Applications of the Calculus by the Transfer Matrix Method for Long Rectangular Plates Under Uniform Vertical Loads
Cosmin-Sergiu Brisc,
Mihai-Sorin Tripa,
Ilie-Cristian Boldor,
Dan-Marius Dumea,
Robert Gyorbiro,
Petre-Corneliu Opriţoiu,
Laurenţiu Eusebiu Chifor,
Ioan-Aurel Chereches,
Vlad Mureşan and
Mihaela Suciu ()
Additional contact information
Cosmin-Sergiu Brisc: 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
Ilie-Cristian Boldor: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Dan-Marius Dumea: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Robert Gyorbiro: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Petre-Corneliu Opriţoiu: Department of Land Measurements and Cadaster, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Laurenţiu Eusebiu Chifor: Department of Automation, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Ioan-Aurel Chereches: Department of Road Vehicles and Transport, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Vlad Mureşan: Department of Automation, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Mihaela Suciu: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Mathematics, 2025, vol. 13, issue 13, 1-20
Abstract:
The aim of this work is to present an original, relatively simple, and elegant approach to the analysis of long rectangular plates subjected to uniformly distributed vertical loads acting on various surfaces. Plate analysis is important in many fields, especially where components are either rectangular plates or can be approximated as such. The Transfer Matrix Method is increasingly used in research, as evidenced by the references cited. The advantages of this method lie in the simplicity of its algorithm, the ease of implementation in programming, and its straightforward integration into optimization software. The approach consists of discretizing the rectangular plate by sectioning it with planes parallel to the short sides—i.e., perpendicular to the two long edges. This results in a set of beams, each with a length equal to the width of the plate, a height equal to the plate’s thickness, and a unit width. Each unit beam has support at its ends that replicate the edge conditions of the plate along its long sides. In the study presented, the rectangular plate is embedded along its two long edges, meaning the unit beam is considered embedded at both ends. The Transfer Matrix Method is particularly valuable because it lends itself well to iterative calculations, making it easy to develop software capable of analyzing long rectangular plates quickly. This makes it especially useful for shape optimization applications, which we intend and hope to pursue in future studies.
Keywords: Transfer Matrix Method; Dirac’s function and operators; Heaviside’s function and operators; unit beam; embedded edge; state vector; transfer matrix; long rectangular plate; uniform vertical load on surface; charge density (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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