Deformation Of Circular Cylindrical Shells Research Articles

Elasto-Plastic Analysis of Thick Cylinders Subjected to Internal Electro-Magnetic Loading

AbstractA study of elasto-plastic deformation of circular cylindrical shells subjected to internal electromagnetic forces is presented in this paper. The five governing equations in terms of resultant forces and resultant moments with respect to basic displacement vector components u, v and w are used. Theoretical formulations, based on the first-order shear deformation theory (FSDT), take into consideration transverse shear deformation and rotary inertia. The deformation theory of plasticity is employed for constitutive equations. The cylinders are composed of an elastic-plastic material with the von Mises yield criteria and non-linear plastic behaviour. Galerkin method is employed to convert the partial differential equations (PDEs) to ordinary differential equations (ODEs). The Newmark family of methods is used to numerically time integration of system of coupled second order ODEs. In order to prove the validity of the presented method and the solving process, the results obtained with the present analysis are compared with a set of available data. Good agreement observed between the results of the two approaches. Certainly, the aim of this paper is to create a more reliable and precise mathematical model of hollow-cylinders to avoid performing several experiments.

Saint-Venant’s problem for Cosserat shells with voids

In this paper we investigate the mechanical behavior of Cosserat shells made from a material with voids. We formulate Saint-Venant’s problem for cylindrical shells and determine the solution of the relaxed problem. Then, we apply the theoretical results to study the deformation of circular cylindrical shells. We also compare the solution of Saint-Venant’s problem for Cosserat shells with corresponding results from the classical theory of shells.

Complementary energy method for cylindrical shells using second order stress functions

A new stress function-based complementary energy approach and a finite element model are developed for linear axisymmetrical deformations of circular cylindrical shells. The three-dimensional equilibrium equations and stress boundary conditions are satisfied a priori with second order stress functions without employing the Lagrange multiplier method or penalty function procedure. This can be achieved (i) by utilization of the fact that three out of the six coordinates of the second order stress function tensor can be set to zero, and (ii) by using truncated polynomial expansions for stresses and stress functions in the thickness direction. Kirchhoff-type kinematical assumptions are not applied. The second order stress functions-based equilibrium element developed satisfies the continuity requirement for surface tractions at the element boundaries and gives accurate solutions for thin and moderately thick shells. Results are compared with elasticity and shell theory solutions.

Two- and three-dimensional results for rotationally symmetric deformations of circular cylindrical shells

Previous considerations by asymptotic expansion procedures of the relation between elasticity theory results and thin-shell theory results for the case of rotationally symmetric deformations of an edge-loaded semi-infinite circular cylindrical shell are supplemented by an analysis of this problem for a shell possessing a limiting-type orthotropy, such that transverse normal strains vanish identically. It is shown that assuming this kind of orthotropy has the important benefit of allowing the derivation of exact expressions for the edge zone solution contribution, when such exact expressions are not possible for the problem of the shell with more general properties of the material. One result of the present analysis is an answer to the following question. Given a shell with arbitrarily prescribed edge displacements (compatible with the assumed type of orthotropy), what is the asymptotically exact form of the corresponding conditions for this same problem, treated within the framework of two-dimensional thin-shell theory?

On an Accurate Theory for Circular Cylindrical Shells

The accuracy of the characteristic roots obtained from solving a pair of complex conjugate fourth-order differential equations which govern the deformation of circular cylindrical shells is studied. Roots of the characteristic equations of the pair of fourth-order equations can be readily obtained in simple closed forms, unlike the Flu¨gge and other unreduced equations for circular cylindrical shells for which roots of the characteristic equations can only be found approximately by complicated numerical processes. In the present paper, roots from the pair of equations are computed for a range of significant parameters and comparisons are made with solutions based on other known equations. These results show that the pair of complex conjugate fourth-order equations has at least the same accuracy as the Flu¨gge equation and is as accurate as an equation can be within the scope of the Kirchhoff assumptions. The pair of complex conjugate governing equations for the homogeneous solutions of circular cylindrical shells is as follows: Lw=0andLw¯=0, in which L=(∇2+1)∇2+i1k∂2∂α2+k(1−ν)∂2∂β2−∂2∂α2∇2+∂2∂β2,L¯=thelinearcomplexconjugateoperatorofL,k=h2a3(1−ν2),h=thickness,a=radiusofcylinder,ν=Poisson’sratio,w=radialdisplacement. The particular solutions can be found from nonhomogeneous equation LLw¯=a4D∇4Z. It may be shown that the simplified equations, such as Donnell, Morley, Novozhilov, and other equations can be readily obtained from the present equation.

Errata: "Roots of the Cylindrical Shell Characteristic Equation for Harmonic Circumferential Edge Loading"

The roots of Fliigge's complete characteristic equation for small deformations of circular cylindrical shells loaded along the curved edges are compared with those of various widely used approximations to the equation. The roots are found to be extremely sensitive to small changes in the coefficients of the equations when the half-wave length of the circumferential variation of the applied edge load is of the order of three wall thicknesses or less. For these rapid circumferential load variations the roots of the complete equation not only deviate widely from those of the approximate equations but cease to be all complex as has been commonly supposed.

Accurate Fourth Order Equation for Circular Cylindrical Shells

A pair of complex conjugate fourth-order partial differential equations which govern the deformation of circular cylindrical shells is presented. This pair of equations has at least the same accuracy as the Flugge equation and is as accurate as an equation can be within the scope of the Kirchhoff assumptions. Because they are complex conjugates, only one of the equations need be considered. The advantage in using the present pair of equations, besides their accuracy, is that the solutions of these equations can be readily found in simple closed forms as shown in the paper. This simplifies the calculations considerably in solving problems of cylindrical shells. Unlike the accurate Flugge equation and other equally accurate equations for cylindrical shells, their solutions can only be found approximately by trial and error.

The Influence of Blast Characteristics on the Final Deformation of Circular Cylindrical Shells

Abstract The final maximum deformation of a reinforced circular cylindrical shell caused by a briefly applied, intense loading is considered. The maximum deformation is obtained in a form which requires a double quadrature of the pressure where the limits of the integration are determined from side conditions. Attempts are made to find a simple analytic approximation, but the attempts are unsuccessful for loads of practical importance. A straightforward graphical-numerical method of solution is devised. Several examples are considered in support of the conclusions. The shell is assumed to be infinitely long, so that end effects may be neglected. The load is assumed to be applied to the entire shell simultaneously. The shell is assumed a perfect cylinder, and the reinforcements are taken as rigid. Finally, the shell is assumed to be made of an ideal rigid-plastic material which satisfies a certain simplified yield condition and the associated flow rule.

円筒壁の塑性弾性変形

円筒壁の塑性弾性変形