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  • 1
    Electronic Resource
    Electronic Resource
    Stokes problems of multiparticle systems: Periodic arrays (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 666-673 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A boundary element method is developed and used to compute the volume-average rheological properties of layered suspensions in a mean simple shearing flow up to a volume concentration of 0.5. The suspension is made up of a periodic array of neutrally buoyant, monosized spheroids in the x and y directions suspended in a Newtonian fluid that is subjected to a mean shear flow in the xz plane. The results for a monolayered suspension of spheres agree well with other simulations and some experimental results. Some new results for prolate and oblate spheroids are also given. Both the volume-average first and second normal stress differences are found to be zero in the simulation in all the cases considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857719
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Stokes problems of multiparticle systems: A numerical method for arbitrary flows (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 453-461 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A boundary element method (BEM) is developed and used to compute the arbitrary Stokes flow of a system of N particles of arbitrary shape and size embedded in a Newtonian fluid. The particles can be assumed to have a specified deformation (this feature is included here in anticipation of some applications in biophysics). Hydrodynamic and nonhydrodynamic forces are assumed to act in general; Brownian forces are neglected; and the Stokes flow field is assumed to be arbitrary. The method is benchmarked against the exact solution of two equal spheres in free settling motion by Goldman, Cox, and Brenner [Chem. Eng. Sci. 21, 1151 (1966)]. The handling of a finite bounding surface (i.e., arbitrary flow field, container walls) is tested with the calculation of the effective shear viscosity of a dilute suspension of monosized rigid spheres. The benchmarks show that the method performs satisfactorily. Also reported are the results for three spheres, arranged either in equispaced linear or triangular configuration (fixed or free settling under gravity). The effect of the hydrodynamic interaction with a rigid plane boundary (half-space problem) is automatically treated by the use of the special image of the Kelvin state [N. Phan-Thien, J. Elasticity 13, 231 (1983)]. This is illustrated by considering the problem of free settling of particles near a rigid no-slip planar boundary; specifically, some results for two equal spheres are reported. It is shown that the particle motion near the solid plane is fundamentally different from its motion in the far field, and thus the relative divergence of particles and the reversal of their angular velocity is observed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857414
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Three-dimensional study of extrusion processes by Boundary Element Method. (1988)
    Springer
    Rheologica acta 27 (1988), S. 639-648 
    Details
    ISSN: 1435-1528
    Keywords: Boundary Element Method ; three-dimensionalextrusion ; complexviscoelastic flow ; axisymmetric-equivalentswell ratio
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract This paper describes an implementation of a Boundary Element method to solve a general three-dimensional viscoelastic flow problem. The Boundary Element method is formulated in terms of unknown boundary velocity and traction fields. The fluid is incompressible and is modelled by a differential constitutive equation. The steady-state stress field is obtained by a “time marching” process of integration. For the first time, some results for steady state isothermal creeping flow extrusion of a viscoelastic fluid from triangular and square dies are described. The concept of an “axisymmetric-equivalent swell ratio” is introduced to compare the present results with the results of axisymmetric extrusion studies reported in the literature. It is shown that reasonable agreement is achieved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01337460
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On the Beltrami-Michell compatibility condition and its relatives (1985)
    Springer
    Archive of applied mechanics 55 (1985), S. 13-16 
    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 Es werden kurze Beweise in Tensorschreibweise für die VertrÄglichkeitsbedingungen von Beltrami-Michell gegeben. Die Beweise verwenden eine wiederholte Anwendung des inversen Lemmas von Poincaré. Eine kleine AbÄnderung führt auf die Ergebnisse von Gurtin.
    Notes: Summary Short proofs using dyadic notations are derived for the Beltrami-Michell condition, as well as its associated relative. The proofs use repeated applications of Inverse Poincaré Lemma. A slight variation produces Gurtin's results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00539546
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  • 5
    Electronic Resource
    Electronic Resource
    Boundary element solution for half-space elasticity or stokes problem with a no-slip boundary (1986)
    Springer
    Computational mechanics 1 (1986), S. 259-268 
    Details
    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 We report an implementation of the Boundary Element Method (BEM) for half-space elasticity or Stokes problems with a plane interface (the boundary of the half space). With a proper choice of the singularity solution this plane interface, on which the displacement or velocity vector is zero, does not need to be discretized. For a large class of problems involving translating or rotating bodies a simplification of the boundary element formulation is possible, with a resulting improvement in the accuracy of the numerical results. The three-dimensional boundary element program was tested with the moving sphere problem and was found to be satisfactory in all cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00273702
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Boundary element method for finite elasticity (1990)
    Springer
    Computational mechanics 6 (1990), S. 205-219 
    Details
    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 This paper describes some integral formulations and implementations of a Boundary Element Method to solve two- and three-dimensional finite deformation problems of rubber-like materials. The integral equations are formulated in terms of unknown incremental displacement and total boundary traction fields, or alternatively in terms of the incremental displacement and incremental boundary traction fields. The elastic material is either compressible or incompressible with given constitutive equations. Both formulations are implemented and tested. The uniaxial elongation and simple shear deformations of a model material are successfully simulated by both formulations. Some non-trivial examples are performed using the first formulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00350238
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  • 7
    Electronic Resource
    Electronic Resource
    Three-dimensional study of extrusion processes by Boundary Element Method. (1988)
    Springer
    Rheologica acta 27 (1988), S. 21-30 
    Details
    ISSN: 1435-1528
    Keywords: Boundary Element Method ; three-dimensionalextrusion ; complexviscous flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract In this paper we report an implementation of a Boundary Element Method (BEM) dealing with three-dimensional extrusion problems of viscous fluid. Die shapes with and without sharp corners and their influence on the final shape of extrudate have been studied: both shrinkage and swelling of the extrudates relative to the original die shapes have been discovered. The first half of this paper deals with the problem of implementing isoparametric boundary elements. It is followed by results of test problems, and finally the results of extrusion study are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01372446
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    On the representation of elastic displacement fields in terms of three harmonic functions (1979)
    Springer
    Journal of elasticity 9 (1979), S. 325-333 
    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 In this paper the representation of displacement fields in linear elasticity in terms of harmonic functions is considered. In the original work of Papkovich and Neuber four harmonic functions were presented with a subsequent reduction to three on the grounds that only three are sufficient for the representation of displacements fields. This reduction is unsubstantiated and several authors have investigated the generality of the Papkovich-Neuber solutions. The paper derives by simple means the conditions under which it is possible to omit one of the four harmonic functions and considers the significance of the subsequent three function form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00041103
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    Paper (German National Licenses)
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