Abstract
Using web functions, we approximate the Dirichlet integral which represents the torsional rigidity of a cylindrical rod with planar convex cross-section Ω. To this end, we use a suitably defined piercing function, which enables us to obtain bounds for both the approximate and the exact value of the torsional rigidity. When Ω varies, we show that the ratio between these two values is always larger than ¾; we prove that this is a sharp lower bound and that it is not attained. Several extremal cases are also analyzed and studied by numerical methods.
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Accepted February 8, 2002¶Published online August 29, 2002
Communicated by C. A. Stuart
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Crasta, G., Fragalà, I. & Gazzola, F. A Sharp Upper Bound for the¶Torsional Rigidity of Rods¶by Means of Web Functions. Arch. Rational Mech. Anal. 164, 189–211 (2002). https://doi.org/10.1007/s002050200205
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DOI: https://doi.org/10.1007/s002050200205