From: David Wilkinson Subject: Re: A rubber plate problem Date: Tue, 15 Aug 2000 10:26:39 +0100 Newsgroups: sci.math,sci.math.num-analysis Summary: [missing] I think the name is Timoshenko. However, I doubt whether you will find this problem solved anywhere because of the corner fixings. Since the corners of a rectangular plate are points and all the loads of the reaction forces to restrain the plate and let it vibrate are carried through them in your problem the stresses will be infinite there. This means the strains will be infinite there as well. While the infinities are limited to a vanishingly small region and do not indicate infinite deflections, they are still there as singularities and will probably present difficulties to both numerical and analytical solutions. The solutions I have seen for rectangular membranes have zero deflection round the edges so everything is finite. In article <39983B9E.ABB5E50B@liberate.com>, Baolai G. writes >Sounds like a classical problem except that the plate >is point loaded at corners. You didn't mention clearly >what "release it" really means. > >The equation should be a description of the shape or >the forces (e.g. tension), and possibly temperature, etc. >of the plate. > >You may want to check references in the mathematical >theory of elasticity and classical works in mechanics. >A book by Timoshinko ("Theory of Elasticity"? I dont >remember exactly the spelling of his and the name of >the book) has a large collection of classical problems. > >Baolai Ge > >Min-Zhi Shao wrote: > >> I think this should be a classical problem but >> I couldn't find it in my math books. >> >> Say I have a rectangular rubber plate. Then I >> have its four corners pinned and release it. >> What is the equation and solution to this problem? >> >> I'd appreciate it very much if you could point >> me any references, web sites, and in particular >> the formal mathematical name of this problem. >> >> Thanks! >> >> a. l. a. >> >> __________________________________________________ >> Do You Yahoo!? >> Kick off your party with Yahoo! Invites. >> http://invites.yahoo.com/ > -- David Wilkinson ============================================================================== From: =?iso-8859-1?Q?J=E9r=F4me?= Juillard Subject: Re: A rubber plate problem Date: Tue, 15 Aug 2000 10:07:31 +0200 Newsgroups: sci.math,sci.math.num-analysis "Theory of elastic stability", by Timoshenko and Gere, Mc-Graw Hill Book Company, 1961... contains an awful lot of formulas, the worst of them being those for the plates... I wish you a lot of pleasure sorting them out. "Baolai G." wrote: [quote of previously-quoted message deleted --djr]