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  • Articles  (19)
  • Other Sources
  • Applied Mathematics  (14)
  • stress intensity factor
  • 1995-1999  (3)
  • 1980-1984  (16)
  • Mathematics  (19)
  • Geography
  • 1
    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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  • 2
    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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  • 3
    Electronic Resource
    Electronic Resource
    The interaction of ultrasound with contacting asperities: Applications to crack closure and fatigue crack growth (1984)
    Springer
    Journal of nondestructive evaluation 4 (1984), S. 203-212 
    Details
    ISSN: 1573-4862
    Keywords: Acoustic diffraction ; acoustic transmission ; asperity contact ; crack closure ; fatigue cracks ; mode conversion ; NDE ; stress intensity factor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract The partial contact of two rough fatigue crack surfaces leads to transmission, reflection, diffraction, and mode conversion of an acoustic signal at those contacts. This paper reviews recent experimental and theoretical efforts to understand and quantify such contact on actual fatigue cracks in greater detail. It is shown that the size and density of individual contacts, or asperities, can be estimated from acoustic measurements. Furthermore, it is shown that this information is useful to provide the static stress across a partially closed crack as well as the “effective” stress intensity range which activates fatigue crack propagation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00566225
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  • 4
    Electronic Resource
    Electronic Resource
    The effect of a thin inclusion of high rigidity in an elastic body (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 251-270 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study an elastic body comprising an inclusion whose thickness is 2∊ and for which Lamé's constants are λ∊ and μ. We are interested in the limit behaviour of the inclusion, when ∊ → 0 and μ∊ → ∊; that is when the inclusion becomes thiner and more rigid. Different behaviours are possible, according to the rate at which μ∊ converges to infinity; the limit inclusion may “vanish” if it is not very rigid, but also it may be entirely solid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020302
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  • 5
    Electronic Resource
    Electronic Resource
    Galerkin approximations for the equation Lu + Nu = f (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 286-290 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Introducing the concept of a supercontinuous operator, we obtain a general convergence theorem for Galerkin approximations. Under the stronger assumption that N is a monotone operator with N(0) = 0, we show norm convergence of the unique Galerkin approximations to the unique solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040119
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  • 6
    Electronic Resource
    Electronic Resource
    Mathematische Behandlung ernes Modells der Haemodialyse (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 393-404 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a simple mathematical model for the process of hemodialysis is presented. This model is based on a system of two linear differential equations of first order with partly discontinuous coefficients that describe the time-development of the concentrations of a certain toxin (like urea) in the intra- and extracellular part of the human body. The main result is the existence of periodic positive solutions of this system under the natural assumption that the generation of the toxin and its removal by hemodialysis are periodic processes. These periodic positive solutions are also computed numerically for a realistic choice of the coefficients of the modelling differential equations.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030127
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  • 7
    Electronic Resource
    Electronic Resource
    The impedance boundary value problem for the time harmonic Maxwell equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 475-487 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of a unique solution to Maxwell's equations defined in an exterior domain with impedance boundary condition is established for all frequencies. This is accomplished by reducing this problem to that of solving a system of singular integral equations and then regularizing this system such that the Riesz theory is applicable. We also consider the inverse problem in which it is desired to determine the impedance from a knowledge of the far field pattern. By restricting the impedance to lie a priori in a compact set results are obtained on the existence, uniqueness, and stability of the solution to this inverse scattering problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030133
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  • 8
    Electronic Resource
    Electronic Resource
    Bifurcation problems for discrete variational inequalities (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 243-258 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The buckling of a beam or a plate which is subject to obstacles is typical for the variational inequalities that are considered here. Birfurcation is known to occur from the first eigenvalue of the linearized problem. For a discretization the bifurcation point and the bifurcating branches may be obtained by solving a constrained optimization problem. An algorithm is proposed and its convergence is proved. The buckling of a clamped beam subject to point obstacles is considered in the continuous case and some numerical results for this problem are presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040116
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  • 9
    Electronic Resource
    Electronic Resource
    Faedo-galerkin approximations in equations of evolution (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 41-54 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the evolution equation u' = Au + Nu u(0) = φu is a function on a real interval [0, T] with values in a Hilbert space H, A is a linear operator in H generating a continuous semigroup eAt and N is a nonlinear operator in H.We show that 1Existence of the exact solution implies existence of the Faedo-Galerkin Approximations.2Existence of the Faedo-Galerkin Approximations implies existence of the exact solution.3Uniform convergence of the Faedo-Galerkin Approximations to the exact solution.The Paper consists of two parts. In the first five sections we require that A possesses a complete orthonormal system of eigenfunctions, in section 6 we drop this requirement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060104
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  • 10
    Electronic Resource
    Electronic Resource
    Transmutation via the momentum plane (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 467-495 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Transmutation methods are developed for equations of the form x2 ϕ“ + x2(k2” - q̃(x)) ϕ = (v2 - (1/4)) ϕ, with v as spectral variable, which correspond to problems in quantum scattering theory at fixed energy k2 (here v ˜ l + (1/2) with l complex angular momentum). Spectral formulas for transmutation kernels are constructed and the machinery of transmutation theory developed by the author for spectral variable k is shown to have a version here. General Kontrorovič-Lebedev theorems are also proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060129
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