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Research Article
Modeling of the Complexity Propagation of Crack in a Ductile Material Under Complex Solicitation in Crack Tip: Introduction of a Matrix of Stress Intensity Factors of Bifurcation
Pierre Marie Wakeu Pola*,
Guy Edgar Ntamack,
Fabien Kenmogne,
Joseph Yves Jeff Effa,
Stephane Tchuente
Issue:
Volume 12, Issue 3, June 2024
Pages:
50-58
Received:
28 February 2024
Accepted:
27 March 2024
Published:
17 May 2024
Abstract: In fracture and damage mechanics, modeling of crack propagation has always been a source of difficulties. Numerous works have been carried out on this case at the crack tip, introducing new parameters: the Stress Intensity Factor (K); which is the local Irwin parameter, and also the Rice integral (J), the Griffith's energizing method, in which J and G are the global parameters around the crack tip. The problem of the crack remains very complex and difficult problem to be solved. Several methods are used to investigate the crack problem, namely the method of gradient, the numerical methods by finite elements, as well as the thermodynamic approach and the classical methods of Irwin, Griffith or Rice, according to the Intensity Stress Factor. This study adds to the work already carried out. Using the analytical analysis method of equations, we manage to show that the Stress Intensity Factor has a matrix of rank 3 at the crack tip, which is a better form since it includes complex combination cases of crack mode and bifurcation. Furthermore, when the material is subjected to complex stress, after analysis we emerge from a new singularity in (r) which is different from the classical mode. Finally, we are shown the new form of singularity, which is frequency dependent. This work can explain many situations, for example, the case of certain structural disasters showing the presence of cracks for complex or uncontrollable stress.
Abstract: In fracture and damage mechanics, modeling of crack propagation has always been a source of difficulties. Numerous works have been carried out on this case at the crack tip, introducing new parameters: the Stress Intensity Factor (K); which is the local Irwin parameter, and also the Rice integral (J), the Griffith's energizing method, in which J an...
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Research Article
Evaluation of the Shortest Route Possible in Distribution of Fish Product in Western Kenya Region
Issue:
Volume 12, Issue 3, June 2024
Pages:
59-65
Received:
7 March 2024
Accepted:
25 March 2024
Published:
17 May 2024
Abstract: This comprehensive study delves deeply into the intricate process of optimizing fish product distribution routes in the expansive Western Kenya region, with an explicit focus on understanding and refining the operational strategies employed by Victory Farm Limited. Leveraging the Hungarian Method, celebrated for its unparalleled effectiveness in the realm of combinatorial optimization, the research endeavors to meticulously evaluate and fine-tune the shortest and most efficient transportation routes for seamlessly ferrying fish products from Kisumu Logistic Center to a myriad of distribution depots and retail markets scattered across the Western Kenya region's diverse landscape. Through an exhaustive analysis that spans road networks, logistical constraints, and the ever-evolving dynamics of market demand, this study systematically identifies and delineates optimal routes that not only minimize the distance traversed but also significantly mitigate associated transportation costs, all while steadfastly adhering to stringent standards for punctuality and product quality. Furthermore, by synergistically integrating sophisticated mathematical modeling techniques, meticulously executed through Python programming, with a robust foundation of real-world data meticulously sourced from Victory Farm Limited, this research endeavors to provide invaluable insights and pragmatic recommendations aimed at fortifying and enhancing the overall efficiency and profitability of fish product distribution operations throughout Victory Farm Western Kenya depots. In essence, the anticipated outcomes of this study transcend the realm of theoretical conjecture, poised instead to catalyze tangible advancements in the sustainable development of the region's burgeoning aquaculture sector, thereby fostering a lasting legacy of economic prosperity and environmental stewardship for generations to come.
Abstract: This comprehensive study delves deeply into the intricate process of optimizing fish product distribution routes in the expansive Western Kenya region, with an explicit focus on understanding and refining the operational strategies employed by Victory Farm Limited. Leveraging the Hungarian Method, celebrated for its unparalleled effectiveness in th...
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Research Article
Lagrange Interpolation in Matrix Form for Numerical Differentiation and Integration
Rui Wang*,
Binh-Le Ly,
Wei-Chau Xie,
Mahesh Pandey
Issue:
Volume 12, Issue 3, June 2024
Pages:
66-78
Received:
15 April 2024
Accepted:
6 May 2024
Published:
19 June 2024
Abstract: Numerical differentiation has been widely applied in engineering practice due to its remarkable simplicity in the approximation of derivatives. Existing formulas rely on only three-point interpolation to compute derivatives when dealing with irregular sampling intervals. However, it is widely recognized that employing five-point interpolation yields a more accurate estimation compared to the three-point method. Thus, the objective of this study is to develop formulas for numerical differentiation using more than three sample points, particularly when the intervals are irregular. Based on Lagrange interpolation in matrix form, formulas for numerical differentiation are developed, which are applicable to both regular and irregular intervals and can use any desired number of points. The method can also be extended for numerical integration and for finding the extremum of a function from its samples. Moreover, in the proposed formulas, the target point does not need to be at a sampling point, as long as it is within the sampling domain. Numerical examples are presented to illustrate the accuracy of the proposed method and its engineering applications. It is demonstrated that the proposed method is versatile, easy to implements, efficient, and accurate in performing numerical differentiation and integration, as well as the determination of extremum of a function.
Abstract: Numerical differentiation has been widely applied in engineering practice due to its remarkable simplicity in the approximation of derivatives. Existing formulas rely on only three-point interpolation to compute derivatives when dealing with irregular sampling intervals. However, it is widely recognized that employing five-point interpolation yield...
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,
Cleophas Kweyu
