Metal Gauge Design on Rectangular Membrane

Dear Sir, This is Thangamani, doing research on sensor design. Ihave gone through Mr. Robert Dean (RF CMOS Designer, MEMS Optical,Inc) article that available on internet ( if not mistaken its fromMEMS forum) discussed analytical solution about rectangular membrane.Since i am doing research on sensor design, i am looking foranalytical solution for metal gauge on rectangular membrane. Most ofthe published articles had discussed only about circular membrane,gauge on circular membrane (W K Schomburg, et al., "The Design ofMetal Strain Gauges on Diaphragms" J.Micromech. Microeng. 14 (2004)page 1101 - 1108 ) and rectangular plates but i could not find anypublication on "analytical solution for metal gauge on rectangularmembrane". Hence could you help me to provide more information aboutthis issue. Also i have few questions in my mind which i couldn't getanswer,

1. How the industry / researcher optimized design of gauge onrectangular membrane before FEA tool introduced?

2. How the industry / researcher calculated the active region onrectangular membrane (substrate) to design gauge (grid) pattern beforeFEA (FEM) Tool (like ANSYS) introduced.

3. How the industry / researcher designed gauge (grid) pattern onrectangular membrane 2 or 3 decades ago without a theoreticalexplanation (analytical solution)?

4. Since metal foil strain gauges (rectangular strain gauge) stilldominates due to many features, why could not find a theoreticalstudy (analytical solution) on internet.

Could you please provide answer to my query. This is my humble request.I apologize for taking your time to answer these questions.

Yours Truly

Thangamani Uthirapathi

Centre for Artificial Intelligence
School of Eng & IT
Universiti Malaysia Sabah
Kota Kinabalu, Sabah
MALAYSIA - 88999