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Asymptotic analysis of Poisson's equation in a thin domain and its application to thin‐walled elastic beams and tubes
Author(s) -
Rodríguez José M.,
Viaño Juan M.
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199802)21:3<187::aid-mma941>3.0.co;2-h
Subject(s) - image warping , mathematics , timoshenko beam theory , mathematical analysis , a priori and a posteriori , torsion (gastropod) , poisson distribution , poisson's equation , limit (mathematics) , beam (structure) , physics , medicine , philosophy , statistics , surgery , epistemology , artificial intelligence , computer science , optics
We study the limit behaviour of solution of Poisson's equation in a class of thin two‐dimensional domains, both simply connected or single‐hollowed, 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 thickness parameter tends to zero. As an important application of abstract 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 torsion, warping and Timoshenko functions and constants that should be used in the open and closed thin‐walled elastic beam theories. © 1998 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.