Anisotropic cylindrical shell element based on discrete Kirchhoff theory

Murthy, Sridhara S; Gallagher, Richard H.

doi:10.1002/nme.1620191207

Cited by 17 publications

(2 citation statements)

References 8 publications

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“…The method of discretizing the Kirchhoff-Love hypotheses was first proposed in [8] and was then widely used in designing thin plates and shells [5,7,15].…”

Section: A Methods For Solving Geometrically Nonlinear Problems For Ormentioning

confidence: 99%

Stress–Strain State of Flexible Orthotropic Cylindrical Shells with a Reinforced Circular Hole

2015

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The stress-strain state of flexible orthotropic cylindrical shells with a reinforced circular hole under static loading is analyzed numerically. The incremental-loading procedure, modified Newton-Kantorovich method, and finite-element method are used. The effect of geometrical nonlinearity, the orthotropy of the material, and the stiffness of the reinforcement in a shell subject to uniform internal pressure on the distribution of stresses, strains, and displacements along the hole edge and in the zone of their concentration is studied Keywords: flexible orthotropic cylindrical shell, geometrical nonlinearity, stress concentration, reinforced circular hole, finite deflections, internal pressureIntroduction. Traditionally, a shell with a reinforced hole is considered as a structure that consists of the shell proper and a one-dimensional thin rod reinforcing it. The stress-strain state (SSS) of each of these components is described by an applied theory and has its peculiarities. Therefore, the development of a theory that describes the SSS of shells with reinforced holes involves difficulties associated with the necessity of describing the combined action of components with different dimensionality and satisfying the interface conditions [4,7]. Note that the same difficulties are encountered in studying the SSS of ribbed shells [3,6,12,17].Most results on stress concentration in isotropic and anisotropic shells with reinforced holes were obtained by solving linear elastic problems with analytic, variational, and numerical methods and are reviewed in [4,7,11,16].Much fewer studies are concerned with nonlinear boundary-value problems of stress concentration, but mainly for shells of revolution under an axisymmetric load [4, 10, 13].Very few publications report on solution of nonlinear two-dimensional problems for shells with reinforced holes. For example, the effect of plastic strains and finite deflections on the SSS of isotropic shells with a reinforced curved hole was analyzed in [7,20]. A nonclassical approach to the design of thin composite shells with reinforced curved holes that employs the same formulas for the shell and the reinforcement was proposed in [14], where some numerical results on the nonlinear deformation of a flexible orthotropic cylindrical shell with a reinforced circular hole under uniform internal pressure are presented.It is of considerable interest to study the effect of a reinforced hole on the stability of composite shells [9,18,19].In what follows, we will use the approach described in [14] to formulate geometrically nonlinear problems for thin orthotropic cylindrical shells with a reinforced circular hole, outline a numerical method for solving this class of problems, and study the effect of geometrical nonlinearity, the orthotropy of the material, and the stiffness of the reinforcement on the distribution of displacements, strains, and stresses in the zone of their concentration.1. Problem Formulation. Basic Nonlinear Equations. Consider a thin cylindrical shell of radius R and thicknes...

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“…The method of discretizing the Kirchhoff-Love hypotheses was first proposed in [8] and was then widely used in designing thin plates and shells [5,7,15].…”

Section: A Methods For Solving Geometrically Nonlinear Problems For Ormentioning

confidence: 99%

Stress–Strain State of Flexible Orthotropic Cylindrical Shells with a Reinforced Circular Hole

2015

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“…They considered isotropic as well as multilayered anisotropic materials. Sridhara murthy and Gallagher [7] applied a triangular thin shell element, based on Discrete Kirchhoff Theory with three nodes and 27 dof to the analysis of an orthotropic cylinder with a circular hole subjected to axial tension. Han and Gould [8] developed and applied a special finite element model that combined an axisymetric shell element, a general shell element and a transition element to the problem of cylindrical shell with a circular cutout under axial tension.…”

Section: Introductionmentioning

confidence: 99%

An Improved Finite Element Model to Study Stress Concentration Around an Elliptical Cutout in Pressure Vessel : Application- Part II

R. Vijayakumar,

G. Ramamurthy,

K.M. Rao

et al. 2023

joast

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The application of finite element method (FEM) to the solution of cutout and inclusion problems in Filament Wound Fibre Reinforced Plastic (FWFRP) pressure vessel is considered. The analysis of pressurised laminated composite shell, which can be regarded as a heterogeneous body consisting of a finite number of orthotropic layers bonded together, with an elliptical hole is carried out. The influence of uniform shear force distribution along the hole boundary is studied. The numerical results of pressurised laminated composite shell with transverse elliptical hole filled by edge bonded elastic cover are also presented. Predicted stress distribution through the thickness of composite shell with cutout/inclusion at critical locations on the hole boundary is presented in graphical form and discussed.

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A survey of recent shell finite elements

Yang

Saigal

Masud

et al. 2000

Int. J. Numer. Meth. Engng.

266

126

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Since the mid-1960s when the forms of curved shell "nite elements were originated, including those pioneered by Professor Gallagher, the published literature on the subject has grown extensively. The "rst two present authors and Liaw presented a survey of such literature in 1990 in this journal. Professor Gallagher maintained an active interest in this subject during his entire academic career, publishing milestone research works and providing periodic reviews of the literature. In this paper, we endeavor to summarize the important literature on shell "nite elements over the past 15 years. It is hoped that this will be a be"tting tribute to the pioneering achievements and sustained legacy of our beloved Professor Gallagher in the area of shell "nite elements. This survey includes: the degenerated shell approach; stress-resultant-based formulations and Cosserat surface approach; reduced integration with stabilization; incompatible modes approach; enhanced strain formulations; 3-D elasticity elements; drilling d.o.f. elements; co-rotational approach; and higher-order theories for composites.

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Anisotropic cylindrical shell element based on discrete Kirchhoff theory

Cited by 17 publications

References 8 publications

Stress–Strain State of Flexible Orthotropic Cylindrical Shells with a Reinforced Circular Hole

Stress–Strain State of Flexible Orthotropic Cylindrical Shells with a Reinforced Circular Hole

An Improved Finite Element Model to Study Stress Concentration Around an Elliptical Cutout in Pressure Vessel : Application- Part II

A survey of recent shell finite elements

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