Multi-material topology optimization for the transient heat conduction problem using a sequential quadratic programming algorithm

Transient heat conduction analysis involves extensive computational cost. It becomes more serious for multi-material topology optimization, in which many design variables are involved and hundreds of iterations are usually required for convergence. This article aims to provide an efficient quadratic...

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Published in:Engineering optimization Vol. 50; no. 12; pp. 2091 - 2107
Main Authors: Long, Kai, Wang, Xuan, Gu, Xianguang
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.12.2018
Taylor & Francis Ltd
Subjects:
Asymptotes
Computational efficiency
Computing time
Conduction heating
Conductive heat transfer
Cost analysis
Design optimization
Isotropic material
Iterative methods
multi-material topology optimization
Quadratic programming
sequential quadratic programming
Series expansion
Taylor series
thermal compliance
Topology optimization
Transient heat conduction
Weight
ISSN:0305-215X, 1029-0273
Online Access:Get full text
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Abstract Transient heat conduction analysis involves extensive computational cost. It becomes more serious for multi-material topology optimization, in which many design variables are involved and hundreds of iterations are usually required for convergence. This article aims to provide an efficient quadratic approximation for multi-material topology optimization of transient heat conduction problems. Reciprocal-type variables, instead of relative densities, are introduced as design variables. The sequential quadratic programming approach with explicit Hessians can be utilized as the optimizer for the computationally demanding optimization problem, by setting up a sequence of quadratic programs, in which the thermal compliance and weight can be explicitly approximated by the first and second order Taylor series expansion in terms of design variables. Numerical examples show clearly that the present approach can achieve better performance in terms of computational efficiency and iteration number than the solid isotropic material with penalization method solved by the commonly used method of moving asymptotes. In addition, a more lightweight design can be achieved by using multi-phase materials for the transient heat conductive problem, which demonstrates the necessity for multi-material topology optimization.
AbstractList Transient heat conduction analysis involves extensive computational cost. It becomes more serious for multi-material topology optimization, in which many design variables are involved and hundreds of iterations are usually required for convergence. This article aims to provide an efficient quadratic approximation for multi-material topology optimization of transient heat conduction problems. Reciprocal-type variables, instead of relative densities, are introduced as design variables. The sequential quadratic programming approach with explicit Hessians can be utilized as the optimizer for the computationally demanding optimization problem, by setting up a sequence of quadratic programs, in which the thermal compliance and weight can be explicitly approximated by the first and second order Taylor series expansion in terms of design variables. Numerical examples show clearly that the present approach can achieve better performance in terms of computational efficiency and iteration number than the solid isotropic material with penalization method solved by the commonly used method of moving asymptotes. In addition, a more lightweight design can be achieved by using multi-phase materials for the transient heat conductive problem, which demonstrates the necessity for multi-material topology optimization.
Author Long, Kai
Gu, Xianguang
Wang, Xuan
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  givenname: Xianguang
  surname: Gu
  fullname: Gu, Xianguang
  organization: School of Automobile and Traffic Engineering, Hefei University of Technology
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Snippet Transient heat conduction analysis involves extensive computational cost. It becomes more serious for multi-material topology optimization, in which many...
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SubjectTerms Asymptotes
Computational efficiency
Computing time
Conduction heating
Conductive heat transfer
Cost analysis
Design optimization
Isotropic material
Iterative methods
multi-material topology optimization
Quadratic programming
sequential quadratic programming
Series expansion
Taylor series
thermal compliance
Topology optimization
Transient heat conduction
Weight
Title Multi-material topology optimization for the transient heat conduction problem using a sequential quadratic programming algorithm
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