Applications of the Calculus by the Transfer Matrix Method for Long Rectangular Plates Under Uniform Vertical Loads
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| Yayımlandı: | Mathematics vol. 13, no. 13 (2025), p. 2181-2201 |
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| Yazar: | |
| Diğer Yazarlar: | , , , , , , , , |
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MDPI AG
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| Online Erişim: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 022 | |a 2227-7390 | ||
| 024 | 7 | |a 10.3390/math13132181 |2 doi | |
| 035 | |a 3229153486 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 084 | |a 231533 |2 nlm | ||
| 100 | 1 | |a Cosmin-Sergiu, Brisc |u Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania; cosmin.brisc@rezi.utcluj.ro (C.-S.B.); cristian.boldor@rezi.utcluj.ro (I.-C.B.); dan.dumea@campus.utcluj.ro (D.-M.D.); gyorbiro.ka.robert@campus.utcluj.ro (R.G.) | |
| 245 | 1 | |a Applications of the Calculus by the Transfer Matrix Method for Long Rectangular Plates Under Uniform Vertical Loads | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a 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. | |
| 653 | |a Load | ||
| 653 | |a Calculus | ||
| 653 | |a Vertical loads | ||
| 653 | |a Shape optimization | ||
| 653 | |a Rectangular plates | ||
| 653 | |a Boundary conditions | ||
| 653 | |a Matrix methods | ||
| 653 | |a Software development | ||
| 653 | |a Transfer matrices | ||
| 700 | 1 | |a Mihai-Sorin, Tripa |u Department of Design Engineering and Robotics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania; mihai.tripa@muri.utcluj.ro | |
| 700 | 1 | |a Ilie-Cristian, Boldor |u Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania; cosmin.brisc@rezi.utcluj.ro (C.-S.B.); cristian.boldor@rezi.utcluj.ro (I.-C.B.); dan.dumea@campus.utcluj.ro (D.-M.D.); gyorbiro.ka.robert@campus.utcluj.ro (R.G.) | |
| 700 | 1 | |a Dan-Marius, Dumea |u Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania; cosmin.brisc@rezi.utcluj.ro (C.-S.B.); cristian.boldor@rezi.utcluj.ro (I.-C.B.); dan.dumea@campus.utcluj.ro (D.-M.D.); gyorbiro.ka.robert@campus.utcluj.ro (R.G.) | |
| 700 | 1 | |a Gyorbiro, Robert |u Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania; cosmin.brisc@rezi.utcluj.ro (C.-S.B.); cristian.boldor@rezi.utcluj.ro (I.-C.B.); dan.dumea@campus.utcluj.ro (D.-M.D.); gyorbiro.ka.robert@campus.utcluj.ro (R.G.) | |
| 700 | 1 | |a Petre-Corneliu, Opriţoiu |u Department of Land Measurements and Cadaster, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania; petre.opritoiu@mtc.utcluj.ro | |
| 700 | 1 | |a Chifor Laurenţiu Eusebiu |u Department of Automation, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania; laurentiu.chifor@aut.utcluj.ro (L.E.C.); vlad.muresan@aut.utcluj.ro (V.M.) | |
| 700 | 1 | |a Chereches Ioan-Aurel |u Department of Road Vehicles and Transport, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania; aurel.chereches@auto.utcluj.ro | |
| 700 | 1 | |a Mureşan Vlad |u Department of Automation, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania; laurentiu.chifor@aut.utcluj.ro (L.E.C.); vlad.muresan@aut.utcluj.ro (V.M.) | |
| 700 | 1 | |a Suciu Mihaela |u Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania; cosmin.brisc@rezi.utcluj.ro (C.-S.B.); cristian.boldor@rezi.utcluj.ro (I.-C.B.); dan.dumea@campus.utcluj.ro (D.-M.D.); gyorbiro.ka.robert@campus.utcluj.ro (R.G.) | |
| 773 | 0 | |t Mathematics |g vol. 13, no. 13 (2025), p. 2181-2201 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3229153486/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3229153486/fulltextwithgraphics/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3229153486/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |