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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Bibliographic Details
Published in:Structural and multidisciplinary optimization Vol. 55; no. 2; pp. 477 - 491
Main Authors: Zuo, Wenjie, Saitou, Kazuhiro
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2017
Springer Nature B.V
Subjects:
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 Access:Get full text
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Summary: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.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-016-1513-3