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  • Articles  (12)
  • Other Sources
  • CR: 5.17  (6)
  • ac potential difference  (3)
  • stress intensity factor  (3)
  • 1980-1984  (12)
  • Mathematics  (12)
  • Geography
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  • Articles  (12)
  • Other Sources
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  • 1
    Electronic Resource
    Electronic Resource
    Parasitic voltages induced by artificial flaws when measured using the ac field technique (1981)
    Springer
    Journal of nondestructive evaluation 2 (1981), S. 195-202 
    Details
    ISSN: 1573-4862
    Keywords: ac potential difference ; fatigue crack measurement ; slots ; artificial flaws ; parasitic voltages ; NDE
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract The development of a successful and accurate instrument for measuring surface-breaking cracks in metals using the ac field technique has raised several interesting theoretical problems. Measurements with the instrument, known as the Crack Microgauge, do not rely on any prior calibration against an artificial flaw such as a saw-cut in a test block, but some users accustomed to such a calibration from other devices have nevertheless wished to use the instrument in that fashion and have in some instances reported erroneous results. In this paper, we develop a simple theory to explain and quantify this phenomenon. We calculate the parasitic voltages induced in the instrument probe due to the finite opening possessed by an artificial flaw, and we use these results to reinterpret the instrument readings. Controlled experimental measurements on artificial flaws of rectangular cross-section made in aluminum and in steel are found to be in good agreement with the theory. It is shown, however, that application of the theory requires additional information about the internal phase shift associated with the instrument. To enhance the accuracy of the theory, the effect of the corners of the artificial flaws was also considered, although it was not very influential in this work.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00570731
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  • 2
    Electronic Resource
    Electronic Resource
    Acoustic measurements of stress fields and microstructure (1980)
    Springer
    Journal of nondestructive evaluation 1 (1980), S. 67-77 
    Details
    ISSN: 1573-4862
    Keywords: stress fields ; microstructure ; J integral ; stress intensity factor ; harness acoustic velocity ; acoustic elasticity ; NDE
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract A very precise system for measuring two-dimensional velocity fields in solid samples has been used for nondestructive measurements of both externally applied and residual inhomogeneous stresses in solids,J integrals, stress intensity factors of cracks, and hardness of quenched steel. The longitudinal velocity measurement is based on precise determination of the propagation transit time through the stressed solid specimen using a small diameter, water-coupled acoutic transducer, which is scanned mechanically over the sample. Changes in velocity are then related to changes of stress in the sample by the theory of acoustoelasticity. Similar measurements show a high degree of correlation between longitudinal velocity changes and changes in microstructure in steel samples. Applications to problems of solid mechanics and material science illustrate the utility of this nondestructive measuring technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00566232
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  • 3
    Electronic Resource
    Electronic Resource
    Approximation of time-dependent free boundaries (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 179-199 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; Primary 65N30 ; Secondary 35R35 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Two problems are considered in the paper: the first of them is connected with elliptic variational inequalities and consists in developing a moving obstacle algorithm for approximating the unknown free boundary; the other problem is linked with numerical solution of the Stefan problem, which is formulated in the similar way as in the elliptic case. Some computational aspects are also discussed in the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400538
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  • 4
    Electronic Resource
    Electronic Resource
    On multi-grid methods for variational inequalities (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 65-76 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider here a general class of algorithms for the numerical solution of variational inequalities. A convergence proof is given and in particular a multi-grid method is described. Numerical results are presented for the finite-difference discretization of an obstacle problem for minimal surfaces
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400918
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  • 5
    Electronic Resource
    Electronic Resource
    On conforming finite element methods for the inhomogeneous stationary Navier-Stokes equations (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 173-194 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider the stationary Navier-Stokes equations, written in terms of the primitive variables, in the case where both the partial differential equations and boundary conditions are inhomogeneous. Under certain conditions on the data, the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. A conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved. In addition, the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given. Numerical examples, using an efficient choice of finite element spaces, are also provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395310
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  • 6
    Electronic Resource
    Electronic Resource
    Deferred corrections using uncentered end formulas (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 21-33 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65B05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The trapezoidal rule with deferred corrections using uncentered end formulas is shown to converge. While the proof technique is more specialized than the standard asymptotic expansion approach, it has some advantages. In addition to providing a more complete theoretical justification for current implementations of deferred corrections with the trapezoidal rule, the approach given here will hopefully apply for several other discretization methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396367
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  • 7
    Electronic Resource
    Electronic Resource
    On the convergence of difference schemes for the approximation of solutionsu ∈ W 2 m (m〉0.5) of elliptic equations with mixed derivatives (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 223-232 
    Details
    ISSN: 0945-3245
    Keywords: AMS: 65N10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper deals with such estimates of the rate of convergence of difference methods, which are compatible with the smoothness of the exact solutionu ∈ W 2 m (Ω),m〉0.5, of elliptic equations with mixed derivatives: The error in the norm of the discrete Sobolev spaceW 2 s (ω), ω denoting the set of grid points, is shown to be of the orderO(|h| m−s), 0≦s〈m.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01410107
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  • 8
    Electronic Resource
    Electronic Resource
    Iterative solutions of nonlinear initial value differential equations in Chebyshev series using Lie series (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 1-13 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 34A45, 34A50, 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper Lie series are presented in Chebyshev form and applied to the iterative solution of initial value problems in differential equations. The resulting method, though algebraically complicated, is of theoretical interest as a generalisation of Taylor series methods and iterative Chebyshev methods. The theory of the method is discussed and the solutions of some simple scalar equations are analysed to illustrate the behaviour of the process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01463994
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  • 9
    Electronic Resource
    Electronic Resource
    Eddy current probe response to open and closed surface flaws (1981)
    Springer
    Journal of nondestructive evaluation 2 (1981), S. 1-21 
    Details
    ISSN: 1573-4862
    Keywords: eddy current ; ferromagnetic resonance ; fatigue crack ; stress intensity factor ; crack opening ; displacement ; closure stress
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract A general theory of eddy current flaw response, appropriate to both standard low frequency and ferromagnetic resonance (FMR) probes, is developed for simple two-dimensional and three-dimensional open and closed surface flaw geometries. This analysis, based on the assumption of a uniform interrogating field applied to the flaw by the probe, shows that flaw opening responses increase with the operating frequency of the probe. Experimental results using both types of probe confirm this result for realistic practical geometries, where variations of crack mouth opening displacement under load provide useful information about crack dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00614993
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  • 10
    Electronic Resource
    Electronic Resource
    The ac field around a plane crack in a metal surface when the skin depth is large (1982)
    Springer
    Journal of nondestructive evaluation 3 (1982), S. 19-24 
    Details
    ISSN: 1573-4862
    Keywords: ac potential difference ; eddy current ; fatigue crack measurement ; skin effect equation ; large skin depth ; NDE
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract This paper considers the solution of the skin-effect or Helmholtz equation, ∇2ψ=k 2ψ, for the two-dimensional flow of a uniform alternating current perturbed by a plane crack of uniform depth. Herek is the ratio of crack depthd to skin depth δ. When the skin depth is large compared with the crack depth andk f 0, the quasi-static approach to this problem ignores the terms on the right-hand side and constructs solutions from Laplace's equation which are essentially dc solutions and are correct to orderk. In this paper we consider behavior near the limit when the skin depth is large and give solutions which are correct to orderk 2. In an example we relate the results to the interpretation of readings from an ac potential difference instrument applied to the measurement of surface-breaking cracks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00566951
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