VM236

VM236
Hysteresis Calculation of a Beam Under Electrostatic Load

Overview

Reference:

J. R. Gilbert, G. K. Ananthasuresh, S. D. Senturia, "3D Modeling of Contact Problems and Hysteresis in Coupled Electro-Mechanics", MEMS, 1996, pp. 127-132.

Analysis Type(s):

Static (ANTYPE = 0)

Element Type(s):

2D Coupled-Field Solid Elements (PLANE223, KEYOPT(1) = 1001)

2D 4-Node Structural Solid Elements (PLANE182)

3D Node-to-Node Contact Elements (CONTA178)

Input Listing:

vm236.dat

Test Case

A beam of length L = 80 μm at a height T = 0.5 μm is suspended 0.7 μm above a ground plane and is clamped at either end. Using this beam, model the hysteresis (pull-in and release behaviors) when it is placed under electrostatic load.

Figure 397: Beam Under Electrostatic Load

Beam at beginning and unloading.

Beam at pull-in voltage.

Model the hysteresis (pull-in and release behaviors) of a structural beam under electrostatic load.

Material Properties

Geometric Properties

EX = 169E3

NUXY = 0.25

PERX = 1

MU = 0

Beam Length = 80 microns

Beam Height = 0.5 microns

Gap = 0.7 microns

V(1) = 11.0V

V(2) = 14.5V

V(3) = 18.0V

Analysis Assumptions and Modeling Notes

Using symmetry at a length L=40 μm, the solid beam is modeled with quad shaped PLANE182 elements. The air gap is modeled with 2D coupled-field PLANE223 elements with KEYOPT(1) = 1001 for an electroelastic analysis. Node-Node contact is modeled in the air gap using CONTA178 elements. The beam is constrained in the X and Y directions on the left side and is free only in the Y-direction along the span. The beam is suspended 0.7 μm over the ground plane with a contact stop at 0.1μm.

Results Comparison

	Target	Mechanical APDL	Ratio
UY @ 11.0V	-0.0722	-0.0724	1.002
UY @ 14.5V	-0.1451	-0.1456	1.004
UY @ 18.0V	-0.6004	-0.6002	1.000
UY @ 14.5V	-0.6002	-0.6002	1.000
UY @ 11.0V	-0.0723	-0.0725	1.002