In this paper, we develop original analytical electro-thermal and thermo-mechanical models for the U-shaped electrothermal actuator. Dynamics of the temperature distribution and displacement are obtained as a direct relationship between the system dimensions, material properties and electrical input. The electrothermal model provides an exact solution of the hybrid PDEs that describe the electrothermal behavior for each of the actuator's three connected arms. The solution is obtained using a new calculation method that allows representing an integrable function by an hybrid infinite sum of sine and cosine functions. Displacement at the actuator's tip is then calculated using a quasistatic model based on the superposition and virtual works principles. Obtained temperature and displacement solutions are then discussed and compared with finite element method (FEM) simulations via ANSYS and experimental results. Comparisons showed good agreement making the proposed modeling a reliable alternative which paves the way for improving the design and optimizing the dimensions of U-shaped micro-actuators.
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