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  • 1
    Electronic Resource
    Electronic Resource
    Diffusion through perforated membranes (1987)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 61 (1987), S. 813-816 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The diffusion process through a thin membrane, perforated by several holes of arbitrary shape, is considered. A general theorem is established which relates the total flux through each hole with the concentration distribution of some chemical species, prescribed in the hole, by a system of linear algebraic equations. The theorem is applied to the case of arbitrarily located elliptical holes. Several specific examples are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.338127
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  • 2
    Electronic Resource
    Electronic Resource
    External circular crack under arbitrary shear loading (1996)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 717-729 
    Details
    ISSN: 1420-9039
    Keywords: Linear elasticity ; external circular crack ; shear loading ; exact solution ; integral equation ; stress intensity factor ; fracture mechanics ; mixed boundary value problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An exact closed form solution in terms of elementary functions has been obtained to the governing integral equation of an external circular crack in a transversely isotropic elastic body. The crack is subjected to arbitrary tangential loading applied antisymmetrically to its faces. The recently discovered method of continuity solutions was used here. The solution to the governing integral equation gives the direct relationship between the tangential displacements of the crack faces and the applied loading. Now a complete solution to the problem, with formulae for the field of all stresses and displacements, is possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00915271
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  • 3
    Electronic Resource
    Electronic Resource
    Reissner-Sagoci problem for non-classical domains (1989)
    Springer
    Archive of applied mechanics 59 (1989), S. 422-433 
    Details
    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 Behandelt wird das Problem der Torsion eines transversal-isotropen elastischen Halbraums durch einen Stempel mit beliebiger ebener Stirnfläche. Gewonnen wird eine analytische Näherungslösung, die auf neueren Resultaten des Autors in der Potentialtheorie beruht. Eine allgemeine Beziehung zwischen Torsionsmoment und -winkel wird aufgestellt. Für Stempel mit polygonaler, rechteckiger, rhombischer bzw. kreuzförmiger Stirnfläche werden spezielle Formeln angegeben.
    Notes: Summary The problem of torsion of a transversely isotropic elastic half-space by a punch of general planform is considered. An approximate analytical solution is derived by a method based on some new results in potential theory obtained by the author earlier. A general relationship is established between the torque and the torsion angle. Some specific formulae are derived for punches having the planform of a polygon, a rectangle, a rhombus and a cross.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00534309
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  • 4
    Electronic Resource
    Electronic Resource
    Elastic half-space with several domains subjected to tangential displacements (1989)
    Springer
    Archive of applied mechanics 60 (1989), S. 73-82 
    Details
    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 Behandelt wird das gemischte Randwertproblem für einen transversal-isotropn olastischen Halbraum, wenn eine gleichmäßaige Tangentialverschiebung einiger Oberflächenbereiche beliebiger Gestalt vorgeschrieben und der Rest des Randes spannungsfrei ist. Die Aufgabenstellung kann auf zweierlei Weise interpretiert werden: Als zwei elastische Halbräume, die längs einiger beliebig gestalteter Randbereiche miteinander verbunden sind, oder als das Kontaktproblem des Halbraumes mit einigen flexiblen Stempeln, für die verschiedene Tangentialverschiebungen vorgegeben sind. Aufgestellt wird ein allgemeines Theorem, welches die resultierenden Tangentialkräfte auf allen Bereichen mit ihren Verschiebungen durch ein System linearer algebraischer Gleichungen verknüpft. Angewandt wird das Theorem auf elliptische Bereiche mit beliebiger Position und gleichförmiger Tangentialverschiebung. Einige spezielle Beispiele werden vorgestellt.
    Notes: Summary The mixed boundary value problem for a transversely isotropic elastic half-space is considered for the case when uniform tangential displacements are prescribed over several domains of arbitrary shape, and the rest of the half-space boundary is stress free. The problem can be interpreted either as that of two elastic half-spaces interconnected by several regions of general shape and subjected to remote shear loading, or as a contact problem of several flexible punches, connected to the half-space, with different tangential displacements prescribed. A general theorem is established which relates the resulting tangential forces, acting on each domain, with their generalized displacements through a system of linear algebraic equations. The theorem is applied to the case of arbitrarily located elliptical domains subjected to uniform tangential displacements. Several specific examples are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00538810
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  • 5
    Electronic Resource
    Electronic Resource
    Axisymmetric bonded punch problem: A complete solution (1990)
    Springer
    Archive of applied mechanics 60 (1990), S. 213-224 
    Details
    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: Übersieht Für die Spannungs- und Verschiebungsfelder eines transversal-isotropn elastischen Halbraums, der unter Haftbedingung von einem axialsymmetrischen Stempel belastet ist, werden explizite Formeln hergeleitet. Die dazu benutzte Methode beruht auf neueren Ergebnissen des Autors in der Potentialtheorie. Als Beispiel wird ein zentrisch belasteter, flacher Kreisstempel behandelt. Als numerische Ergebnisse werden die Verschiebungsfelder in der Umgebung eines haftenden und glatten Stempels bei gleichen Parameterbedingungen zum Vergleich vorgestellt.
    Notes: Summary Explicit expressions are derived for the field of stresses and displacements around an axisymmetric punch bonded to a transversely isotropic elastic half-space. The method is based on the new results in potential theory obtained by the author earlier. A flat centrally loaded circular punch is considered as an example. Specific computations were performed in order to compare the elastic field in the vicinity of a bonded punch with similar parameters for a smooth punch.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00577858
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  • 6
    Electronic Resource
    Electronic Resource
    Internal circular crack under normal antisymmetric loading (1991)
    Springer
    Archive of applied mechanics 61 (1991), S. 2-17 
    Details
    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 Für das Titelproblem wird hier erstmals eine vollständige Lösung mit expliziten Ausdrücken für die Spannungen und Verschiebungen im transversal-isotropen Raum mit zwei Einzellasten senkrecht zu einem Kreisriß angegeben. Die Herleitung beruht auf neueren Ergebnissen des Autors in der Potentialtheorie. Die Ergebnisse können als Greensche Funktionen für den allgemeinen Fall antisymmetrischer Relastung benutzt werden, so daß dessen vollständige Lösung durch Quadraturen darstellbar ist. Schließlich werden verschiedene Anwendungen in der Bruchmechanik betrachtet.
    Notes: Summary A complete solution is given for the first time to the title problem. Explicit expressions are derived for the field of stresses and displacements in a transversely isotropic space weakened by a penny-shaped crack and subjected to two antisymmetrically applied normal concentrated forces. The method is based on the new results in potential theory obtained by the author earlier. The presented results may be used as Green's functions for a general case of antisymmetric loading so that the complete solution can be presented in quadratures. Several specific applications to fracture mechanics are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00788133
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  • 7
    Electronic Resource
    Electronic Resource
    On the potential flow through membranes (1985)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 36 (1985), S. 616-623 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Une membrane est modelée comme un plan impérmeable perforé parN trous de rayons arbitraires, qui ne se croisent pas. L'action réciproque entre les trous est etudiée à l'aide d'une représentation spéciale de la fonction de Green sous forme d'un intégral. Le flux à travers chaque trou est déterminé explicitement par un système d'équations algébriques linéaires, développées pour ce modèle. Plusieurs exemples de configurations spécifiques des trous sont considérés.
    Notes: Abstract A membrane is modelled as an impermeable plane perforated byN nonintersecting holes of arbitrary radii. The interaction between the pores is investigated using a special integral representation of the Green's function. The flux through each pore is determined explicitly through the system of linear algebraic equations developed for this model. Examples of specific hole configurations are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945301
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  • 8
    Electronic Resource
    Electronic Resource
    Mixed boundary value problem of potential theory in toroidal coordinates (1991)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 42 (1991), S. 680-707 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A new approach is presented for solving the title problems. The method presents further extension of previously obtained results to the case of toroidal coordinates. The method allows us to solve non-axisymmetric problems exactly and in closed form, with no integral transform or special function expansions involved. Some integrals of fundamental value, involving distances between several points, are established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00944766
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  • 9
    Electronic Resource
    Electronic Resource
    Dirichlet problem for an annular disk (1993)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 44 (1993), S. 333-347 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A general formulation is given for the first time to the title problem. The method is based on the new results in potential theory obtained by the author earlier. The problem is reduced to a two-dimen-sional integral equation with an elementary non-singular kernel. Several specific examples are considered. Exact solution has been obtained in terms of the iterated kernel.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00914289
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  • 10
    Electronic Resource
    Electronic Resource
    Continuation of some solutions in potential theory and their applications to elastic contact and crack problems (1993)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 44 (1993), S. 909-922 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The following mixed boundary value problem is considered: arbitrary tangential displacements are prescribed inside a circle, while the tangential and normal stresses outside the circle are zero. In this case, a direct and simple formula is derived for the tangential displacements outside the circle in terms of prescribed displacements inside, thus making the tangential displacement known all over the boundary. The original problem is no longer mixed, and the complete solution becomes readily available. Another solution for the case, when arbitrary tangential displacements are prescribed outside a circle, is derived in a similar manner. The reciprocal theorem is used to derive the continuation formulae for the tangential stresses inside and outside a circle. Application of these results to contact and crack problems is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00942816
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