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

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.

KEYWORDS:

• Transient heat conduction
• multi-material topology optimization
• thermal compliance
• sequential quadratic programming

Acknowledgement

The authors are grateful to Professor Krister Svanberg for the open-source MMA program.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was financially supported by the Fundamental Research Funds for the Central Universities [number 2017MS077], the National Natural Science Foundation of China [number 51405123] and the Foundation of Hunan Province Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle [number KF1602].