Materials

This paper presents the results of a further stage of the authors’ research into the lateral torsional buckling of hot-rolled bisymmetric I-beams, spatially elastically restrained at the support nodes, i.e., against: (1) warping, (2) rotation in the lateral torsional buckling plane and (3) rotation in the main bending plane M_y. The analysis considered the entire range of variation in node stiffness, from free support in bending M_y and full freedom of warping and rotation in the lateral torsional buckling plane, to full restraint of the beam at the nodes. The authors introduced a general approximation formula (AF) for the critical moment of lateral torsional buckling M_cr, simultaneously considering the three elastic fixity indexes for basic and frequently occurring loading schemes in engineering practice. In order to facilitate the calculations, the authors have included the full sequence of formulas for the successive components of the critical moment, derived in the authors’ previous papers. The ability to more accurately consider the actual conditions of the spatial elastic restraint of the beam at the nodes leads to a more accurate calculation of M_cr. The results obtained were compared with FEM (LTBeamN software, v. 1.0.3) by performing a large number of calculations and numerical simulations. The agreement of the AF/FEM results was achieved at a level sufficient from the engineering point of view (mean value 1.006, standard deviation 0.028, coefficient of variation 2.8%). Detailed calculations were carried out for different section types (I, H) and different combinations of fixity index values. The application of approximation formulas in practical calculations is demonstrated on an example. The formulas derived in the paper can be used, among other things, to verify the correctness of FEM calculations, including the correct modelling of elastic support restraints, which is important in design practice.

Orthodontic treatment, offering significant benefits for oral function and facial aesthetics, is in high demand among both adolescent and adult populations. Orthodontic appliances pose challenges for maintaining oral hygiene and increase the risk of dental and periodontal diseases. With advances in dental materials and the use of nanoparticles, a significant amount of research has focused on modifying orthodontic appliances with nanoparticles to reduce bacterial adhesion and biofilm formation. Silver nanoparticles are one of the most popular antibacterial materials in medical research. This article presents current evidence on silver nanoparticle-incorporated orthodontic appliances, including brackets, molar bands, archwires, elastomeric ligatures, mini-implants, and acrylic retainers. Silver nanoparticles and modified silver nanoparticles exhibit robust antibacterial activity when applied to the surfaces of orthodontic appliances. However, there are exceptions in which, on a few orthodontic appliances, the silver nanoparticle incorporation actually increased biofilm formation. Moreover, a silver nanoparticle incorporation may introduce adverse effects, such as cytotoxicity, and increase surface roughness. It is also worth noting that most of the studies were conducted in vitro. Long-term clinical studies are necessary to evaluate the stability, safety, and clinical efficacy of silver nanoparticle-incorporated orthodontic appliances under real-world conditions.

In this study, using the newly designed high-entropy alloy TiCoCrFeMn as an example, mathematical models for determining the true hardness from microhardness measurements in the regime dominated by elastic deformation were analyzed. It was found that the PSR model, which accounts for the variability in the elastic component of the applied indenter load, provides the best agreement with macroscopic hardness measurements. Analysis of the load variation law revealed a correlation between the Young’s modulus and the Meyer coefficient, which formed the basis for developing a model for determining this material parameter from microhardness measurements. The proposed methodology, applicable to small laboratory specimens, was shown to be consistent with the results obtained from crack-length measurements.