ASYMPTOTIC ANALYSIS OF POISSONS-EQUATION IN A THIN DOMAIN AND ITS APPLICATION TO THIN-WALLED ELASTIC BEAMS AND TUBES

We study the limit behaviour of solution of Poisson's equation in a cl ass of thin two-dimensional domains, both simply connected or single-h ollowed, as its thickness becomes very small. The method is based on a transformation of the original problem into another posed on a fixed domain, obtention of a priori estimates and convergence results when t hickness parameter tends to zero. As an important application of abstr act results we obtain the limit expressions for functions appearing in elastic beam theories as torsion and warping functions. In this way, we provide a mathematical justification and a correct definition of to rsion, warping and Timoshenko functions and constants that should be u sed in the open and closed thin-walled elastic beam theories. (C) 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.