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  4. Solving topology optimization problems using cellular automata and mortar finite element method

Solving topology optimization problems using cellular automata and mortar finite element method

MMC.
2020;
Volume 7, Number 2
: pp. 239–247
https://doi.org/10.23939/mmc2020.02.239
Received: March 24, 2020
Revised: May 12, 2020
Accepted: May 15, 2020

Mathematical Modeling and Computing, Vol. 7, No. 2, pp. 239–247 (2020)

Authors:
  1. Yu. O. Yashchuk
  2. K. Tajs-Zielinska
1
Ivan Franko National University of Lviv
2
Cracow University of Technology

Currently topology optimization is widely used by engineers for different practical problems.  Researches by different authors offer algorithms of using cellular automata in these problems, and most recent publications introduce a mesh-refinement procedure to decrease numerical efforts.  In this article, we propose to apply a mortar finite element method for solving topology optimization problems using cellular automata.  This methodology enables us to handle the non-conforming meshes, which can arise in the refinement process.  We present a formulation of the algorithm and analyse its computational complexity by applying to a test problem.

topology optimization
finite element method
cellular automata
adaptive mesh refinement
mortar functions
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