Stresses In Shells Of Revolution Research Articles

Simplified selection of optimal shell of revolution

Relevance. Architects and engineers, designing shells of revolution, use in their projects, as a rule, spherical shells, paraboloids, hyperboloids, and ellipsoids of revolution well proved themselves. But near hundreds of other surfaces of revolution, which can be applied with success in building and in machine-building, are known. Methods. Optimization problem of design of axisymmetric shell subjected to given external load is under consideration. As usual, the solution of this problem consists in the finding of shape of the meridian and in the distribution of the shell thickness along the meridian. In the paper, the narrower problem is considered. That is a selection of the shell shape from several known types, the middle surfaces of which can be given by parametrical equations. The results of static strength analyses of the domes of different Gaussian curvature with the same overall dimensions subjected to the uniformly distributed surface load are presented. Variational-difference energy method of analysis is used. Results. Comparison of results of strength analyses of six selected domes showed that a paraboloid of revolution and a dome with a middle surface in the form of the surface of rotation of the z = - a cosh( x/b ) curve around the Oz axis have the better indices of stress-strain state. These domes work almost in the momentless state and it is very well for thin-walled shell structures. New criterion of optimality can be called “minimum normal stresses in shells of revolution with the same overall dimensions, boundary conditions, and external load”.

Field equations, equations of motion, and energy functionals for thick shells of revolution with arbitrary curvature and variable thickness from a three-dimensional theory

This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.

INTERLAMINAR STRESSES IN SHELLS OF REVOLUTION

SUMMARY A comparative study of the interlaminar stresses in shells of revolution has been made between first order shear deformation theory (FSDT), higher order shear deformation theory with thickness stretch (HSDT7), higher order shear deformation theory with higher order inplane displacement terms (HSDT9) and three-dimensional finite element (3D) models. A semi-analytical approach is used for all the models. Interlaminar stresses are evaluated using equilibrium equations in the cases of FSDT, HSDT7 and HSDT9 models as interlaminar stresses obtained from constitutive equations are not correct. For the 3D model an eight-noded quadratic quadrilateral semi-analytic solid element is used whereas for equivalent single layer (ESL) theories a three-noded isoparametric curved element is used. Crossply parabolic and hyperbolic caps subjected to uniform external pressure and a simply supported cylindrical shell subjected to an internal sinusoidal pressure are considered in the present study.

Determination of residual stresses in glass shells by a computational-experimental method

A method is proposed for determining the technological residual stresses in glass shells of revolution based on the solution of inverse problems of shell theory with proper stresses and the use of experimental data obtained by the photoelastic method.

Application of the method of removed elements to the investigation of residual stresses in thin shells of revolution made of composite materials

1. The distribution of residual stresses in the investigated shells is very nonaxisymmetric, whereas the elastic characteristics of the material of the shells are only slightly nonaxisymmetric. 2. Residual stresses attain their most substantial values at the bottoms of structures, and the most dangerous ones are circumferential residual stresses. 3. Residual stresses due to thermoelastic contraction of shells, determined theoretically, describe the distribution of residual stresses in shells only qualitatively.

Cut-out element method for experimental study of residual stresses in shells of revolution made of composite materials

Cut-out element method for experimental study of residual stresses in shells of revolution made of composite materials

Complementary methods in the problems of the state of stress in shells of revolution: PMM vol. 42, no. 4, 1978. pp. 724–730

Minimum energy and orthogonal projection methods are discussed for the problems of the state of stress in orthotropic shells of revolution, of variable thickness. The methods provide approximate solutions and make it possible to estimate their error in the energetic norm. The formulation of the orthogonal projections method which is the complementary of the minimum energy method, makes possible the estimation of the errors of the approximate solutions in the energetic norm. It was given in [1], where the above methods were also used in connection with the three-dimens-ional problems of the theory of elasticity, and for plates of constant thickness.

Non-linear discontinuity stresses in shells of revolution under internal pressure

The problem considered in this paper is the determination of the stresses near a discontinuity of thickness and meridian curvature across a circle of latitude of a thin shell of revolution under internal pressure. It is assumed that there is no discontinuity of meridian slope, but an eccentricity between the middle surfaces on the two sides of the discontinuity is included. The derivation is based upon a non-linear theory for the boundary layer stresses which is valid when the normal deflexion of the shell is of the order of the thickness. Explicit expressions for the stresses are derived, with an accuracy of order √( t r ) .

Circumferential Stresses in Pressure Vessel Shells of Revolution

Circumferential Stresses in Pressure Vessel Shells of Revolution

Closure to “Discussions of ‘Circumferential Stresses in Pressure Vessel Shells of Revolution’” (1963, ASME J. Eng. Ind., 85, pp. 216–217)

Closure to “Discussions of ‘Circumferential Stresses in Pressure Vessel Shells of Revolution’” (1963, ASME J. Eng. Ind., 85, pp. 216–217)

Membrane Stresses in Hyperboloid Shells of Revolution

Computation of membrane stresses and of corresponding deformations for hyperboloid shell of revolution under most general loading is reduced to evaluation of simple integrals; for determination of wind effects, diagrams capable of simplifying computations are presented and approximate formula is suggested.

Membrane Stresses in Hyperboloid Shells of Revolution

Computation of membrane stresses and of corresponding deformations for hyperboloid shell of revolution under most general loading is reduced to evaluation of simple integrals; for determination of wind effects, diagrams capable of simplifying computations are presented and approximate formula is suggested.

On the solution of a class of problems in membrane theory of thin shells

I t is shown that membrane stresses in shells of revolution for the class of problems for which the normal stress resultants are of the form ƒ ( z) cos θ and the shear stress resultant is of the form ƒ ( z) sin θ admit a particularly simple solution in terms of a stress function U which has earlier been considered. This fact is illustrated by solving the problem of flexure of a cantilever shell, and also the problem of a shell with hydrostatic lateral load. The formulas for the latter case are specialized to the form which they assume for an ellipsoidal shell, to enable comparison with an earlier solution of this problem.

Arithmetic and Gestalt Psychology

Previous articleNext article No AccessArithmetic and Gestalt PsychologyJohn W. DickeyJohn W. Dickey Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Elementary School Journal Volume 39, Number 1Sep., 1938 Article DOIhttps://doi.org/10.1086/457564 Views: 2Total views on this site Citations: 3Citations are reported from Crossref PDF download Crossref reports the following articles citing this article:Wilhelm Flügge Direct Stresses in Shells of Revolution, (Jan 1960): 18–107.https://doi.org/10.1007/978-3-662-01028-0_2 A SURVEY OF MATHEMATICAL EDUCATION, ETS Research Bulletin Series 1955, no.22 (Aug 2014): i–165.https://doi.org/10.1002/j.2333-8504.1955.tb00931.xWilliam A. Brownell Chapter I : Theoretical Aspects of Learning and Transfer of Training, Review of Educational Research 9, no.33 (Jul 2016): 255–273.https://doi.org/10.3102/00346543009003255