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Perturbation Sensitivity Analysis and Dynamic Topology Optimization for Heat Conduction Structure

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Abstract

Topology optimization is a fundamental problem for steady heat conduction. Due to the unidirectional treatment for the intermediate density elements in the traditional topology optimization, we propose a Bi-Directional Interpolation Model (BDIM) that intermediate density elements are judged by a threshold, and establish optimization model. Besides, considering the generation of new hole boundary in the process of heat conduction enhancement topology optimization, we study the perturbation sensitivity analysis with respect to new hole, and present an adaptive dynamic boundary method for the new boundary in the optimization process. Furthermore, based on the domain perturbation technique and Lebesgue differential theory, the topological derivative formulas with different objective functions subjected to three kinds of boundary conditions are derived for the control system of Poisson equation. Finally, a number of numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method for designing the heat conduction structure.

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Acknowledgements

The authors gratefully acknowledge the financial support from the Talent Foundation of Science & Technology Department of Guizhou Province (20175117), Major Science and Technology Special Project of Guizhou province (20163001) and Key Laboratory Project of Guizhou Provincial Education Department (GY20143026).

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Authors and Affiliations

  1. School of Mechanical Engineering, Guizhou University, Guiyang, 550025, China

    Jiachun Li, Zhongfei Zou & Yuewei Chen

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  1. Jiachun Li
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Correspondence to Jiachun Li.

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Li, J., Zou, Z. & Chen, Y. Perturbation Sensitivity Analysis and Dynamic Topology Optimization for Heat Conduction Structure. Wireless Pers Commun 103, 657–676 (2018). https://doi.org/10.1007/s11277-018-5468-0

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