Convergence analysis of hybrid cellular automata for topology optimization

This article is devoted to the application of the cellular automata mathematical apparatus to the problem of continuous optimization. The cellular automaton with an objective function is introduced as a new modification of the classic cellular automaton. The algorithm of continuous optimization, which is based on dynamics of the cellular automaton having the property of geometric symmetry, is obtained. The results of the simulation experiments with the obtained algorithm on standard test functions are provided, and a comparison between the analogs is shown.

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“…A similar direction is presented in papers [10][11][12]. The solution of structural optimization problems is also considered.…”

Section: Introductionmentioning

confidence: 88%

The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton

et al. 2016

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“…This method, thanks to its efficiency and simplicity, has been found useful by researchers representing various branches of modern engineering, including topology optimization. The Cellular Automata approach was discussed within the topology optimization area for the first time by Inou et al [28], but the majority of papers appeared only during the last two decades, see [29][30][31][32][33][34][35][36]. This paper presents the idea of Cellular Automata utilized in the topology optimization of graded multi-material structures, that is optimization of FGM structures as well as multi-material structures including the FGM interface.…”

Section: Introductionmentioning

confidence: 99%

Cellular Automata Approach to Topology Optimization of Graded Multi-Material Structures

Tajs-Zielińska

Bochenek

2023

Applied Sciences

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Despite decades of progress, structural topology optimization is still one of the most important areas of engineering optimal design. The intensive research within this area has been stimulated by the development of efficient methods and algorithms on one side and the needs and demands of contemporary engineering on the other. Over the years, the practical aspect of topology optimization has become one of the most significant issues within the design community. Simultaneously, the range of design applications has been broadening. Among many research areas where topology optimization is present, attention has been paid to the design of multi-material structures. The gradation of the material properties has a significant influence on the final layout of the structure, so this problem can be treated as an extension of the classical task of the topology optimization of structures made of a material with uniform distributions of properties. While working with multi-material structures, the important role plays an interface between parts made of materials with different properties. In this paper, the implementation of interfaces made of functionally graded materials (FGM) is proposed. A functionally graded interface means that continuous and smooth changes of properties are assigned to a particular direction from one material surface to another. This paper presents the idea of topology optimization of graded multi-material structures using a simple, fast convergent technique based on the Cellular Automata approach. The proposal is to take the advantage of the versatility of efficient professional finite element-based structural analysis software and the simplicity of the original heuristic topology generator, to build a tool for the optimization of FGM structures as well as multi-material structures including the FGM interface.

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“…Since then many papers have been published on that subject. The majority of them have appeared during the last two decades, see [34][35][36][37][38][39], for example.…”

Section: Introductionmentioning

confidence: 99%

Bulletin of the Polish Academy of Sciences: Technical Sciences

Tajs-Zielińska,

Bochenek

2021

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Developing novel methods, approaches and computational techniques is essential for solving efficiently more and more demanding up-to-date engineering problems. Designing durable, light and eco-friendly structures starts at the conceptual stage, where new efficient design and optimization tools need to be implemented. Nowadays, apart from the traditional gradient-based methods applied to optimal structural and material design, innovative techniques based on versatile heuristic concepts, like for example Cellular Automata, are implemented. Cellular Automata are built to represent mechanical systems where the special local update rules are implemented to mimic the performance of complex systems. This paper presents a novel concept of flexible Cellular Automata rules and their implementation into topology optimization process. Despite a few decades of development, topology optimization still remains one of the most important research fields within the area of structural and material design. One can notice novel ideas and formulations as well as new fields of their implementation. What stimulates that progress is that the researcher community continuously works on innovative and efficient topology optimization methods and algorithms. The proposed algorithm combined with an efficient analysis system ANSYS offers a fast convergence of the topology generation process and allows obtaining well-defined final topologies.

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Convergence analysis of hybrid cellular automata for topology optimization

Cited by 20 publications

References 29 publications

The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton

The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton

Cellular Automata Approach to Topology Optimization of Graded Multi-Material Structures

Bulletin of the Polish Academy of Sciences: Technical Sciences

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