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  • 1
    Electronic Resource
    Electronic Resource
    Small strain deformations of elastic beams and rods including large deflections (1986)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 37 (1986), S. 491-513 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Eine konsistente Theorie, bei der linearelastisches Verhalten und Verzerrungen klein vorausgesetzt, jedoch große Verschiebungen und Drehungen zugelassen sind, wird auf die Verbiegung und Verdrehung eines Stabes unter Endlasten und Eigengewicht angewendet. Die Theorie ergibt Lösungen für Geometrien und Belastungen im mittleren Bereich zwischen dem Gültigkeitsbereich der infinitesimalen Theorie und jenem der strukturellen Theorien wie die Kirchhoff'sche Stabtheorie im Bereich der kleinen Verzerrungen und des linear-elastischen Verhaltens.
    Notes: Abstract A consistent theory for linear elastic behavior in which the strains are small but the displacements and rotations can be large is applied to the bending and twisting of a rod or beam by end loads and by its own weight. The theory provides solutions for geometries and loadings between those for which the infinitesimal theory applies and those for which structural theories, such as Kirchhoff s theory for rods, can be used. The results confirm the validity of Kirchhoff's rod theory within the range of small-strain, linear elastic behavior.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945427
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On pseudo-plane deformations for the neo-Hookean material (1986)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 37 (1986), S. 104-113 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Exakte Lösungen für das Problem von pseudo-ebenen finiten Deformationen eines elastischen, inkompressiblen, neo-Hookeschen Materials werden ermittelt und diskutiert. Insbesondere werden dreidimensionale Deformationen studiert, welche durch Ersetzen der Konstanten einer als bekannt vorausgesetzten ebenen Deformation mit Funktionen einer einzigen Raumvariablen erzeugt werden. Resultate für den Ersatz der Konstanten aus Translations- und Rotationsinvarianz sowie aus Dehnungen sind aufgeführt. Schließlich werden zwei spezifische Deformationen betrachtet, welche zu neuen exakten Lösungen für das neo-Hookesche Material führen.
    Notes: Abstract For finite elastic deformations of the incompressible neo-Hookean material the problem of determining exact pseudo-plane deformations is considered. In particular three dimensional deformations are examined which are generated by replacing constants of an assumed known plane deformation with functions of a single space variable. Results are given for replacement of constants arising from translational and rotational invariance and stretchings. Finally two specific deformations are considered which provide new exact solutions for the neo-Hookean material.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00955521
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Load-deformation relations in second-order elasticity (1995)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 46 (1995), S. 479-506 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A method for determining overall load-deformation relations for small-strain elastic deformations has been adapted so that second-order elastic effects can be included in certain overall quantities, such as bending stiffness, without explicit determination of the second-order solution. The approach uses Betti's Reciprocal Theorem. The strains are considered small enough that third-order effects can be neglected but there is no restriction on the magnitude of the displacements. The method is applied to obtain the resultant force and moment to second order for cylindrical bars with arbitrary cross section under torsion, extension and torsion, bending by an end load, and twisting and bending to helical form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00917440
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  • 4
    Electronic Resource
    Electronic Resource
    Small bending of a circular bar superposed on finite extension or compression (1963)
    Springer
    Archive for rational mechanics and analysis 12 (1963), S. 223-248 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary Solutions are presented for the small bending by terminal couples or by a transverse end load of a circular cylinder of incompressible isotropic material which has been initially finitely extended or compressed by axial loading. Numerical results are given for a Mooney material. The results are used to investigate the stability of a circular bar under end thrust. An elementary solution is giver for the small bending by its own weight of a stretched horizontal cylinder.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00281227
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    On certain methods in the stability theory of continuous systems (1963)
    Springer
    Archive for rational mechanics and analysis 12 (1963), S. 354-360 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00281232
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  • 6
    Electronic Resource
    Electronic Resource
    Finite deformation of elastic membranes with application to the stability of an inflated and extended tube (1961)
    Springer
    Archive for rational mechanics and analysis 7 (1961), S. 273-304 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A theory is formulated for the finite deformation of a thin membrane composed of homogeneous elastic material which is isotropic in its undeformed state. The theory is then extended to the case of a small deformation superposed on a known finite deformation of the membrane. As an example, small deformations of a circular cylindrical tube which has been subjected to a finite homogeneous extension and inflation are considered and the equations governing these small deformations are obtained for an incompressible material. By means of a static analysis the stability of cylindrically symmetric modes for the inflated and extended cylinder with fixed ends is determined and the results are verified by a dynamic analysis. The stability is considered in detail for a Mooney material. Methods are developed to obtain the natural frequencies for axially symmetric free vibrations of the extended and inflated cylindrical membrane. Some of the lower natural frequencies are calculated for a Mooney material and the methods are compared.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00250766
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Fundamental solutions for small deformations superposed on finite biaxial extension of an elastic body (1962)
    Springer
    Archive for rational mechanics and analysis 9 (1962), S. 196-224 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Infinite and semi-infinite isotropic elastic bodies in finite biaxial extension are in addition subjected to infinitesimal concentrated forces parallel and perpendicular to the extension plane respectively. In the semi-infinite case the forces are on the plane boundary. The problems are analogous to those for transversely isotropic bodies subjected to the infinitesimal concentrated forces only. Solutions to both categories of problems are given with the aid of potential functions. To facilitate the evaluation, expressions for the resultant force on a surface are given in terms of line integrals around the bounding curve. The solutions to the semi-infinite body problems are derived from those to the infinite body problems by adding appropriate potential functions so as to meet the boundary conditions on the plane surface. Computations for the semiinfinite cases of the superposition problems are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00253345
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Second and higher order effects in a class of problems in plane finite elasticity (1965)
    Springer
    Archive for rational mechanics and analysis 19 (1965), S. 189-214 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00277008
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  • 9
    Electronic Resource
    Electronic Resource
    Buchbesprechungen (1967)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 18 (1967), S. 298-300 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01596927
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  • 10
    Electronic Resource
    Electronic Resource
    Buchbesprechungen (1969)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 20 (1969), S. 430-432 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01590436
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