Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures
This work presents a topology optimization method for symmetric hierarchical lattice structures with substructuring. In this method, we define two types of symmetric lattice substructures, each of which contains many finite elements. By controlling the materials distribution of these elements, the c...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/4/678 |
| _version_ | 1797569795395158016 |
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| author | Zijun Wu Renbin Xiao |
| author_facet | Zijun Wu Renbin Xiao |
| author_sort | Zijun Wu |
| collection | DOAJ |
| description | This work presents a topology optimization method for symmetric hierarchical lattice structures with substructuring. In this method, we define two types of symmetric lattice substructures, each of which contains many finite elements. By controlling the materials distribution of these elements, the configuration of substructure can be changed. And then each substructure is condensed into a super-element. A surrogate model based on a series of super-elements can be built using the cubic B-spline interpolation. Here, the relative density of substructure is set as the design variable. The optimality criteria method is used for the updating of design variables on two scales. In the process of topology optimization, the symmetry of microstructure is determined by self-defined microstructure configuration, while the symmetry of macro structure is determined by boundary conditions. In this proposed method, because of the educing number of degree of freedoms on macrostructure, the proposed method has high efficiency in optimization. Numerical examples show that both the size and the number of substructures have essential influences on macro structure, indicating the effectiveness of the presented method. |
| first_indexed | 2024-03-10T20:15:43Z |
| format | Article |
| id | doaj.art-ad84d8d0d1d648989f46998de04ebd3f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:15:43Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ad84d8d0d1d648989f46998de04ebd3f2023-11-19T22:34:52ZengMDPI AGSymmetry2073-89942020-04-0112467810.3390/sym12040678Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice StructuresZijun Wu0Renbin Xiao1Hubei Key Laboratory of Digital Textile Equipment, Wuhan Textile University, Wuhan 430073, ChinaSchool of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, ChinaThis work presents a topology optimization method for symmetric hierarchical lattice structures with substructuring. In this method, we define two types of symmetric lattice substructures, each of which contains many finite elements. By controlling the materials distribution of these elements, the configuration of substructure can be changed. And then each substructure is condensed into a super-element. A surrogate model based on a series of super-elements can be built using the cubic B-spline interpolation. Here, the relative density of substructure is set as the design variable. The optimality criteria method is used for the updating of design variables on two scales. In the process of topology optimization, the symmetry of microstructure is determined by self-defined microstructure configuration, while the symmetry of macro structure is determined by boundary conditions. In this proposed method, because of the educing number of degree of freedoms on macrostructure, the proposed method has high efficiency in optimization. Numerical examples show that both the size and the number of substructures have essential influences on macro structure, indicating the effectiveness of the presented method.https://www.mdpi.com/2073-8994/12/4/678topology optimizationsymmetric microstructurelattice structuresurrogate model |
| spellingShingle | Zijun Wu Renbin Xiao Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures Symmetry topology optimization symmetric microstructure lattice structure surrogate model |
| title | Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures |
| title_full | Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures |
| title_fullStr | Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures |
| title_full_unstemmed | Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures |
| title_short | Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures |
| title_sort | substructure based topology optimization for symmetric hierarchical lattice structures |
| topic | topology optimization symmetric microstructure lattice structure surrogate model |
| url | https://www.mdpi.com/2073-8994/12/4/678 |
| work_keys_str_mv | AT zijunwu substructurebasedtopologyoptimizationforsymmetrichierarchicallatticestructures AT renbinxiao substructurebasedtopologyoptimizationforsymmetrichierarchicallatticestructures |