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Multiphase topology optimization with a single variable using the phase‐field design method
Author(s) -
Seong Hong Kyoung,
Kim Cheol Woong,
Yoo Jeonghoon,
Lee Jaewook
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6052
Subject(s) - topology optimization , mathematical optimization , variable (mathematics) , isotropy , computation , mathematics , constraint (computer aided design) , function (biology) , field (mathematics) , topology (electrical circuits) , probability density function , sensitivity (control systems) , computer science , algorithm , mathematical analysis , geometry , finite element method , engineering , statistics , physics , structural engineering , quantum mechanics , combinatorics , pure mathematics , evolutionary biology , electronic engineering , biology
Summary In this study, a multimaterial topology optimization method using a single variable is proposed by combining the solid isotropic material with penalization method and the reaction‐diffusion equation. Unlike ordinary multimaterial optimization, which requires several variables depending on the number of material types, this method intends to represent various materials as one variable. The proposed method combines two special functions in the sensitivity analysis of the objective function to converge the design variable into prespecified density values defined for each of the multimaterials. The composition constraint based on a normal distribution function is also introduced to estimate the distribution of each target density value in a single variable. It enables density exchange between multiple materials by increasing or decreasing the amount of a specific material. The proposed method is applied to structural and electromagnetic problems to verify its effectiveness, and its usefulness is also confirmed from the viewpoint of cost and computation time.