Multi-material topology optimization using ordered SIMP interpolation

In this paper an ordered multi-material SIMP (solid isotropic material with penalization) interpolation is proposed to solve multi-material topology optimization problems without introducing any new variables. Power functions with scaling and translation coefficients are introduced to interpolate th...

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Veröffentlicht in:	Structural and multidisciplinary optimization Jg. 55; H. 2; S. 477 - 491
Hauptverfasser:	Zuo, Wenjie, Saitou, Kazuhiro
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2017 Springer Nature B.V
Schlagworte:	Computational Mathematics and Numerical Analysis Elastic properties Engineering Engineering Design Interpolation Isotropic material Iterative methods Materials selection Modulus of elasticity Phase transitions Research Paper Theoretical and Applied Mechanics Topology optimization Topology optimization Multi-material design Ordered SIMP
ISSN:	1615-147X, 1615-1488
Online-Zugang:	Volltext
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Abstract	In this paper an ordered multi-material SIMP (solid isotropic material with penalization) interpolation is proposed to solve multi-material topology optimization problems without introducing any new variables. Power functions with scaling and translation coefficients are introduced to interpolate the elastic modulus and the cost properties for multiple materials with respect to the normalized density variables. Besides a mass constraint, a cost constraint is also considered in compliance minimization problems. A heuristic updating scheme of the design variables is derived from the Kuhn-Tucker optimality condition (OC). Since the proposed method does not rely on additional variables to represent material selection, the computational cost is independent of the number of materials considered. The iteration scheme is designed to jump across the discontinuous point of interpolation derivatives to make stable transition from one material phase to another. Numerical examples are included to demonstrate the proposed method. Because of its conceptual simplicity, the proposed ordered multi-material SIMP interpolation can be easily embedded into any existing single material SIMP topology optimization codes.
AbstractList	In this paper an ordered multi-material SIMP (solid isotropic material with penalization) interpolation is proposed to solve multi-material topology optimization problems without introducing any new variables. Power functions with scaling and translation coefficients are introduced to interpolate the elastic modulus and the cost properties for multiple materials with respect to the normalized density variables. Besides a mass constraint, a cost constraint is also considered in compliance minimization problems. A heuristic updating scheme of the design variables is derived from the Kuhn-Tucker optimality condition (OC). Since the proposed method does not rely on additional variables to represent material selection, the computational cost is independent of the number of materials considered. The iteration scheme is designed to jump across the discontinuous point of interpolation derivatives to make stable transition from one material phase to another. Numerical examples are included to demonstrate the proposed method. Because of its conceptual simplicity, the proposed ordered multi-material SIMP interpolation can be easily embedded into any existing single material SIMP topology optimization codes.
Author	Zuo, Wenjie Saitou, Kazuhiro
Author_xml	– sequence: 1 givenname: Wenjie surname: Zuo fullname: Zuo, Wenjie email: zuowenjie@jlu.edu.cn organization: State Key Laboratory of Automotive Simulation and Control, Jilin University, School of Mechanical Science and Engineering, Jilin University – sequence: 2 givenname: Kazuhiro surname: Saitou fullname: Saitou, Kazuhiro organization: Department of Mechanical Engineering, University of Michigan
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Keywords	Topology optimization Multi-material design Ordered SIMP
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Snippet	In this paper an ordered multi-material SIMP (solid isotropic material with penalization) interpolation is proposed to solve multi-material topology...
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StartPage	477
SubjectTerms	Computational Mathematics and Numerical Analysis Elastic properties Engineering Engineering Design Interpolation Isotropic material Iterative methods Materials selection Modulus of elasticity Phase transitions Research Paper Theoretical and Applied Mechanics Topology optimization
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Title	Multi-material topology optimization using ordered SIMP interpolation
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