International centre for mechanical sciences courses and lectures, vol 240. Yang 1965 proceedings of ninth midwestern mechanics conference 3, part 2, 215228. The first solution in the field of buckling of thin shells was given in lorenzs paper on axially symmetric buckling of axially compressed cylinders ref. Elastic coliducting shells in alternating electromagiietic fields a.
Similarily, displacement vector can be divided into two components. Theory and analysis of elastic plates and shells second edition j. Thin nearly flat elastic shells with stretching and bending problem presented by dr. The magnitude of frequency shift is comparable to analytical predictions made for thin. This book aims to develop the analysis through membrane theory to bending theory for shells and to limit the type of mathematics used. Differences in the response of thin nonshallow spherical shells resulting from the choice of the adopted shell theory classical or improved are addressed analytically and through a. In fact, as will be seen later, if in thin shell appears as a loadcarrying element in some part of virtually every item of modern industrial equipment. The theory of simple elastic shells 11 all modulus in 21 and 22, excluding c 4, were found from the tasks in which they determine the main terms of asymptotic expansions. The work done by kraus 16 is one of few works performed on the dynamic thermoelastic analysis of spherical shells. Reddy distinguished professor and holder of the oscar s.
Criteria for finite element discretization of shells of. The justification underlying the dmv straindisplacement relations is the same as those enumerated above i. On the foundations of the theory of thin elastic shells. Shells and shell theory a thinwalled cylindrical tank has high bending flexural stresses at the base. The shell under investigation is assumed to be sufficiently thin to neglect the curvature effect through the thickness. Variational equations for thin elastic shells sciencedirect. Genin school ofmechanical engineering, purdue university, west lafayette, indiana 47907, u.
Also, the shell is considered to be constituted from homogenous and isotropic material. In fact, the thin shell places a severe demand on both element. There is a tendency for this information to be overlooked, with the notion that a proper finite element and enough computing power are adequate to tame any structural system. This is especially true of the aerospace, nuclear, marine, and petrochemical industries where dramatic and sophisticated uses of shells are currently being made in missiles and space vehicles, submarines, nuclear reactor vessels, refinery equipment, and the like. Dashed white lines highlight the likely range of titans ice shell thickness, 50200km. Methods for thin nearly flat elastic shells with stretching. Theory of elastic thin shells discusses the mathematical foundations of shell theory and the approximate methods of solution. Venants solution of the flexure problem that a beam in which the material is disposed at a distance from. We consider an isotropic linearly elastic spherical shell deformed by a topographic load imposed at the surface.
The present volume was originally published in russian in 1953, and remains the only text which formulates as completely as possible the different sets of basic equations and various approximate methods of shell analysis emphasizing asymptotic integration. Tutorial 7 theories of elastic failure thin shells. Dynamic coupled thermoelastic response of thin spherical. Whrrney 1969 journal of composite materials 3, 534547. Linear elastic theory of thin shells presents membrane and bending theories for open and closed cylindrical shells and shells of arbitrary shape. Tutorial 7 theories of elastic failure thin shells 1. Use a finer mesh where there are discontinuities or abrupt changes in the structure. We build on the discussion in 8,10,20 and present a rigorous derivation of a set of asymptotic theories for the shape of residually strained thin lamina with nontrivial curvatures, i.
In fact, as will be seen later, if in thin elastic shells harry kraus download bok. The theory of simple elastic shells holm altenbach1 and pavel a. Thin elastic shells journal of applied mechanics asme. Theory of small deformations of a thin elastic shell. The elastic properties of the shell are represented by youngs modulus e and poissons ratio. Particular emphasis is placed on the formulation of elastic. A cylindrical water storage tank fabricated from steel and buttwelded together is to be 10m in diameter and 5m high. The allowable stress in tension for the selected steel is. This work presents the dynamic coupled thermoelastic response of thin spherical shells subjected to a transverse thermal shock. Thin elastic shells with variable thickness for lithospheric. A 2d gdq solution for static and free vibration analysis authors. An improved firstapproximation theory for thin shells nasa report 24 june, 1959. Methods for thin nearly flat elastic shells with stretching and bending \frozen shapes.
Thin elastic shells an introduction to the theoretical foundations and the analysis of their static and dynamic behavior. Rev july, 2008 numerical and experimental investigations on preload effects in air foil journal bearings. Resonance frequencies of a spherical aluminum shell. The theory of simple elastic shells 3 where 1 is the unity second rank tensor. Analytical investigations 011 collapse ofcylindrical. Department of civil and environmental engineering, washington university, st. The finite element method, prenticehall, englewood cliffs, n. The frequency shift appears to be smaller for longitudinal modes than for bending wave modes. Kolos, on the derivation of twodimensional equations in the theory of thin elastic plates, journal of applied mathematics and mechanics, 1965, 29, 1, 151crossref 17 p.
General equations governing the deformations of a thin elastic shell have been given by various authors e. Elastic wave propagation in heterogeneous cylindrical shells. Models for elastic shells with incompatible strains. Received 1 november 1974 variational equations are derived for thin elastic shells of arbitrary geometry from their related nonlinearmodalequations,the advantages. Freeform laminated doublycurved shells and panels of. Since the failure of thin walled structures is more often caused by buckling, the issue of the linear and nonlinear buckling analysis of plates and shells is given much attention in the book. If the inline pdf is not rendering correctly, you can download the pdf file here. Vlasov 1949, their further generalizations obtained by including the transverse shear stresses e.
On the flexure of thin cylindrical shells and other thin. The present volume was originally published in russian in 1953, and remains the only text which formulates as completely as possible the different sets of basic equations and various approximate methods of shell analysis. Instability of thin circular cylindrical shells, proceedings symposium on hydromechanically loaded shells, university press, hawaii, honolulu, pp. Deformation of an elastic shell with variable thickness. Please redirect your searches to the new ads modern form or the classic form. Full text of nonlinear theory of thin elastic shells see other formats. Naghdi 1957, and many others, see, for example, kraus 1967 or venstel.
An introduction to the theoretical foundations and the analysis of their static and dynamic behavior kraus, harry on. Prediction of natural frequencies of laminated curved panels. So far the equations governing the deformations and stresses of a spherical shell have only been derived under the assumption of a shell of constant thickness. However the possibility of variable shell thickness is only considered at the early stage where the straindisplacement relationships, hookes law and the equilibrium equations are separately derived.
Dynamic coupled thermoelastic response of thin spherical shells. On oneplate planets the spherical geometry of the lithospheric shell plays an important role in the. Prediction of natural frequencies of laminated curved. Naghdi, a new derivation of the general equations of elastic shells, international journal of engineering science, 1963, 1, 4, 509 crossref. Full text of nonlinear theory of thin elastic shells. What must be the minimum thickness for the bottom side plates. This work presents some results on damping aspect of coupled thermoelastic analysis, and a comparison between coupled and. As mentioned in the previous chapter of the notes on shallow shells and dmv theory, these two theories are probably the most widely used shell theory for carrying out analytical analyses of shell buckling. An introduction to the theoretical foundations and the analysis of their static and dynamic behavior. Freeform laminated doublycurved shells and panels of revolution resting on winklerpasternak elastic foundations. Measurements of the vibrational response of a spherical aluminum shell subject to changes in the interior pressure clearly demonstrate that resonance frequencies shift higher as the pressure is increased. Dynamic elastic plastic buckling of structural elements. The effect of transverse shear deformations on the bending of laminated plates. On the flexure of thin cylindrical shells and other thin sections.
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