Kurt Frischmuth, Michael Hänler, Francesco dell'Isola
Numerical methods versus asymptotic expansion for torsion of hollow elastic beams
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Abstract: We consider the torsion problem for a hollow elastic beam. In a series of papers dell'Isola et al.(1994, \cite{iso2,iso3}) a uniform method for the derivation of classical formulas for the torsional rigidity by Bredt, Prandtl and Vlasov was derived using an asymptotic expansion. We show that this expansion yields useful approximations for torsional rigidity if properly applied. Note that it does not converge in general. For the evaluation we use a numerical solution obtained by a Finite Difference Method. Finally, we examine the results of both methods for two example domains.
Keywords: elliptic boundary value problems, torsion problems, asymptotic expansions