About Calculus Through the Transfer Matrix Method of a Beam with Intermediate Support with Applications in Dental Restorations

Otilia Cojocariu-Oltean, Mihai-Sorin Tripa, Iulia Bărăian, Doina-Iulia Rotaru and Mihaela Suciu ()
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Otilia Cojocariu-Oltean: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Mihai-Sorin Tripa: Department of Design Engineering and Robotics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Iulia Bărăian: Department of Automation, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Doina-Iulia Rotaru: Department of Odontology, “Iuliu Haţeganu” University of Medicine and Pharmacy of Cluj-Napoca, 400012 Cluj-Napoca, Romania
Mihaela Suciu: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Mathematics, 2024, vol. 12, issue 23, 1-14

Abstract: This work presents an original and very interesting approach to a calculus problem involving beams with intermediate supports through the transfer-matrix method, a very easy method to program to quickly obtain good results. To exemplify the applicability of this approach in dentistry, the calculus of a dental bridge on three poles is explored. Dental restorations are very important for improving a person’s general state of health as a result of improving mastication and esthetic appearance. The approach used in this study consists of presenting a theoretical study about an indeterminate beam with an intermediate support and then particularizing it for application in a dental restoration case, with a dental bridge on three poles and two missing teeth between the three poles. The bridge is assimilated to a simple static indeterminate beam. This paper is unique in that it involves the application of the transfer-matrix method for a case study in dental restoration. The assimilation of a dental bridge with a statically undetermined beam, resting on the extremities and on an intermediate support, is an original approach. The results obtained in the presented case study were validated by comparison with those obtained through the classical calculation of the Resistance of Materials, with Clapeyron’s equation of three moments. Due to the ease and elegance of solving various problems with the TMM, this approach will continue to be relevant to other original case studies with different modeling requirements, and these applications will be presented in future research.

Keywords: beam with intermediate support; transfer matrix method; charge density; Dirac’s function and operators; Heaviside’s function and operators; dental restoration; dental bridge; dental crown (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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