Topology optimization of transient nonlinear heat conduction using an adaptive parameterized level-set method

ABSTRACT

In this article, topology optimization of transient nonlinear heat conduction problems is solved by a parameterized level-set method. Nonlinear density-based and continuum shape sensitivity analyses are conducted for topology generation and shape optimization. Meanwhile, the backward time transient adjoint structures are derived. To suppress dependence of the initial guess for the parameterized level-set-based topology optimization, the solid isotropic material with penalization method is adopted to generate the initial topology design. Then, the parameterized level-set method is further performed to obtain the optimal shape. The material volume is strictly controlled by restricting the coefficients of radial basis functions within a dynamic bound, which can avoid incorrect topological results due to topological changes. Finally, three numerical examples are solved with the parameterized level-set method, which demonstrates that the proposed approach can obtain complex topological details with smooth boundaries for transient nonlinear heat conduction problems.

KEYWORDS:

• Topology optimization
• parameterized level set
• transient nonlinear heat conduction
• nonlinear finite element method

Acknowledgements

The authors are grateful to Professor K. Svanberg for the assistance on the MMA and GCMMA algorithms.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partly supported by National Natural Science Foundation of China [grant no. 51775344].