two-dimensional elastic solid which has a boundary surface angle and which is loaded by an internal point source of expansion. An exact analytic solution for the stress is obtained, for general surface angle and source position, and evaluated numerically for several representative cases of wedges and notches. The singular behaviour given by the leading terms near the angle vertex is found to be highly localized, and there is little or no stress enhancement near the source. For many combinations of boundary angle and source location, however, a local region of significant enhancement occurs on that part of the surface nearest the source. Implications of these results are discussed, with particular reference to surface steps.     

Shape optimization of bonded patch to cylindrical shell structures

Adhesive bonding has been widely used to join or repair metallic and composite structural components to achieve or restore their designated structural stiffness and strengths. However, current analysis methods and empirical databases for composite bonded patch repairs or joints are limited to flat structures, and there exists a very limited knowledge on the effect of curvature on the performance and durability of composite bonded joints and repairs. Recently, a novel finite element formulation was presented for developing adhesive elements for conducting 2.5‐D simplified stress analysis of bonded repairs to curved structures. This paper presents the work on optimal shape design of a bonded curved composite patch using the newly developed adhesive element. The Sequential Linear Programming (SLP) method is employed as the optimization algorithm in conjunction with a fully implemented mesh generation algorithm into which new features have been incorporated. The objective of shape optimization is to minimize the maximum stress in the entire adhesive layer to ensure that the bonded patch effectively works together with the parent structure in service. Several different objective functions, related to possible failure mechanisms of the adhesive layer, are proposed to optimize the shape of a bonded patch. Copyright © 2003 John Wiley & Sons, Ltd.     

Acceleration fields induced by hypervelocity impacts on spacecraft structures

This paper presents an overview of the hypervelocity impact test campaign ongoing in the frame of the ESA contract “spacecraft disturbances from hypervelocity impact”. The project aims at analyzing the propagation of shocks due to hypervelocity impacts from the external shell of a spacecraft to its internal components. The object of the study is the GOCE satellite, which has been recognized to be very sensitive to small disturbances because of its payload that has been designed to measure even very low acceleration levels. In the first step presented hereafter, the test campaign has been focused on the qualification of the background environment inside the impact chamber and on the determination of the vibration levels induced by perforating and non-perforating hypervelocity projectiles on simple aluminum plates. The results currently obtained and a preliminary data analysis will be presented in the following.