Stability of smooth and ribbed shells of revolution in a nonuniform stress-strain state (survey)

Gavrilenko, G. D.

doi:10.1007/bf00846784

Cited by 6 publications

(13 citation statements)

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“…It means that the dynamic and stability problems of such shells are considered within the framework of discrete models, while the dynamic and stability analysis of periodically, densely ribbed cylindrical shells investigated in this paper is carried out within continuum models. The discrete approach is in detail discussed in monographs [2,6]. Moreover, in the mentioned monographs it can be found an extensive review of papers and books dealing with stability and dynamic problems of widely ribbed shells as well as of densely stiffened shells treated as homogeneous orthotropic structures.…”

Section: Introductionmentioning

confidence: 99%

On dynamics and stability of thin periodic cylindrical shells

Tomczyk

2006

International Journal of Differential Equations

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The object of considerations is a thin linear-elastic cylindrical shell having a periodic structure along one direction tangent to the shell midsurface. The aim of this paper is to propose a new averaged nonasymptotic model of such shells, which makes it possible to investigate free and forced vibrations, parametric vibrations, and dynamical stability of the shells under consideration. As a tool of modeling we will apply the tolerance averaging technique. The resulting equations have constant coefficients in the periodicity direction. Moreover, in contrast with models obtained by the known asymptotic homogenization technique, the proposed one makes it possible to describe the effect of the period length on the overall shell behavior, called a length-scale effect.

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Section: Introductionmentioning

confidence: 99%

On dynamics and stability of thin periodic cylindrical shells

Tomczyk

2006

International Journal of Differential Equations

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“…This cannot be done in full with analytical approaches. Therefore, use should be made of the finite-element method [8,[10][11][12][13].…”

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“…The precritical state is assumed to be homogeneous and membrane. The third method is based on the theory of imperfect thin-walled ribbed shells with an inhomogeneous membrane precritical state [6][7][8][9][10][11][12]. The fourth method regards the shell and ribs as a solid, i.e., as a three-dimensional medium [5].…”

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confidence: 99%

“…We used a special modified software package for critical-load analysis that is capable of analyzing not only general distributions of initial imperfection but also their different types: from local to localized in any direction. Relevant studies for smooth shells are reported in [8,13], while there are just a few examples of ribbed shells with general and longitudinally localized deflections [10].It is necessary to assess the effect of some types of localized (bounded circumferentially but not longitudinally) imperfections on the critical load. This cannot be done in full with analytical approaches.…”

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confidence: 99%

“…This cannot be done in full with analytical approaches. Therefore, use should be made of the finite-element method [8,[10][11][12][13].It is generally known how to determine the minimum critical load. A portion of the shell bounded by its length and a kth of its circumference is covered by a mesh.…”

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Effect of localized imperfections on the critical loads of ribbed shells

Gavrilenko

Matsner

2010

Int Appl Mech

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A numerical approach to the assessment of the critical stresses for imperfect ribbed shells is developed. Initial deflections occupying a part of the shell surface (they are circumferentially bounded) are considered. The couple stresses and nonlinearity of the precritical state are taken into account. Numerical examples are given Keywords: imperfect ribbed shell, stability, critical loads Introduction. To analyze the precritical state of thin-walled ribbed shells and to determine their critical loads, use is made of one of the four possible methods. One of the methods uses a structurally orthotropic model, another method considers discrete elastic bars joined with the shell [1-4, 6, 14]. The precritical state is assumed to be homogeneous and membrane. The third method is based on the theory of imperfect thin-walled ribbed shells with an inhomogeneous membrane precritical state [6][7][8][9][10][11][12]. The fourth method regards the shell and ribs as a solid, i.e., as a three-dimensional medium [5]. Composite shells are analyzed for stability in [15][16][17][18].This present paper uses the third method because the first two have well-known disadvantages and disregard the couple stresses and the nonlinearity of the precritical state.1. Numerical Technique. We used a special modified software package for critical-load analysis that is capable of analyzing not only general distributions of initial imperfection but also their different types: from local to localized in any direction. Relevant studies for smooth shells are reported in [8,13], while there are just a few examples of ribbed shells with general and longitudinally localized deflections [10].It is necessary to assess the effect of some types of localized (bounded circumferentially but not longitudinally) imperfections on the critical load. This cannot be done in full with analytical approaches. Therefore, use should be made of the finite-element method [8,[10][11][12][13].It is generally known how to determine the minimum critical load. A portion of the shell bounded by its length and a kth of its circumference is covered by a mesh. The force and displacement functions are unknown at the nodes of the mesh. The nonlinear system of equations (their finite-difference analog) is solved with prescribed accuracy by the method of successive approximations. The Dl-method is used, i.e., given load parameter, the determinant of the left-hand side of the equations is calculated to detect sign reversals.

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Stability and load-bearing capacity of smooth and ribbed shells with local dents

Gavrilenko

2004

Int Appl Mech

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A method for analysis of the stability and load-bearing capacity of imperfect smooth and ribbed shells is developed. This method is based on the finite-difference method and is implemented as an algorithm for fast calculation of critical forces, as opposed to the finite-element method. The theoretical results discussed include both early and recent results. The emphasis is on shells with local dents. The numerical results are successively corrected and compared with available experimental data for shells with a single dent and with other data. The method enables us to discover new features in the behavior of thin-walled structures under loading: development of precritical state, change in the dent shape, and exhaustion of load-bearing capacity. The lower local critical loads and upper stresses are determined. They correspond to general buckling and agree well with available experimental data.Introduction. Methods combining numerical and classical analytical approaches are of special interest in the theory of shells. This is pointed out in [50, etc.].The present paper briefly describes a numerical approach to the analysis of the stability and load-bearing capacity of imperfect shells. If theoretical solutions are unavailable, we will use experimental data to justify the reliability of the method. Solutions that could improve results obtained within the framework of shell theory can be derived from the three-dimensional theory of deformable bodies and its applications [28][29][30]48].Well-known theoretical studies into the stability of shells with a local dent did not addressed the issue of load-bearing capacity of such shells. Such studies are discussed in Sections 1-3.Background Information and Problem Statement. The new approach and the theoretical results compared with experimental data are described in Sections 4-6. The strength loss process of real thin-walled shells includes, at least, three stages: subcritical, critical, and postcritical. These stages are shown graphically in [40].Consider the following approach to the buckling analysis of shells: (i) analyze the behavior of imperfect shells with a local dent (generally dents) growing in amplitude;(ii) determine the critical (lower) load under which the originally nonloaded dent transforms into a new (loaded) dent; (iii) study the behavior (whether stable or not) of the shell with new dent, which subsequently turns into the postcritical state, using nonlinear shell theory and the generalized mixed equations describing the entire process at all the three stages.The theoretical results are supported by experimental data [33] on stability of shells with dents. Smooth cylindrical shells with a single local dent were the subject of detailed theoretical and experimental research. The experiments involved steel specimens. All the shells were made by the same method and tested under identical conditions. The theoretical analysis was based on the mesh method and nonlinear shell theory. The experimental and theoretical critical forces were compared for shells

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Stability of smooth and ribbed shells of revolution in a nonuniform stress-strain state (survey)

Cited by 6 publications

References 29 publications

On dynamics and stability of thin periodic cylindrical shells

On dynamics and stability of thin periodic cylindrical shells

Effect of localized imperfections on the critical loads of ribbed shells

Stability and load-bearing capacity of smooth and ribbed shells with local dents

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