# Topology optimization of thermal actuator and its support using the level set based multiple–type boundary method and sensitivity analysis based on constrained variational principle

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## Abstract

Thermal actuator uses thermal expansion of an elastic body to produce motion at its output port. It needs to accumulate and amplify small local thermal expansion to ensure its output displacement is large enough. Also, its support should constrain the thermal expansion in irrelevant directions and steer the output displacement to a required direction. In the present paper, the task of designing a thermal actuator is formulated as a topology optimization problem. The design variables include two types of boundaries: the free boundary and the Dirichlet boundary. The optimization problem is solved by using a level set based multiple–type boundary method. Two level set functions are used to represent a thermal actuator and its two types of boundaries. Evolution of the two boundaries is modeled by two independent Hamilton–Jacobi equations. In order to analyze the shape derivatives of the two boundaries, the constrained variational principle is employed to explicitly include the Dirichlet boundary condition into the weak form equation of linear thermoelasticity. Numerical examples in two dimensions are investigated.

## Keywords

Thermal actuator Support Level set Constrained variational principle Topology optimization## Notes

### Acknowledgements

This research work is supported by the National Natural Science Foundation of China (Grant No. 51575203, 51705165), the Natural Science Foundation for Distinguished Young Scholars of Hubei province of China (Grant No. 2017CFA044), the Natural Science Foundation of Hubei province of China (Grant No. 2015CFB443). The insightful comments of the reviewers are cordially appreciated.

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