Bistable conditions

• It turns out that if the beam is made initially curved without prestress, there’ll be conditions for the beam to be bistable.

• The following cosine shape is mathematically proved to be conditionally bistable and its f-d curve is mathematically calculated.

• In Jeffery Lang’s paper, there is a parameter defined as Q=h/t, where h is the apex height, and t is the thickness of the beam.

• In the paper, it is proved that if Q<2.31, the beam cannot be bistable.

• Another requirement for being bistable is that the 2nd mode should be suppressed.

The f-d curve

• His thermal actuator has a 13mN of blocked force and 120 micron of free deflection at a temperature difference of 220 degC.

Layout definition

Mesh settings

• For simulation, one can not solve an arbitrary displacement directly, according to my experience. Instead, one need to increase the displacement bit by bit from zero, and telling Coventor to start the analysis from the result of the previous one.

• In this manner, the simulation will not fail easily, because defining the displacement resolves the large non-linearity of buckling.

100uN force (exaggerate 10 times)

200uN

300uN

Wider beam: 10um wide

Wider beam: 10um wide

• 1mN

Wider beam: 10um wide

• 10mN

100mN

Coventor simulation

• If I define the force and solve for displacement, I can never move on after I’ve reached the maximum force, even if I start from previous result.

A beam with a initial apex height of 80 micron is simulated.

• The simulation was done with a 5 micron step of the centre point displacement, ranging from 0 to 160 micron.

10 micron

80 micron

120 micron

160 micron

Reaction force for 10 micron disp.

Reaction force for 140 micron disp.

Reaction force for 160 micron disp.

Reaction force for 140 micron disp. (showing forces in opposite direction)

That’s all. Thank you very much!