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Mode I Stress Intensity Factors for Surface Planar Cracks in Circular Bodies Under Rotary Bending

100%

Król R. , Grabowski P.

tom Vol. 40, No. 4

19--31

A method of calculating stress intensity factors, using point-load weight function, for twodimensional surface cracks subjected to rotary bending, applied to circular objects is described in the paper. The research has regarded planar cracks in finite circular bodies, which may occur e.g. in shaft cross sections of belt-driven machines. This type of drive is widely spread in the technological lines, therefore the research on improving its fatigue durability is crucial for development of this branch of industry. One of a few advantages of the method which has been applied is the possibility to evaluate stress intensity factor (SIF) values precisely in a quick and simple way. The paper shows the computation for various parameters of shape and size of shafts and cracks. The presented method usually yields conservative results compared to reference values obtained for the same configurations with the finite element method, which gives a good perspective to use such calculated SIFs for life assessment. Checking of these possibility is an essential issue of the work described in the paper.

Lipschitzian superposition operators between spaces of functions of bounded generalized variation with weight

75%

Chistyakov V. V.

tom Vol. 6, nr 2

173-186

We present some properties of real valued functions of bounded generalized variation of Riesz-Orlicz type including weight and characterize Lipschitzian superposition Nemytskii operators which map between spaces (in fact, Banach algebras) of these functions.

Porównanie zmęczeniowego wzrostu pęknięć o kształtach rzeczywistych i zastępczych

63%

Jankowiak A. , Jakubczak H.

tom Z. 4

43-44

W pracy przedstawiono opartą na dwuwymiarowej funkcji wagowej metodę analizy wzrostu rzeczywistych pęknięć zmęczeniowych o dowolnym kształcie. Pokrótce zaprezentowane zostały główne założenia opracowanej procedury obliczeniowej. Zbadano i przeanalizowana dwa przykłady pęknięć o dowolnych kształtach pod kilkoma rozkładami naprężeń. Porównano wyniki trwałości i końcowy kształt dla rzeczywistych kształtów szczelin z wynikami otrzymywanymi z zastosowaniem kształtów zastępczych opartych na szczelinach idealnych. Praca stanowi kontynuację tematyki przedstawionej w pracy [1].

Prediction of residual life of structural components spent on the stable crack growth needs a crack growth analysis starting from an initial crack or crack-like flaw. The method of crack growth analysis based on stress intensity factors determined using point-load weight function for planar cracks under arbitrary mode I stress fields is presented in the paper. Comparison of crack growth results (durability and final shape of cracks) for arbitrary shape cracks and substitute (ideal) shapes like elliptical and corner cracks are presented and discussed, as well.

Solution of fractional integro-differential equations using least squares and shifted legendre methods

63%

Mahdy A. M. S. , Nagdy A. S. , Mohamed D. S.

tom Vol. 23, nr 1

59-70

In recent years, fractional calculus (FC) has filled in a hole in traditional calculus in terms of the effect of memory, which lets us know things about the past and present and guess what will happen in the future. It is very important to have this function, especially when studying biological models and integral equations. This paper introduces developed mathematical strategies for understanding a direct arrangement of fractional integro-differential equations (FIDEs). We have presented the least squares procedure and the Legendre strategy for discussing FIDEs. We have given the form of the Caputo concept fractional order operator and the properties. We have presented the properties of the shifted Legendre polynomials. We have shown the steps of the technique to display the solution. Some test examples are given to exhibit the precision and relevance of the introduced strategies. Mathematical outcomes show that this methodology is a comparison between the exact solution and the methods suggested. To show the theoretical results gained, the simulation of suggested strategies is given in eye-catching figures and tables. Program Mathematica 12 was used to get all of the results from the techniques that were shown.