Hello, During my PhD, I dealt with the mechanical properties of thin films widely used in MEMS. I built a set-up for bulge test (membrane under hydrostatic pressure) and I carried out FEM analysis. With the experimental data and the numerical solutions, I fitted the analytical solutions which was first described by Timoshenko and al, and later by Tabata. I wrote many papers about this work but unfortunately, most of them are in French !!! This is my main paper for circular and rectangular membranes : E. Bonnotte, P. Delobelle, L. Bornier, B. Trolard, G. Tribillon : " Two interferometric methods for the mechanical characterization of thin films by bulging test ", J. of Mat. Res., Vol.12, N°9,16 pages, Sept 97. These are the main authors and papers in that field : M. K. Small, W. DF. NIX : " Analysis of the accuracy of the bulge test in determining the mechanical properties of thin films", J. Mater. Res., Vol 7,6 p 1553-1563, 1992 T. Tsakalakos : " The bulge test : comparison of theory and experiment for isotropic and anisotropic films", Thin Solid Films, Vol 75, p293-305, 1981 E. W. Ross, J. R and W. Prager : " On the theory of the bulge test", Quar. Appl. Math, Vol 12, p86-91, 1954 S timoshenko : "plates and shell" Mc Graw-hill, N Y, 1959 You will find also papers from Tabata, Lin & Senturia, Hill.... But anyway it needs to many parameters to describe the analytical equations and after this work, my conclusion was : FEM are easier, quicker and more precise ! Last remark : with FEM, be carefull in the case a/e > 500 (a = radius of circular membrane and e thickness) : a classical FEM software can't run. Eric At 05:06 PM 7/30/98 +0100, you wrote: > Dear colleages, > > I am looking for an analytical solution to calculate the deflection > and the stress/strain behaviour of a clamped circular/square or > rectangular membrane. It seems there is no complete analytical > model for this published (especially in the rectangular case) and > everybody uses FEM instead. > > I am looking for a plug-in solution able to do the following (yes, > I am optimistic ..) : > > + any geometry/aspect ratio (rectangular case) can be calculated > + deflections bigger than membrane thickness are valid > + deflection and strain/stress values as function of position > > Any hint appreciated. Please ... don't just mention Timoshenko. > > Thanks, > > Werner. > <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< > W J K A R L > MEMS Unit, U of Sheffield Home 'sweet Home : > Mappin Street Cobden View Rd. 7o > Sheffield S1 3JD, UK Sheffield S1o 1HQ > +44 (0) 114 222 5182/5890 South Yorks., UK > Fax (0) 114 272 6391 +44 (0) 114 266 2831 > elp95wjk@sheffield.ac.uk > >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> > What has two legs and three ears ? - A happy Tyson :-) > > mailto:bonnotte@clamart.srpc.slb.com ===================================================== Eric Bonnotte Schlumberger Wireline and Testing SRPC- Clamart 26 rue de la cavee 92140 Clamart FRANCE Tel : +33 (0)1 45 37 22 95 Fax : +33 (0)1 45 37 26 93 =======================================================