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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 7 (1990), S. 89-105 
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The viscoplastic deformation behavior of the shell is governed by any of the more recently proposed unified constitutive models with internal state variables and with the assumption that the total strain rate tensor can be decomposed additively into an elastic and an inelastic part. For the numerical analysis of viscoplastically deformed shells we use a hybrid strain finite element based on a geometrically linear theory of inelastic shells proposed by Kollmann and Mukherjee (1985). This theory gives the reduction of a two-field variational principle originally proposed by Oden and Reddy (1974) for elastic shells to the shell midsurface. It contains strain and displacement rates as variables to be independently varied. The shell formulation of this variational principle is the basis for the present work. First, a general hybrid finite element model is derived in which the shape functions for the strain and displacement rates can be polynomials of different order. Here we use the term “hybrid” in the sense of Pian (1988), i.e. in our two-field finite element the strain rates are condensed statically on the element level, leaving nodal displacements as the only unknowns in the final matrix equation. Then the finite element model is specialized for an axisymmetrically loaded conical shell with linear approximation of the strain rate field and quadratic interpolation of the displacement rates. Special emphasis is given to the derivation of the inelastic pseudo-forces and pseudo-moments. Numerical results for elastically and viscoplastically deformed shells are presented, where viscoplastic deformations are described by Hart's (1976) constitutive model.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 21 (1998), S. 512-525 
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The paper is concerned with large viscoplastic deformations of shells when the constitutive model is based on the concept of unified evolution equations. Specifically the model due to Bodner and Partom is modified so as to fit in the frame of multiplicative viscoplasticity. Although the decomposition of the deformation gradient in elastic and inelastic parts is employed, no use is made of the concept of the intermediate configuration. A logarithmic elastic strain measure is used. An algorithm for the evaluation of the exponential map for nonsymmetric arguments as well as a closed form of the tangent operator are given. On the side of the shell theory itself, the shell model is chosen so as to allow for the application of a three-dimensional constitutive law. The shell theory, accordingly, allows for thickness change and is characterized by seven parameters. The constitutive law is evaluated pointwise over the shell thickness to allow for general cyclic loading. An enhanced strain finite element method is given and various examples of large shell deformations including loading-unloading cycles are presented.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper we discuss and compare three types of 4-node and 9-node finite elements for a recently formulated finite deformation shell theory with seven degrees of freedom. The shell theory takes thickness change into account and circumvents the use of a rotation tensor. It allows for the applicability of three-dimensional constitutive laws and equipes the configuration space with the structure of a vector space. The finite elements themselves are based either on a hybrid stress functional, on a hybrid strain functional, or on a nonlinear version of the enhanced strain concept. As independent variables either the normal and shear resultants, the strain tensor related to the deformation of the midsurface, or the incompatible enhanced strain field are taken as independent variables. The fields of equivalence of these different formulations, their limitations as well as possible improvements are discussed using different numerical examples.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 54 (1984), S. 355-367 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es wird die Reaktion einer dünnen Kreiszylinderschale aus elastisch-viskoplastischem Werkstoff auf eine Belastung durch Innendruck untersucht. Es werden kleine Verschiebungen und die Gültigkeit der kinematischen Hypothese von Love-Kirchhoff vorausgesetzt. Ferner wird angenommen, daß das inelastische Verhalten des Werkstoffs durch ein einheitliches konstitutives Gesetz mit inneren Zustandsvariablen beschrieben wird, wobei der Tensor der Gesamtverzerrungen additiv in einen elastischen und einen inelastischen Anteil aufgespalten werden kann. Unter diesen Voraussetzungen wird die Differentialgleichung für die Radialverschiebung abgeleitet. Für sie wird eine allgemeine Lösung mittels Variation der Konstanten ermittelt und an verschiedene Randbedingungen angepaßt. Bei der Lösung inelastischer Probleme muß der gesamte Belastungspfad verfolgt werden. Dies führt auf ein Anfangswertproblem. Dieses Anfangswertproblem wird für das Werkstoffgesetz von Hart formuliert und numerisch mittels eines impliziten Zeitintegrationsverfahrens gelöst. Abschließend werden numerische Ergebnisse vorgestellt.
    Notes: Summary The response of a thin cylindrical shell of elastic-viscoplastic material to internal pressure is considered. Small displacements and the validity of the kinematical Love-Kirchhoff-hypothesis are presupposed. Further it is assumed that the inelastic behavior of the shell material is governed by a unified constitutive model with internal state variables, where the total strain tensor can be decomposed additively into an elastic and an inelastic part. Under these assumptions the governing differential equation for the radial displacement is derived. A general solution is obtained by the method of variation of parameters and adjusted to different boundary conditions. Solution of inelastic problems requires tracing of the entire loading path which leads to an initial value problem. This initial value problem is formulated for Hart's constitutive model and solved numerically by an implicit time integration procedure. Finally numerical results are presented.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 35 (1966), S. 10-16 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Summary The conditions of compatibility for shells are derived from the vanishing of all components of the Riemann curvature tensor, calculated for the deformed shell continuum. Transverse shear strains and transverse normal strains considered one gets six equations of compatibility. These reduce to three well known equations of compatibility for Love's approximate theory, if transverse shear and transverse normal strains are neglected.
    Notes: Übersicht Die Kompatibilitätsbedingungen der Schalentheorie werden aus der Forderung hergeleitet, daß sämtliche Komponenten des Riemannschen Krümmungstensors für das deformierte Schalenkontinuum verschwinden. Unter Berücksichtigung von Schubverformungen und Querdehnung der Schale ergeben sich sechs Kompatibilitätsbedingungen. Diese gehen bei vernachlässigter Schubverformung und Querdehnung in die drei bekannten Kompatibilitätsbedingungen der Loveschen Approximation über.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 56 (1986), S. 254-264 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: übersicht Der Aufsatz gibt eine exakte Theorie des rotierenden elasto-plastischen Preßverbandes unter den Voraussetzungen infinitesimaler Verzerrungen, idealer Plastizität und der Gültigkeit der Trescaschen Fließbedingung. Die plastischen Dehnungsinkremente werden nach der zugeordneten Fließregel berechnet. Ferner wird vorausgesetzt, daß die Welle während der vollständigen Belastungsgeschichte rein elastisch bleibt. Es wird gezeigt, daß unterhalb einer Grenzdrehzahl die plastische Deformation von nur einer Seite des Trescaschen Sechsecks bestimmt wird. Oberhalb dieser Drehzahl wird eine zweite Seite des Trescaschen Sechsecks beteiligt. In diesem Fall müssen plastische Vordehnungen berücksichtigt werden, die unterhalb der Grenzdrehzahl entstanden. Für beide Drehzahlbereiche werden Lösungen abgeleitet, welche Spannungen und Radialverschiebung umfassen. Schließlich wird ein numerisches Beispiel angegeben.
    Notes: Summary The paper gives a rigorous theory of rotating elasto-plastic shrink fits under the assumptions of infinitesimal strain, ideal plasticity and validity of Tresca's yield condition. The plastic strain increments are computed by the associated flow rule. Furthermore, it is assumed that the shaft remains purely elastic during the entire loading history. It is shown that, below a limit speed, the plastic deformation is governed by one side of the Tresca hexagon only. Beyond this speed, a second face of Tresca's hexagon becomes involved. In this case plastic prestrains accumulated below the limit speed have to be considered. For both speed regimes, solutions comprising stresses and radial displacement are obtained. Finally a numerical example is given.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 31 (1962), S. 250-257 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 31 (1962), S. 384-384 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 35 (1967), S. 362-370 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Summary In an infinite elastic body possessing spherical transversal isotropy the surface of a sphere around the origin is subjected to constant pressure. Laplace's transformation is applied to the equation for the radial displacements. The solution in the subdomain is constructed with aid of modified Bessel functions of the second kind, the order of which depends on the elastic stiffnesses. If the strain energy is positive definite, the elastic stiffnesses are submitted to certain inequalities. Therefore the solution in the subdomain possesses no singularities in the positive half of the complex domain and on the imaginary axis with exception of the origin. By use of the inversion theorem of Laplace's transformation the solution in the time domain is derived. For a special choice of the elastic stiffnesses numerial results are given.
    Notes: Übersicht In einem unendlichen elastischen Körper mit sphärisch transversaler Isotropie wird die Oberfläche einer um den Ursprung geschlagenen Hohlkugel mit konstantem Druck belastet. Die die Wellenausbreitung beschreibende Differentialgleichung wird der Laplace-Transformation unterworfen. Die Bildlösung baut sich aus modifizierten Besselfunktionen zweiter Art auf, deren Zeiger von den elastischen Konstanten abhängt. Ist die Formänderungsenergie des Körpers eine positiv definite quadratische Form, so gelten für die elastischen Konstanten einschränkende Ungleichungen. Sind diese erfüllt, so ist die Bildlösung in der positiven Halbebene und auf der imaginären Achse mit Ausnahme des Ursprungs regulär. Mit Hilfe des Umkehrintegrals der Laplace-Transformation kann die Lösung im Oberraum berechnet werden. Diese Lösung wird numerisch ausgewertet für spezielle Werte der elastischen Konstanten.
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary First, a detailed survey of kinematics of finitely deformed inelastic solids is given. The concept is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts. Since the intermediate configuration is chosen to be isoclinic as suggested by Mandel, this decomposition is unique. In a systematic manner, deformation tensors and strain tensors can be introduced. It is shown that a decomposition of the deformation rate tensor into elastic and inelastic parts is not unique and a kinematic relationship is established between two different definitions of the inelastic part of the deformation rate tensor. In this paper, all the kinematic quantities needed for the description of finite deformations with inelastic constitutive models are derived. Next, a general constitutive theory for finitely deformed viscoplastic materials is given for materials which are structurally isotropic. The elastic part of the model is assumed hyperelastic. The inelastic constitutive equations are based on the concept of internal variables. They are formulated on the intermediate configuration and mapped to the current configuration. The inelastic constitutive frame is specified for a model originally proposed by Brown, Kim and Anand. Further, the implications of small elastic strains are investigated. An improved approximation for the inelastic incompressibility constraint is derived. Numerical experiments for simple shear using different elastic models demonstrate the importance of a sufficiently accurate consideration of the inelastic incompressibility constraint.
    Type of Medium: Electronic Resource
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