Showing posts with label nodes. Show all posts
Showing posts with label nodes. Show all posts

Tuesday, 7 June 2022

Modelling Orthogonal Metal Machining Using Finite Element Analysis | Chapter 13 | Technological Innovation in Engineering Research Vol. 3

The findings of a research of simulation modelling of orthogonal metal machining using the finite element method and AdvantEdgeTM modelling software are presented in this article. The AdvantEdgeTM is a certified CAE software solution for metal cutting optimization that allows users to examine machining operations in both 2D and 3D settings. By progressively moving the cutting tool from the beginning state to steady-state, the cutting process and primarily cutting forces were simulated, while a geometrical chip-separation criterion based on a critical distance at the tool tip criterion was implemented in the AdvantEdgeTM engine. The study's goal was to use the finite element approach to estimate cutting forces, chip formation, and temperature at the tool-chip interface in order to model the cutting process. Friction was simulated and executed along the tool-chip contact using a series of finite element simulations. In order to simulate chip detachment from the workpiece, a finite element nodal technique was used. These simulations yielded results that matched experimental findings. Specifically, it was discovered that during machining, the tool-tip zone experiences the greatest plastic strain rate deformation. Maximum temperature increases were discovered to have occurred along the chip-tool contact as a result of energy dissipation owing to plasticity and friction.


Author(s) Details:

Titus Bitek Watmon,
Department of Agricultural Mechanisation & Irrigation Engineering, Busitema University, P.O. Box 236, Tororo, Uganda.

David Xiao,
School of Architecture Computing and Engineering, University of East London, Docklands Campus, E16 2RD, United Kingdom.

Please see the link here: https://stm.bookpi.org/TIER-V3/article/view/7071

Monday, 24 May 2021

The Out-of-Kilter Algorithm and Its Network Flow Implementations | Chapter 7 | Theory and Practice of Mathematics and Computer Science Vol. 10

 D.R. Fulkerson [1] published the out-of-kilter algorithm, which computes the solution to the minimum-cost flow issue in a flow network. The Out-of-Kilter technique can be used to solve problems like the transportation problem, which can be described as a maximum flow and minimal cost – maximum flow problem. To begin, the algorithm creates an initial flow along the arcs and assigns a number to each of the network's nodes. See, for example, Bazaraa, which employs Complementary Slackness Optimality Conditions (CSOC). The method developed by Jarvis and Sherali [2] looks for out-of-kilter arcs (those that do not satisfy CSOC conditions). If there aren't any, the algorithm is finished. The flow must be increased or decreased to bring arcs that do not satisfy the CSOC theorem into alignment. According to the demand, the algorithm will hunt for a path that either enhances or decreases the flow. This is repeated until all of the arcs are aligned, at which time the procedure is finished. There is no conceivable flow if no paths to improve the system are found. The Out-of-Kilter algorithm is used to determine the best solution to any network flow problem. This comprises transit, assignment, and shortest path problems, among others. Computer solutions are presented using a Pascal programme and Matlab.

Author(s) Details

W. H. Moolman
Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha, South Africa.

View Book :- https://stm.bookpi.org/TPMCS-V10/article/view/1077

Computing and Applications: The Maximum Flow and Minimum Cost – Maximum Flow Problems | Chapter 6 | Theory and Practice of Mathematics and Computer Science Vol. 10

 Both the maximum flow and minimum cost-maximum flow challenges are concerned with determining flows between a source and a destination across a network. The term "maximum flow" refers to any problem in which the goal is to transport as many products, objects, or people as possible between two sites via intermediate places. Maximum flow-lowest cost refers to flow problems including both capacities and expenses. Computing enables one to come at a solution to a problem when provided knowledge about a network (network flow diagram, capacities, and expenses). When the solution is ready, it must be tested on a real-world problem. The usage of R (many packages and functions), specially designed Pascal programmes, and Excel SOLVER in the solution of these problems will be discussed. The following problems' minimum cost-maximum flow solutions will also be discussed: Transportation problem, assignment problem, shortest path problem, caterer problem, maximum flow, minimum cost-maximum flow.

Author(s) Details

W. H. Moolman
Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha, South Africa.

View Book :- https://stm.bookpi.org/TPMCS-V10/article/view/1076