The large deflections of a clamped circular plate are investigated over a wide range of transverse loadings and initial in-plane tension loads. The continuous transition from plate behavior to membrane behavior is described in detail, along with the development of the accompanying edge zone region where properties change rapidly. We give a simple approximation of this edge zone and its properties, provide limits for the validity of small deflection, linear theory, and note the similar effects of large in-plane tension and large transverse loading. The values and trends are presented in general nondimensional form, and should prove useful for the design of thin circular disks for microsensing applications.

1.
Allen, M. G., 1986, “Measurement of Mechanical Properties and Adhesion of Thin Polyimide Films,” M.S. thesis, MIT, Cambridge, MA.
2.
Abramowitz, M., and Stegun, I. A., 1972, Handbook of Mathematical Functions, 9th Ed., Dover, New York.
3.
Anderson, D. A., Tannehill, J. C., and Pletcher, R. H., 1984, Computational Fluid Mechanics and Heat Transfer, Hemisphere, New York.
4.
Chau
H.-L.
, and
Wise
K. D.
,
1987
, “
Scaling Limits in Batch-Fabricated Silicon Pressure Sensors
,”
IEEE Transaction of Electron Devices
, Vol.
ED–34
, pp.
850
858
.
5.
Cho
S. T.
,
Najafi
K.
, and
Wise
K. D.
,
1992
, “
Internal Stress Compensation and Scaling in Ultra-sensitive Silicon Pressure Sensors
,”
IEEE Transaction of Electron Devices
, Vol.
39
, No.
4
, pp.
836
842
.
6.
Clark
S. K.
, and
Wise
K. D.
,
1979
, “
Pressure Sensitivity in Anisotropically Etched Thin-Diaphragm Pressure Sensors
,”
IEEE Transaction of Electron Devices
, Vol.
ED-26
, No.
12
, pp.
1887
1896
.
7.
Friedrichs
K. O.
,
1949
, “
The Edge Effect In Bending and Buckling with Large Deflections
,”
Proceedings of Symposia in Applied Mathematics
, Vol.
1
(Non-Linear Problems in Mechanics of Continua), American Mathematical Society, New York, pp.
188
193
.
8.
Lo¨fdahl
L.
,
Ka¨lvesten
E.
, and
Stemme
G.
,
1994
, “
Small Silicon Based Pressure Transducers for Measurements in Turbulent Boundary Layers
,”
Experiments in Fluids
, Vol.
17
, pp.
24
31
.
9.
McPherson, A., Ramberg, W., and Levy, S., 1942, “Normal-Pressure Tests of Circular Plates with Clamped Edge,” NACA Technical Report 744.
10.
Na´dai, A., 1925, Elastisclie Platten, Julius Springer, Berlin, p. 288.
11.
Roberts
G. O.
,
1971
, “
Computational Meshes for Boundary Layer Problems
,”
Lecture Notes in Physics
, Vol.
8
, Springer-Verlag, New York, pp.
171
177
.
12.
Schellin
R.
, and
Hess
G.
,
1992
, “
A Silicon Subminiature Microphone Based on Piezoresistive Polysilicon Strain Gauges
,”
Sensors and Actuators A
, Vol.
32
, pp.
555
559
.
13.
Sze, S. M., 1994, Semiconductor Sensors, John Wiley and Sons, New York.
14.
Timoshenko, S. P., and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, 2nd Ed., McGraw-Hill, New York.
15.
Voorthuyzen
J. A.
, and
Bergveld
P.
,
1984
, “
The Influence of Tensile Forces on the Deflection of Circular Diaphragms in Pressure Sensors
,”
Sensors and Actuators A
, Vol.
6
, pp.
201
213
.
16.
Way
S.
,
1934
, “
Bending of Circular Plates with Large Deflection
,”
Transactions of the ASME
, Vol.
56
, pp.
627
636
.
17.
Zhen, X., and Zhou, Y., 1990, “Analytical Formulas of Solutions of Geometrically Nonlinear Equations of Axisymmetric Plates and Shallow Shells,” Acta Mechanica Sinca, Vol. 6, No. 1.
This content is only available via PDF.
You do not currently have access to this content.