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Multi-material topology optimization for the transient heat conduction problem using a sequential quadratic programming algorithm
Authors:Kai Long  Xuan Wang  Xianguang Gu
Affiliation:1. Beijing Key Laboratory of Energy Safety and Clean Utilization, North China Electric Power University, Beijing, People’s Republic of China;2. State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, People’s Republic of China;3. Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle, The Education Department of Hunan Province, Changsha University of Science &4. Technology, Changsha, People’s Republic of China;5. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, People’s Republic of China;6. School of Automobile and Traffic Engineering, Hefei University of Technology, Hefei, People’s Republic of China
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
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