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  • 1
    Electronic Resource
    Electronic Resource
    Integral representations for a nonhomogeneous region in couple stress theory of elasticity (1973)
    Springer
    Flow, turbulence and combustion 27 (1973), S. 133-144 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In an infinite space a Cosserat medium (with forced rotations) is subjected to a singular concentrated force. The medium is nonhomogeneous and consist of two regular regions where the elastic constants differ. Formulas are derived for the displacements in both the internal and the external region. With the help of this Green's function matrix integral representations are derived for the displacements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00382483
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  • 2
    Electronic Resource
    Electronic Resource
    Singular solutions and Green's method in micropolar theory of elasticity (1972)
    Springer
    Flow, turbulence and combustion 25 (1972), S. 65-82 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The matrices of fundamental solutions are constructed for a concentrated force as well as a concentrated couple varying harmonically in time and acting in an unbounded micropolar elastic continuum. These solutions are then used to obtain solutions for some other loading singularities. Integral representations, for the displacement and the rotation vectors are obtained by making use of the basic singular solutions. The formal solutions to two fundamental boundary value problems are expressed in terms of integrals which include given surface and body data and Green's functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00382285
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  • 3
    Electronic Resource
    Electronic Resource
    Some problems in plane elastic dielectrics (1976)
    Springer
    Journal of elasticity 6 (1976), S. 295-311 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung Durch Anwendung der Assoziativ-Matrizen-Methode werden Galerkinische Darstellungen für den Verschiebungsvektor, den Polarisierungsvektor und die potentiellen Prüffelder einer statischen ebenen Theorie des elastischen Dielektrikums entwickelt. Von den singulären Lösungen der harmonischen, biharmonischen und Helmholtz-Gleichungen werden grundlegende Matrizenlösungen für das unendliche, ebene und elastische Dielektrikum, das durch konzentrierte Raumkräfte, elektrische Kräfte und Ladungsdichte beansprucht wird, abgeleitet. Unter Verwendung der Randwert-OperatorenY, Z, M, der grundlegenden Matrizen-Lösungen und Betti's Formel, wird eine Spezial-Matrize Λ(x, y) konstruiert und eine Integraldarstellung für (u 1,u 2,P 1,P 2, ϕ) erhalten. Unstetigkeitssätze werden für das Doppelschicht-Potential und denQ-Operator eines einschichtigen Potentials angeführt. Durch Anwendung dieser Sätze werden die Lösungen der inneren und äusseren Grenzwertprobleme zur Lösung eines Systems von fünf singulären Integralgleichungen reduziert. Der Index eines der Systeme wird als Null bewiesen und es wird die Schlussfolgerung gezogen, dass der Fredholmsche Satz und seine Alternativen fur diese Theorie anwendbar sind.
    Notes: Abstract Representations of Galerkin type are obtained for the displacement vector, polarization vector and the potential fields in the static plane theory of elastic dielectrics using the method of associated matrices. Fundamental matrix solutions of an infinite elastic dielectric plane subjected to a concentrated body force, electric force and charge density are derived from the singular solutions of harmonic, biharmonic and Helmholtz equations. Using boundary operatorsY, Z, M, the fundamental matrix solutions, and Betti's formulae, a matrix Λ(x, y) is constructed and an integral representation for (u 1,u 2,P 1,P 2, ϕ) is obtained. Discontinuity theorems are stated for the double layer potential andQ operator of the single layer potential. By means of these theorems, the solutions of interior and exterior boundary value problems are reduced to the solution of a system of five singular integral equations. The index of one of the systems is shown to be zero and it is concluded that Fredholm theorems and its alternatives hold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00041723
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  • 4
    Electronic Resource
    Electronic Resource
    Solution of the problem of a concentrated torque on a semi-space by similarity transformations (1983)
    Springer
    Journal of elasticity 13 (1983), S. 87-90 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Similarity transformations are constructed and used to obtain an exact solution for the axisymmetric boundary value problem of a homogeneous isotropic elastic semi-space subjected to a concentrated torque normal to its surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00041317
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  • 5
    Electronic Resource
    Electronic Resource
    Matrix inversions and singular solutions in the linear theories of elasticity (1974)
    Springer
    Journal of elasticity 4 (1974), S. 235-242 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Elementary matrix multiplications and inversions lead to Galerkin type representations for the steady-state vibration equations of linear classical elasticity, thermoclasticity, Mindlin's couple stress and Eringen's micropolar theories of elasticity. The use of representations and the equations satisfied by potentials is further illustrated by obtaining singular solutions. Some of the results agree with known solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00049266
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  • 6
    Electronic Resource
    Electronic Resource
    Stresses set up by rotation in limacon-shaped blades (1980)
    Springer
    Journal of engineering mathematics 14 (1980), S. 1-16 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary This paper deals with finding the stresses in steadily rotating limacon-shaped thin blades of homogeneous isotropic elastic material. The complex potentials, involving real parameters, have been obtained in closed form. Giving suitable values to the parameters involved, the solutions are derived for the following four positions of the axis of rotation: (a) the line of symmetry of the limacon, (b) any line perpendicular to the line of symmetry and lying in the plane of the blade, (c) any line passing through a point on the line of symmetry and perpendicular to the plane of the blade, (d) normal axis passing through the centroid. The hoop stress and its stationary points have been calculated in all the cases. The results have also been derived for circular blades. The numerical results are presented in the form of tables and graphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00042861
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  • 7
    Electronic Resource
    Electronic Resource
    Similarity transformations for the axisymmetric Boussinesque's problem (1987)
    Springer
    Acta mechanica 68 (1987), S. 171-183 
    Details
    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 Lie's infinitesimal transformation groups, which leave the basic equations of axially symmetric problems of classical elasticity invariant, are constructed. For the case of the axisymmetric Boussinesque's problem of an elastic semi-space subjected to a point force applied normal to its surface, the invariance of boundary and boundary conditions leads to the explicit form of similarity transformations which are used to solve the problem. Expressions for the displacements and stresses derived by this approach, which is believed to be new, are found to agree with the known results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01190881
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  • 8
    Electronic Resource
    Electronic Resource
    Potential methods in the linear couple-stress theory of elasticity (1972)
    Springer
    Acta mechanica 15 (1972), S. 165-176 
    Details
    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
    Description / Table of Contents: Zusammenfassung Die Matrix der Fundamentallösungen wird hergeleitet und zur Angabe einer Integraldarstellung des Verschiebungsvektors und der Feldgleichungen der linearen Momentenspannungstheorie verwendet. Das dynamische Volumspotential sowie die Oberflächenpotentiale der einfachen und der Doppelschicht werden definiert und das Analogon zur Poissonschen Formel erhalten. Formale Lösungen von zwei Randwertproblemen werden in Form von Greensche Matrizen enthaltenden Integraldarstellungen angegeben.
    Notes: Summary The matrix of fundamental solutions is constructed and used to obtain an integral representation for the displacement vector of the field equations of linear couple stress theory. The dynamic volume potential and single and double layer surface potentials are defined and the analogue of Poisson formula is obtained. The formal solutions to two fundamental boundary value problems are expressed by integral representations involving Green's matrices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01304290
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  • 9
    Electronic Resource
    Electronic Resource
    On the axisymmetric Mindlin's problem for a semi-space of granular material (1987)
    Springer
    Acta mechanica 66 (1987), S. 145-159 
    Details
    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 The methods of images and Hankel transforms are used to construct solution to an axisymmetric boundary value problem of a semi-space of transversely isotropic (granular) material due to a point force applied at a distanceh beneath its stress free plane boundaryz=0. Exact closed form expressions are determined for the components of displacements and stresses throughout the interior of the granular semi-space. The solution is then used to derive the surface displacements due to a uniformly distributed force over a circle of radius ‘a’ with centre at (0, 0, −h) in the planez=−h of the semi-space. By a suitable choice of material constants and through a limit process as α1, α2 approach 1, the granular semi-space becomes isotropic and the corresponding results derived in this particular case agree with those presented in [14].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01184290
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  • 10
    Electronic Resource
    Electronic Resource
    On a boundary value problem for an elastic dielectric half-plane (1980)
    Springer
    Acta mechanica 37 (1980), S. 65-74 
    Details
    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
    Description / Table of Contents: Zusammenfassung Auf der Basis von Mindlins Theorie des elastischen Dielektrikums und mit Benutzung der Papkovitch-Darstellungen für Verschiebungs- und Polarisationsvektoren wird mit Hilfe von Fourier-Transformationen eine allgemeine Lösung für Randwertprobleme einer Halbebene mit einer beliebigen Ladungsverteilung gefunden. Es werden explizite Ausdrücke für verschiedene mechanische und elektrische Potentiale für eine Punktladung an der Berandung des elastischen, dielektrischen Halbraums erhalten.
    Notes: Summary Using Papkovitchtype representations for the displacement and polarization vectors and Fourier transforms, a general solution to boundary value problems of a half plane subjected to an arbitrary charge distribution is constructed within Mindlin's theory of elastic dielectrics. Explicit expressions for various mechanical and electric potentials are obtained for a point charge located on the boundary of the elastic dielectric half-space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01441244
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