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Method of regularized sources for two-dimensional Stokes flow problems based on rational or exponential blobs

Wen S., Wang K., Zahoor R., Li M., Šarler B.

Computer Assisted Methods in Engineering and Science

2015

Vol. 22, no. 3

289--300

The solution of Stokes flow problems with Dirichlet and Neumann boundary conditions is performed by a non-singular method of fundamental solutions (MFS) which does not require artificial boundary, i.e., source points of fundamental solution coincide with the collocation points on the boundary. The fundamental solution of the Stokes pressure and velocity is obtained from the analytical solution due to the action of the Dirac delta- type force. Instead of Dirac delta force, a non-singular function called blob, with a free parameter epsilon is employed, which is limited to Dirac delta function when epsilon is limited to zero. The analytical expressions for related Stokes flow pressure and velocity around such regularized sources have been derived for rational and exponential blobs in an ordered way. The solution of the problem is sought as a linear combination of the fields due to the regularized sources that coincide with the boundary and with their intensities chosen in such a way that the solution complies with the boundary conditions. A numerical example for two-dimensional (2D) driven cavity and a flow between parallel plates are chosen to assess the properties of the method. The results of the posed method of regularized sources (MRS have been compared with the results obtained by the fine-grid second-order classical finite difference method (FDM) and analytical solution. The results converge with finer discretisation; however, they depend on the value of epsilon. The method gives reasonably accurate results for the range of epsilon between 0.1 and 0.5 of the typical nodal distance on the boundary. Exponential blobs give slightly better results than the rational blobs; however, they require slightly more computing time. A robust and efficient strategy to find the optimal value of epsilon is needed in the perspective.

Genetic programming modeling of the critical size of inclusions

Kovačič M., Šarler B.

Computer Methods in Materials Science

2011

Vol. 11, No. 1

41-45

Spring steel quality has a major impact on spring life. Spring steel quality depends also on the inclusions presence. 7 dynamically tested and broken springs (51CrV4) were analyzed. The dynamic test result is the number of the cycles before spring breakage. We were interested in dependency of the inclusion size and the distance from the surface of the inclusion on the spring tool life. In the paper the genetic programming method was used. In the proposed concept the mathematical models for spring life undergo adaptation. The results show that the proposed concept can be used in practice.

Jakość stali sprężynowej decyduje o długości życia spręży-ny. Jakość tej stali zależy przede wszystkim od obecności wy-dzieleń. Analizowano 7 sprężyn ze stali 51CrV4 poddanych dynamicznym obciążeniom do zniszczenia. W próbach wy-znaczono liczbę cykli obciążenia do zniszczenia sprężyny. Celem pracy było wyznaczenie zależności pomiędzy wielkością cząstek wydzieleń i ich odległością od powierzchni a czasem życia sprężyny. Do wyznaczenia tej zależności wykorzystano programowanie genetyczne. W zaproponowanym rozwiązaniu pro-wadzona jest adaptacja modelu czasu życia sprężyny. Analiza wyników potwierdziła praktyczne zastosowanie opracowanego modelu.