Example: Microrobot leg 3D

Introduction

• This model shows the movement of a silicon micro-robot leg due to thermal expansion as a function of time.

• The heat transfer and structural mechanics equations are solved sequentially in a time-dependent analysis.

– The heat transfer problem is a transient analysis while the structural problem is modeled in a quasi-static analysis.

• In order to reduce the degrees of freedom a geometry simplification was required for the 3D model removing two layers:

– The thin highly-conductive layer and poorly conductive layer are modeled with the thin conductive shell application mode from the heat transfer module and stiff spring temperature boundary conditions respectively.

– The shell element application from the structural mechanical module is used for modeling the mechanical part.

Geometry

Heating resistors

Cured polyamide (high thermal expansion coefficient)

Silicon leg

• The general heat transfer equation:

• The principle of virtual work for the structural mechanics

Domain Equations

QTk )(

dSdVdVS

t

V

t

V

t )()()( upupεσ sv

Boundary Conditions - heat

Highly conductive layer& stiff spring condition

Highly conductive layer onlyConvective flux

Convective fluxAll other boundaries have thermal insulation conditions

Boundary Conditions – structural mechanics

No displacement

Structural shell element including thermal expansion

All other boundaries are free to move

Results

• The microrobot leg bends due to the heating of the leg

Results

• The maximum displacement at the tip of the leg is 0.6 mm for a heat source of 2e13W/m3 during 9 ms.

Results

• The highly conductive layer and the stiff spring condition accurately model the thin layers.

Results - Animation

Conclusion

• A thermal stress analysis is straight forward to perform in the Structural Mechanics module

• Model shows the possibility to replace thin layers by a specific boundary condition, and save memory:

– Highly conductive layer boundary condition (already implemented)– Stiff spring condition to model a poorly conductive layer– Direct coupling of shell and solid element in structural mechanics

• Large transient multiphysics problem solve sequentially using quasi-static analysis and the manual definition of the linearization point.