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  • 1
    Electronic Resource
    Electronic Resource
    Direct second kind boundary integral formulation for Stokes flow problems (1993)
    Springer
    Computational mechanics 11 (1993), S. 11-27 
    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 A direct boundary element method is formulated for the Stokes flow problem based on an integral equation representation for the components of traction. For problems in which the components of velocity are prescribed on the boundary of the domain, this new formulation results in a hypersingular Fredholm integral equation of the second kind. A method of regularization to evaluate the hypersingular integral is discussed. For certain problems involving flows about particles, the integral equation representation for the tractions is not unique because of the existence of rigid body eigenmodes. A method to constrain out these rigid body modes is also discussed. Several example problems are considered in which this new formulation is compared to more traditional boundary element formulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370070
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The effect of a moving sink on selective withdrawal from a discretely stratified fluid (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 2720-2722 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effect of a moving sink on the selective withdrawal process from a discretely stratified fluid is studied experimentally. The critical, draw-down flow rate can be increased significantly by employing a moving sink. The distortion of the interface between the two layers caused by the moving sink gives rise to a secondary effect, which is dependent on whether the sink speed is less than or greater than the interfacial wave speed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866551
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The numerical solution of Stokes flow in a domain with re-entrant boundaries by the boundary element method (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 327-338 
    Details
    ISSN: 0271-2091
    Keywords: Boundary element method ; Stokes flow ; Re-entrant boundaries ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical solutions are presented for two-dimensional low Reynolds number flow in a rotating tank with stationary barriers. The boundary element method is employed, assuming straight panels and quadratic source distribution. The feasibility of repositioning the nodes as a way to minimize the error is explored. A stretching parameter places smaller elements near the re-entrant regions. Elementary error analysis shows uniform improvement in the solution with stretching. The changing eddy pattern for different numbers and sizes of the barriers is compared with experimental results.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080306
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  • 4
    Electronic Resource
    Electronic Resource
    A parallel-supercomputing investigation of the stiffness of aligned, short-fiber-reinforced composites using the Boundary Element Method (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3477-3491 
    Details
    ISSN: 0029-5981
    Keywords: composite materials ; aligned short fibers ; boundary element method ; modulus of elasticity ; parallel supercomputing ; Halpin-Tsai equations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Computational experiments are carried out in three-dimensional, multi-fibre specimens with the objective of determining the influence of fibre volume fraction (φ) and aspect ratio (ar) on the effective tensile modulus of aligned, discontinuous fibre-reinforced composites. The Boundary Element Method (BEM), implemented on a 1840-node Intel Paragon parallel supercomputer using a torus-wrap mapping, enables the prediction of the tensile behaviour of composite specimens consisting of up to 200 discrete aligned short fibres, randomly dispersed in an elastic matrix. Statistical averages of the computed effective longitudinal moduli are compared with the predictions of the Halpin-Tsai equation and are found to be in good agreement for low values of ar and φ. However, as ar and/or φ increase, the predictions of the Halpin-Tsai equation fall below the computed moduli. Consideration of the finite packing efficiency of the fibres as proposed by Lewis and Nielsen results in a generalized form of the Halpin-Tsai equation whose predictions are in very good agreement with the BEM calculations for the entire range of φ and ar examined. The scatter in the computed moduli decreases with increasing number of fibres, reflecting the ‘homogenization’ of the specimen brought about by consideration of larger numbers of smaller fibres. This scatter grows with increasing φ and ar, reflecting an increase in the magnitude and complexity of inter-fibre interactions. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 5
    Electronic Resource
    Electronic Resource
    Construction of stiffness matrices to maintain the convergence rate of distorted finite elements (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1927-1944 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: High-order elements are an option for providing an enhanced rate of convergence. However, it is not widely known that if a high-order element based on a mapping from a master-element space is distorted by displacing one of the side nodes slightly from the traditional midside position then the rate of convergence drops one order. The proof for a three-node element in one dimension has been given previously. Here, a numerical demonstration is presented to show how quickly the rate is lost as the second node is moved from the midpoint. For a six-node triangular element, a similar convergence study is performed in two dimensions in which one of the side nodes is moved off centre along a straight line joining the vertices of the triangle. Again, a loss in the order of convergence is shown although the loss is only apparent for sufficiently small element size. To prevent this drop in the rate of convergence as a side node is displaced, a procedure is given for developing the element stiffness matrix without formulating element basis functions. For the six-node triangle, a complete quadratic representation is retained, but at the expense of element compatibility between nodes. The numerical investigation shows that convergence appears to be retained but that the error associated with the incompatibility is greater than the error obtained with the use of distorted isoparametric elements. The results of this study are particularly appropriate for domains with curved boundaries and for non-linear problems in which node positions are updated according to the deformation history.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361109
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    An efficient boundary element method for a class of parabolic differential equations using discretization in time (1987)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 3 (1987), S. 187-197 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new boundary element method using discretization in time is proposed to solve a class of parabolic differential equations. The method treats the term containing the time derivative as a forcing term. This necessitates the introduction of additional unknowns in the interior of the domain. At the same time, however, values for the dependent variable are determined directly in the interior. The boundary element formulation is reduced to essentially solving a Poisson equation. The accuracy and efficiency of the method are demonstrated with several examples.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690030304
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