The Creep of Moderately Thick Shells of Revolution Under Axisymmetrical Load

Takezono, Shigeo; Uchida, Katsuaki

doi:10.1007/978-3-642-81598-0_7

Cited by 9 publications

(10 citation statements)

References 9 publications

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“…1-3 (the solid lines represent the solution obtained by our technique, and the triangles stand for the solution from [17]). Figures 1 and 2 show how the meridional (σ zz ) and hoop (σ ϕϕ ) stresses, respectively, change across the thickness in the section z = 0.1756 m. The variation of the radial displacement u r along the length is demonstrated in Fig.…”

Section: Finite-element Solution Algorithm For Thermoviscoelastoplastmentioning

confidence: 99%

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On finite-element solution of spatial thermoviscoelastoplastic problems

Lelyukh

Shevchenko

2006

Int Appl Mech

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A finite-element algorithm is proposed for the analysis of the thermoviscoelastoplastic stress-strain state of bodies under complex loading (thermal and mechanical). It is assumed that an arbitrary element of the body deforms along a rectilinear or slightly curved path. The three-dimensional stress-strain state of the body's elements is determined using the iterative method of additional strains. The technique is tested by analyzing the three-dimensional viscoelastic stress-strain state of a hollow cylinder and the thermoplastic state of a disk Keywords: thermoviscoelastoplastic stress-strain state, finite-element technique, iterative method of additional strains, viscoelastic stress-strain state, hollow cylinder, thermoplastic state, diskThe finite-element method (FEM) is one of the most universal numerical methods for solving boundary-value problems. It allows doing structural analysis with regard to physical nonlinearity. However, the finite-element solution of spatial problems frequently involves significant technical difficulties associated with the implementation of efficient discretization algorithms; therefore, spatial objects are, as a rule, designed in a simplified formulation (axisymmetric or plane) [13][14][15][16]. The performance of the FEM can be improved by combining it with the variable separation method. This approach is called the semianalytic finite-element method (SFEM) [6]. Its application domain is limited to homogeneous bodies of revolution and prismatic bodies with hinged ends. The recently developed moment scheme of the SFEM has greatly expanded the range of problems solved by this method [1][2][3]12]. Moreover, the recent advances in computer technology make it possible to further develop the finite-element displacement method to solve nonlinear spatial problems of solid mechanics. When combined with efficient algorithms of successive approximations, such as different modifications of the Newton-Raphson method, this approach is distinguished by a relatively simple and clear procedure of deriving the discrete kinematic relations for unknown variables and the governing equations. Moreover, the spatial formulation of the problem imposes almost no restrictions on the geometry of the object of interest and on the type and spatial distribution of loads. The present paper addresses a finite-element technique of solving a three-dimensional thermoviscoelastoplastic stress-strain problem for three-dimensional bodies.1. Problem Formulation and Governing Equations. Consider, in an orthogonal curvilinear coordinates σ ϕϕ , an isotropic deformable solid of volume V bounded by a surface Σ. Suppose that at the initial point in time t = 0, the body, which is in natural stress-strain-free state at a temperature T 0 , begins to be subjected to nonuniform heating, body forces q i , and surface forces q i acting on a portion Σ t of the surface. The other portion Σ u of the surface can be fixed in a certain fashion, i.e., displacements r u can be prescribed on it. Suppose that the strain paths of an arbitrar...

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Section: Finite-element Solution Algorithm For Thermoviscoelastoplastmentioning

confidence: 99%

“…Numerical Results. To test our technique, let us determine, as a first example, the viscoelastic stress-strain state of a hollow cylinder [17]. By symmetry, it is sufficient to examine half a sector of ϕ =6°.…”

Section: Finite-element Solution Algorithm For Thermoviscoelastoplastmentioning

confidence: 99%

On finite-element solution of spatial thermoviscoelastoplastic problems

Lelyukh

Shevchenko

2006

Int Appl Mech

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“…Eq. (15) will be used in the following analyses of the creep deformation in a thin-walled shell made from a material with the same behavior in tension and compression to test the proposed below numerical integration algorithm against the numerical data by Takezono and Fujioka (1981) based on the power function of the hardening measure in the creep description.…”

Section: Constitutive Modelmentioning

confidence: 99%

“…However, they assumed the same creep deformation and same creep damage development in tension and compression for the materials of shells (Altenbach and Naumenko, 1997;Hayhurst, 1981;Hyde et al, 2003;Kojic and Bathe, 1987;Miuazaki, 1987;Morachkovskii and Zolochevskii, 1980;Penny and Marriott, 1995;Rabotnov, 1969;Shariyat and Eslami, 1996;Sichov, 1998Sichov, , 2003Takezono and Fujioka, 1981;Zolochevskii and Morachkovskii, 1982;Morachkovsky, 1978, 1979). For the first time, the creep deformation of shells with non-branched meridian taking into account different behavior of materials in tension and compression has been analyzed by Zolochevsky (1980Zolochevsky ( , 1982, and subsequently by Betten and Borrmann (1987) and Altenbach and Zolochevsky (1991).…”

Section: Introductionmentioning

confidence: 96%

Analysis of creep deformation and creep damage in thin-walled branched shells from materials with different behavior in tension and compression

Zolochevsky

Galishin

Sklepus

et al. 2007

International Journal of Solids and Structures

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A constitutive model for describing the creep and creep damage in initially isotropic materials with different properties in tension and compression has been applied to the modeling of creep deformation and creep damage growth in thinwalled shells of revolution with the branched meridian. The approach of establishing the basic equations for axisymmetrically loaded branched shells under creep deformation and creep damage conditions has been introduced. To solve the initial/boundary-value problem, the fourth-order Runge-Kutta-Merson's method of time integration with the combination of the numerically stable Godunov's method of discrete orthogonalization is used. The solution of the boundary value problem for the branched shell at each time instant is reduced to integration of the series of systems of ordinary differential equations describing the deformation of each branch and the shell with basic meridian. Some numerical examples are considered, and the processes of creep deformation and creep damage growth in a shell with non-branched meridian as well as in a branched shell are analyzed. The influence of the tension-compression asymmetry on the stress-strain state and damage evolution in a shell with non-branched meridian as well as in a branched shell with time are discussed.

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“…[4,5,14,26,28]. However, little effort has been made for studies on the applicability of shell models to the creep-related CDM.…”

Section: Introductionmentioning

confidence: 98%

On the use of solid- and shell-type finite elements in creep-damage predictions of thinwalled structures

Altenbach

Kushnevsky

Naumenko

2001

Archive of Applied Mechanics (Ingenieur Archiv)

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Solid-and shell-type ®nite elements available for plasticity and creep analysis are applied to the creep-damage prediction of a thinwalled pipe bend under uniform internal pressure. Conventional creep-damage material model with scalar damage parameter is used. Based on the comparative numerical study, performed using solid and shell elements, the applicability frame of the shell concept is discussed. Particularly, if a dependence on the stress state is included in the material model, the cross-section assumptions of the ®rst-order shear deformation theory should be re®ned. The possibilities to modify the through-thickness approximations are demonstrated on the beam equations. The ®rst-order shear-deformation beam theory is discussed in detail. It is shown that if the damage evolution signi®cantly differs for tensile and compressive stresses, the classical parabolic transverse shear-stress distribution and the shear-correction coef®cient have to be modi®ed within time-step simulations.Key words Creep-damage analysis, pipe bend, ®nite element, beam IntroductionThe continuum damage mechanics (CDM) and the ®nite element (FE) method provide basic tools for the stress analysis and the life-time prediction of thinwalled structures exposed to elevated temperatures. Starting from the material science and the continuum mechanics, various models are proposed. They include physically based state variables and consider stressstate dependence, e.g., different sensitivity of the damage evolution to tension or compression stresses as well as damage-induced anisotropy, [27]. Since such models allow for more realistic predictions of the material behaviour at elevated temperatures, the question arises how accurate the available structural models of beams, plates or shells and the corresponding FE implementations represent the time-dependent stress redistributions. With respect to the analysis of thinwalled structures, two possibilities are available. The ®rst one is the use of general three-dimensional equations and solid FEs in the numerical analysis. The second one is the application of shell equations and shell-based FEs, usually of the Reissner±Mindlin type, [18]. The solid concept can be considered as general for structural analysis, particularly for studying damage effects. However, the numerical effort for the approximate solving of threedimensional equations is not comparable with that for the shell theory. In addition, the shell theory allows to simplify the general geometrically nonlinear analysis, since the magnitude of the deformation can be estimated by the magnitude of the rotation of the normal to the midsurface, [17]. Since the creep behaviour of metals and alloys is usually characterised by small strain developing with time at moderate stresses, the simpli®ed shell equations (including the geometrically nonlinear terms in the sense of moderate rotations) can be applied, [2].

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The Creep of Moderately Thick Shells of Revolution Under Axisymmetrical Load

Cited by 9 publications

References 9 publications

On finite-element solution of spatial thermoviscoelastoplastic problems

On finite-element solution of spatial thermoviscoelastoplastic problems

Analysis of creep deformation and creep damage in thin-walled branched shells from materials with different behavior in tension and compression

On the use of solid- and shell-type finite elements in creep-damage predictions of thinwalled structures

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