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  • Artikel  (9)
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  • AMS(MOS): 65N30  (3)
  • Bifurcation  (3)
  • stress intensity factor  (3)
  • 1980-1984  (9)
  • Mathematik  (9)
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  • Artikel  (9)
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  • 1
    Digitale Medien
    Digitale Medien
    Acoustic measurements of stress fields and microstructure (1980)
    Springer
    Journal of nondestructive evaluation 1 (1980), S. 67-77 
    Details
    ISSN: 1573-4862
    Schlagwort(e): stress fields ; microstructure ; J integral ; stress intensity factor ; harness acoustic velocity ; acoustic elasticity ; NDE
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00566232
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  • 2
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): AMS(MOS): 65N30 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01395310
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  • 3
    Digitale Medien
    Digitale Medien
    Approximation of tricomi problem with Neumann boundary condition (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 371-391 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G 1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The Tricomi problem with Neumann boundary condition is reduced to a degenerate problem in the elliptic region with a non-local boundary condition and to a Cauchy problem in the hyperbolic region. A variational formulation is given to the elliptic problem and a finite element approximation is studied. Also some regularity results in weighted Sobolev spaces are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01405569
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  • 4
    Digitale Medien
    Digitale Medien
    On mixed finite element methods for first order elliptic systems (1981)
    Springer
    Numerische Mathematik 37 (1981), S. 29-48 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A physically based duality theory for first order elliptic systems is shown to be of central importance in connection with the Galerkin finite element solution of these systems. Using this theory in conjunction with a certain hypothesis concerning approximation spaces, optimal error estimates for Galerkin type approximations are demonstrated. An example of a grid which satisfies the hypothesis is given and numerical examples which illustrate the theory are provided.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396185
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  • 5
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): eddy current ; ferromagnetic resonance ; fatigue crack ; stress intensity factor ; crack opening ; displacement ; closure stress
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00614993
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  • 6
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Acoustic diffraction ; acoustic transmission ; asperity contact ; crack closure ; fatigue cracks ; mode conversion ; NDE ; stress intensity factor
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00566225
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  • 7
    Digitale Medien
    Digitale Medien
    Bifurcations at a cusp singularity with applications (1984)
    Springer
    Acta applicandae mathematicae 2 (1984), S. 101-138 
    Details
    ISSN: 1572-9036
    Schlagwort(e): 58F ; 70K ; 92 ; Bifurcation ; vector field ; saddle-node singularity ; cusp singularity ; saddle connection ; normal form ; unfolding ; versal family ; population dynamics ; oscillators
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider families of vector fields which exhibit a cusp singularity for some values of the parameters. Algebraic conditions are obtained for these families to have versal properties. This enables the topologically distinct, structurally stable types of phase portrait which occur in the family near to the bifurcation point to be predicted. Applications of these results in population dynamics and oscillation theory are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00046575
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  • 8
    Digitale Medien
    Digitale Medien
    Hopf bifurcation in a stomatal oscillator (1982)
    Springer
    Journal of mathematical biology 12 (1982), S. 1-11 
    Details
    ISSN: 1432-1416
    Schlagwort(e): Bifurcation ; Stomata ; Oscillation ; Nonlinear dynamics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Stomata are microscopic openings in leaves of green plants which permit gas exchange. This paper presents a parameter study of a model of a stomatal oscillator first derived by Delwiche and Cooke in 1977. We prove the existence of an unstable limit cycle by using the theory of the Hopf bifurcation. Other bifurcations exhibited by the model are also discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00275199
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  • 9
    Digitale Medien
    Digitale Medien
    A model of evolutionary appearance of dissipative structure in ecosystems (1983)
    Springer
    Journal of mathematical biology 18 (1983), S. 13-23 
    Details
    ISSN: 1432-1416
    Schlagwort(e): Ecosystem ; Evolution ; Autonomous oscillations ; issipative structure ; Bifurcation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The interrelation between autonomous oscillations in local systems and stable dissipative structures in spatially distributed systems is analyzed. Darwinian evolution in populations comprising the ecosystem is shown to be able to cause the qualitative rearrangements of dynamic modes and smooth appearance of oscillations in local systems. The same evolutionary mechanisms analyzed within bilocal systems, may lead to appearance of dissipative structures (both smooth and sharp).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00275907
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