Three-point bending tests. Part I: Mathematical study and asymptotic analysis
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Abstract
The goal of this work is to study the static behaviour of a three-dimensional elastic beam when is subjected to a three-point
bending test. In the rst part, under suitable compatibility conditions on the applied forces and on the geometry of the
beam, we will prove the existence of a unique solution for the associated contact elastic problem; these conditions of
compatibility on the data come from the absence of a Dirichlet condition on the beam boundary. In the second part, we
will study the asymptotic behaviour of this problem; in particular, we will deduce the one-dimensional models associated
to the displacement components, and we will give the existence and uniqueness of solution for them. Moreover, we will
give an expression for the normal axial stress in the beam which is related to the modulus of rupture of brittle materials. In
the nal part of the work, we will deal with the regularity of the solution for the bending problem and we will prove some
properties of the coincidence set
Description
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.
Bibliographic citation
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
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https://doi.org/10.1002/mma.1434Sponsors
This research was supported by CICYT-FEDER (DPI2004-01993, MTM2008, 05682) and Xunta de Galicia (project PGIDIT05PXIC20701PN).
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