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Optimized Radius of Influence Domain in Meshless Approach for Modeling of Large Deformation Problems

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

The determination of the optimized size of the support domain remains still an open question in meshless methods because there is no theoretical value or validated formula. This optimal value depends on density and distribution of points and also on the nature of the considered problem, e.g., boundary value problems, integral equations, delay-differential equations, etc. Since no theoretical value of the support domain size has been determined, finding the optimized size of the influence domain requires several tests and experiments. Despite its high computational cost, this classical method is not efficient and its optimal choice is not determined precisely. Moreover, the optimized size of the support domain varies with respect to the simulation parameters and/or the physical variables during the simulation evolution; it can be very difficult to control the optimal size using the classical method. The present investigation discusses an efficient meshfree method based on the strong form of Moving Least Square (MLS) method. The numerical solution of the proposed approach was carried out using an optimization approach to calculate the optimized radius of the influence domain. The numerical results of the proposed approach were tested and compared to the Finite Element Method (FEM) and to the MLS approach based on a fixed support domain. The CPU time of the present approach and the MLS approach with a fixed support domain are provided.

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  1. Hassan II University of Casablanca, National Higher School of Arts and Crafts of Casablanca, SEISEE Laboratory, 20670, Casablanca, Morocco

    Abdelaziz Timesli

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  1. Abdelaziz Timesli
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Timesli, A. Optimized Radius of Influence Domain in Meshless Approach for Modeling of Large Deformation Problems. Iran J Sci Technol Trans Mech Eng 46, 541–551 (2022). https://doi.org/10.1007/s40997-021-00427-3

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  • DOI: https://doi.org/10.1007/s40997-021-00427-3

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