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  4. Optimal variable support size for mesh-free approaches using genetic algorithm

Optimal variable support size for mesh-free approaches using genetic algorithm

MMC.
2021;
Volume 8, Number 4
: pp. 678–690
https://doi.org/10.23939/mmc2021.04.678
Received: May 23, 2021
Accepted: June 07, 2021

Mathematical Modeling and Computing, Vol. 8, No. 4, pp. 678–690 (2021)

Authors:
  1. S. Hassouna
  2. A. Timesli
1
Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM Casablanca)
2
Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM Casablanca)

The main difficulty of the meshless methods is related to the support of shape functions.  These methods become stable when sufficiently large support is used.  Rather larger support size leads to higher calculation costs and greatly degraded quality.  The continuous adjustment of the support size to approximate the shape functions during the simulation can avoid this problem, but the choice of the support size relative to the local density is not a trivial problem.  In the present work, we deal with finding a reasonable size of influence domain by using a genetic algorithm coupled with high order mesh-free algorithms which the optimal value depends on the accuracy and stability of the results.  The proposed strategy provides guarantees about the growth of approximation errors, monitor the level of error, and adapt the evaluation strategy to reach the required level of accuracy.  This allows the adaptation of the proposed algorithm with problem complexity.  This new strategy in meshless approaches are tested on some examples of structural analysis.

large deformations
strong form
meshless method
genetic algorithm
automatic choice of nearest neighbors
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