RT Journal Article
T1 Three-point bending tests. Part I: Mathematical study and asymptotic analysis
A1 Quintela Estévez, Peregrina
A1 Sánchez Rúa, María Teresa
K1 Modulus of rupture
K1 Contact conditions
K1 Assymptotic analysis
AB The goal of this work is to study the static behaviour of a three-dimensional elastic beam when is subjected to a three-pointbending test. In the  rst part, under suitable compatibility conditions on the applied forces and on the geometry of thebeam, we will prove the existence of a unique solution for the associated contact elastic problem; these conditions ofcompatibility on the data come from the absence of a Dirichlet condition on the beam boundary. In the second part, wewill study the asymptotic behaviour of this problem; in particular, we will deduce the one-dimensional models associatedto the displacement components, and we will give the existence and uniqueness of solution for them. Moreover, we willgive an expression for the normal axial stress in the beam which is related to the modulus of rupture of brittle materials. Inthe  nal part of the work, we will deal with the regularity of the solution for the bending problem and we will prove someproperties of the coincidence set
PB Wiley
SN 0170-4214
YR 2011
FD 2011
LK http://hdl.handle.net/10347/32448
UL http://hdl.handle.net/10347/32448
LA eng
NO Quintela, P., Sánchez, M.T. (2011). Three-point bending tests. Part I: Mathematical study and asymptotic analysis. Mathematical Methods in the Applied Sciences, 34(10), pp. 1211-1235
NO This is the peer reviewed version of the following article: Quintela, P., Sánchez, M.T. (2011). Three-point bending tests. Part I: Mathematical study and asymptotic analysis. Mathematical Methods in the Applied Sciences, 34(10), pp. 1211-1235, which has been published in final form at https://doi.org/10.1002/mma.1434. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
NO This research was supported by CICYT-FEDER (DPI2004-01993, MTM2008, 05682) and Xunta de Galicia (project PGIDIT05PXIC20701PN).
DS Minerva
RD 22 abr 2026