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Explicit control of 2D and 3D structural complexity by discrete variable topology optimization method

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2022年 389卷 114302-114302页

作者： Liang, Yuan Yan, XinYu Cheng, GengDong Dalian Univ Technol Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian 116023 Peoples R China

The structural complexity (the number of holes) of the 2D or 3D continuum structures can be measured by their topology invariants (i.e., Euler and Betti numbers). controlling the 2D and 3D structural complexity is significant in topology optimization design because of the various consideration, including manufacturability and necessary structural redundancy, but remains a challenging subject. In this paper, we propose a programmable Euler-Poincare formula to efficiently calculate the Euler and Betti numbers for the 0-1 pixel-based structures. This programmable Euler-Poincare formula only relates to the nodal density and nodal characteristic vector that represents the nodal neighbor relation so that it avoids manually counting the information of the vertices, edges, and planes on the surfaces of the structure. As a result, the explicit formulations between the structural complexity (the number of holes) and the discrete density design variables for 2D and 3D continuum structures can be efficiently constructed. Furthermore, the discrete variable sensitivity of the structural complexity is calculated through the programmable Euler-Poincare formula so that the structural complexity control problem can be efficiently and mathematically solved by Sequential Approximate Integer Programming and Canonical relaxation algorithm Various 2D and complicated 3D numerical examples are presented to demonstrate the effectiveness of the method. We further believe that this study bridges the gap between structural topology optimization and mathematical topology analysis, which is much expected in the structural optimization community. (c) 2021 Elsevier B.V. All reserved.

关键词： Topology optimization structural complexity control Topology invariants Euler and Betti number Integer programming

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A direct approach to controlling the topology in structural optimization

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COMPUTERS & STRUCTURES 2020年 227卷 106141-000页

作者： Zhao, Zi-Long Zhou, Shiwei Cai, Kun Xie, Yi Min RMIT Univ Ctr Innovat Struct & Mat Sch Engn Melbourne Vic 3001 Australia XIE Archi Struct Design Shanghai 200092 Peoples R China

structural shape and topology optimization has undergone tremendous developments in recent years due to its important applications in many fields. However, effectively controlling the structural complexity of the optimization result remains a challenging issue. The structural complexity is usually characterized by the distribution and geometries of interior holes. In this work, a new approach is developed based on the graph theory and the set theory to control the number and size of interior holes of the optimized structures. The minimum distance between the edges of any two neighboring holes can also be constrained. The structural performance and the effect of the structural complexity control are well balanced by using this approach. We use three typical numerical examples to verify the effectiveness of the developed approach. The optimized structures with and without constraints on the structural complexity are quantitatively compared and analyzed. The present methodology not only enables the designer to have a direct control over the topology of the optimized structures, but also provides diverse and competitive solutions. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： structural optimization structural complexity control Interior holes Diverse and competitive solutions

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A thinning algorithm based approach to controlling structural complexity in topology optimization

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2022年 207卷

作者： He, Yunzhen Zhao, Zi-Long Cai, Kun Kirby, James Xiong, Yulin Xie, Yi Min RMIT Univ Ctr Innovat Struct & Mat Sch Engn Melbourne 3001 Australia Beihang Univ Inst Solid Mech Sch Aeronaut Sci & Engn Beijing 100191 Peoples R China

Shape and topology optimization techniques aim to maximize structural performance through material redis-tribution. Effectively controlling structural complexity during the form-finding process remains a challenging issue. structural complexity is usually characterized by the number of connected components (e.g., beams and bars), tunnels, and cavities in the structure. Existing structural complexity control approaches often prescribe the number of existing cavities. However, for three-dimensional problems, it is highly desirable to control the number of tunnels during the optimization process. Inspired by the topology-preserving feature of a thinning algorithm, this paper presents a direct approach to controlling the topology of continuum structures under the framework of the bi-directional evolutionary structural optimization (BESO) method. The new approach can explicitly control the number of tunnels and cavities for both two-and three-dimensional problems. In addition to the structural topology, the minimum length scale of structural components can be easily controlled. Nu-merical results demonstrate that, for a given set of loading and boundary conditions, the proposed methodology may produce multiple high-performance designs with distinct topologies. The techniques developed from this study will be useful for practical applications in architecture and engineering, where the structural complexity usually needs to be controlled to balance the aesthetic, functional, economical, and other considerations.

关键词： Topology optimization structural complexity control Diverse and competitive structural designs BESO Thinning algorithm

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A hole-filling based approach to controlling structural complexity in topology optimization

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2023年 416卷

作者： He, Yunzhen Zhao, Zi-Long Lin, Xiaoshan Xie, Yi Min RMIT Univ Ctr Innovat Struct & Mat Sch Engn Melbourne 3001 Australia Beihang Univ Inst Solid Mech Sch Aeronaut Sci & Engn Beijing 100191 Peoples R China

Shape and topology optimization problems are usually associated with geometrical restrictions. Effective control of structural complexity during the optimization process is important for various considerations, e.g., functionality, manufacturability, and aesthetics. Most existing approaches characterize structural complexity as the number of cavities. However, for three-dimensional structures, the genus (i.e., the number of tunnels) should also be considered as an additional topological constraint. In this paper, a hole-filling method is integrated into the bi-directional evolutionary structural optimization (BESO) computational framework to control the number and size of existing cavities and tunnels during the form-finding process. In the hole-filling method, excess cavities are filled with solid material and excess tunnels are covered by building sheet-like patches. The minimum size of the truss-like components and the minimum thickness of the sheet-like components can be controlled separately. Several two-and three-dimensional compliance minimization problems are presented to demonstrate the effectiveness and potential applications of the proposed approach. The structural performances of the optimized structures with and without complexity control are compared and analyzed. The results show that the developed methodology can produce structurally efficient designs with controllable topologies. It is also demonstrated that the generation of sheet-like components can considerably increase the stiffness of the optimized structure. The proposed approach is capable of generating diverse and competitive designs for architects and engineers to achieve a fine balance between architectural novelty and structural efficiency.& COPY;2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Topology optimization structural complexity control Diverse and competitive structural designs Topological constraints

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