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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Computing 31 (1983), S. 105-114 
    ISSN: 1436-5057
    Keywords: Primary 65D30 ; 65D32 ; secondary 41A55 ; Cauchy-principal values ; finite-part integrals ; convergence ; Jacobi quadratures ; Lagrange polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In diesem Artikel sind hinreichende Bedingungen, welche die Konvergenz von Quadratursätzen des Elliott-und Hunter-Typus für die Bestimmung von gewichteten Cauchy Hauptwert-Integralen der Form sicherstellen, hergeleitet. Die gleichzeitige Konvergenz beider Quadraturen im Intervall (−1, +1) wurde für eine Klasse von Hölderstetigen Funktionenf(f∈H μ ) nachgewiesen. Im Artikel sind auch Korrekturen von gewissen früheren Darlegungen über die Konvergenz von solchen Quadraturen enthalten. Ferner wurde eine einfache Herleitung der Elliott-und Hunterschen Quadratursätze für die Bestimmung derp-ten Ableitung des obenstehenden Integrals gegeben und hinreichende Bedingungen für die Konvergenz der Hunterschen Quadratur wurden erhalten. Die Konvergenz dieses Integrals wurde somit für Funktionenf, für welchef (p) ∈H μ gilt, sichergestellt.
    Notes: Abstract In this paper sufficient conditions are derived to ensure the convergence of the Elliott and Hunter types of quadrature rules for the evaluation of weighted Cauchy principal-value integrals of the form: The simultaneous convergence in the interval (−1, 1) of both quadratures was established for a class of Hölder-continuous functionsf(f∈H μ ). Corrections of some previous statements on the subject of convergence of such quadratures are also included. Moreover, a simple derivation of the Hunter and Elliott types of quadrature rules for the evaluation of the derivative of thep-th-order of the abovestated integral was given and sufficient conditions for the convergence of the Hunter-type quadrature were obtained. Thus, the convergence of this integral was ensured for functionsf such thatf (p) ∈H μ .
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Colloid & polymer science 261 (1983), S. 825-833 
    ISSN: 1435-1536
    Keywords: Polymers ; Slow-brittle-fracture ; Toughness ; Caustics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A slow crack growth was achieved in initially edge-cracked specimens made of a high-molecular weight PMMA by regulating the cross-head speed of loading by a computer-driven testing machine. The strain rate $$\dot \varepsilon $$ used during the tests varied between $$\dot \varepsilon $$ =1× l0−6 s−1 and 1×10−4 s−1. It was shown that, in this zone of slow quasi-static loading of brittle polymethylmethacrylate specimens under conditions of plane stress, the crack initiated for a critical value of loading, at some characteristic zone of strain-rate variation at the crack tip. It was established that for strain rate between $$\dot \varepsilon $$ =0.18×10−5 s−1 and $$\dot \varepsilon $$ =0.45×10−4 s−1 brittle cracks were propagating always slowly with velocities in the range ofc=3 to 5×10−2 m/s. For values ofv s outside this transition zone fracture was typically brittle with high crack-propagation velocities. As the strain rate was varying beyond the stable low-velocity region, a two-step crack velocity pattern was operative, where the one step took always low values, and the other step corresponded to crack-propagation velocities significantly higher than these limits, tending to typical brittle-fracture velocities of the material. Oscillations of the velocityc at the transition zones, or, in many cases all over the zone of slow propagation of the crack, indicated the unstable character of crack propagation, influenced by different stress raisers and especially by the opposite longitudinal boundary of the specimen. Stress intensity factor values during crack propagation, evaluated from the front (cuspoid) and the rear (external) caustic, which remained alwaysk g-dominant, were following similar trends as the variation of the crack propagation velocity.
    Type of Medium: Electronic Resource
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