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Scientific paper - Original scientific paper
Analytical Solution for the Problem of Pure Bending of Orthotropic Micropolar Plate
Zbornik radova (Građevinski fakultet Sveučilišta u Rijeci), 27 (2024), 1; 123-137. https://doi.org/10.32762/zr.27.1.8
Jurković, Damjan; Jelenić, Gordan; Grbčić Erdelj, Sara

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Jurković, D., Jelenić, G. & Grbčić Erdelj, S. (2024). Analytical Solution for the Problem of Pure Bending of Orthotropic Micropolar Plate. Zbornik radova (Građevinski fakultet Sveučilišta u Rijeci), 27. (1), 123-137. doi: 10.32762/zr.27.1.8

Jurković, Damjan, et al. "Analytical Solution for the Problem of Pure Bending of Orthotropic Micropolar Plate." Zbornik radova (Građevinski fakultet Sveučilišta u Rijeci), vol. 27, no. 1, 2024, pp. 123-137. https://doi.org/10.32762/zr.27.1.8

Jurković, Damjan, Gordan Jelenić and Sara Grbčić Erdelj. "Analytical Solution for the Problem of Pure Bending of Orthotropic Micropolar Plate." Zbornik radova (Građevinski fakultet Sveučilišta u Rijeci) 27, no. 1 (2024): 123-137. https://doi.org/10.32762/zr.27.1.8

Jurković, D., Jelenić, G. and Grbčić Erdelj, S. (2024) 'Analytical Solution for the Problem of Pure Bending of Orthotropic Micropolar Plate', Zbornik radova (Građevinski fakultet Sveučilišta u Rijeci), 27(1), pp. 123-137. doi: 10.32762/zr.27.1.8

Jurković D, Jelenić G, Grbčić Erdelj S. Analytical Solution for the Problem of Pure Bending of Orthotropic Micropolar Plate. Zbornik radova (Građevinski fakultet Sveučilišta u Rijeci) [Internet]. 2024 [cited 2025 March 22];27(1):123-137. doi: 10.32762/zr.27.1.8

D. Jurković, G. Jelenić and S. Grbčić Erdelj, "Analytical Solution for the Problem of Pure Bending of Orthotropic Micropolar Plate", Zbornik radova (Građevinski fakultet Sveučilišta u Rijeci), vol. 27, no. 1, pp. 123-137, 2024. [Online]. Available at: https://urn.nsk.hr/urn:nbn:hr:157:640718. [Accessed: 22 March 2025]

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Metadata
Title (english)Analytical Solution for the Problem of Pure Bending of Orthotropic Micropolar Plate
Title (croatian)Analitičko rješenje problema čistog savijanja ortotropne mikropolarne ploče
AuthorDamjan Jurković
AuthorGordan Jelenić
AuthorSara Grbčić Erdelj
Author's institutionUniversity of Rijeka
Faculty of Civil Engineering
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Basic Technical Sciences
Abstract (english)
When analysing the problem of pure bending of a plate, it can be noticed that, for cylindrical bending, a spatial problem collapses into a plane-strain problem. For such a boundary-value problem of the Cosserats' continuum, three engineering parameters are required: Young’s modulus, Poisson’s ratio and the characteristic length for bending. Here we consider an orthotropic form of such a problem, whereby two Young’s moduli, four Poison’s ratios and one characteristic length for bending are found to be sufficient to propose a mathematical model of this problem. General equations of the isotropic micropolar continuum are introduced, and the analytical solution for the pure bending of an isotropic micropolar plate is generalized to the case of orthotropic microstructure. By defining the ratio of a distributed force and a distributed moment boundary conditions required for the pure-bending state, a closed-form solution to this problem is obtained in terms of displacement, strains and stress functions. It is shown that the derived results reduce to the isotropic ones if a material isotropy is assumed.
Abstract (croatian)
Pri analizi problema čistog savijanja ploče moguće je uočiti kako se, za cilindrično savijanje, prostorni problem može svesti na problem ravninskog stanja deformacija. Za takav problem rubnih vrijednosti Cosseratovog kontinuuma potrebna su tri materijalna parametra: Youngov modul elastičnosti, Poissonov koeficijent i karakteristična duljina za savijanje. Ovdje razmatramo ortotropni oblik takvog problema, gdje su dva Youngova modula, četiri Poissonova koeficijenta i jedna karakteristična duljina za savijanje dovoljni za definiranje matematičkog modela problema. Predstavljene su opće jednadžbe izotropnog mikropolarnog kontinuuma, te je analitičko rješenje za problem čistog savijanja mikropolarne ploče generalizirano na slučaj ortotropne mikrostrukture. Definiranjem omjera rubnih uvjeta distribuiranih sila i distribuiranih momenata potrebnih za stanje čistog savijanja dobiveno je rješenje u zatvorenom obliku, izraženo preko funkcija pomaka, deformacija i naprezanja. Prikazano je da se uvođenjem materijalne izotropije izvedeni izrazi svode na poznate izotropne rezultate.
Keywords (english)
Keywords (croatian)
Languageenglish
Languagecroatian
Publication typeScientific paper - Original scientific paper
Publication statusPublished
Peer reviewPeer review - domestic
Publication versionPublished version
Journal titleZbornik radova (Građevinski fakultet Sveučilišta u Rijeci)
Numberingvol. 27, no. 1, pp. 123-137
p-ISSN0350-8552
e-ISSN2584-6159
DOIhttps://doi.org/10.32762/zr.27.1.8
URN:NBNurn:nbn:hr:157:640718
Publication2024
ProjectNumber: IP-2018-01-1732
Title (croatian): Koncept nepomičnog pola u numeričkom modeliranju Cosseratovog kontinuuma
Title (english): The concept of a stationary pole in the numerical modeling of the Cosserat continuum
Acronym: FIMCOS
Leader: Gordan Jelenić
Jurisdiction: Croatia
ProjectNumber: uniri-tehnic-18-248 1415
Title (croatian): Računski i eksperimentalni postupci za određivanje materijalnih parametara Cosseratovog kontinuuma
Title (english): Computational and experimental procedures for assessment of material parameters in Cosserats' continuum
Leader: Gordan Jelenić
Jurisdiction: Croatia
Document URLhttps://hrcak.srce.hr/324024
Type of resourceText
Access conditionsOpen access
Terms of useLicence Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) icon
Created on2025-03-21 08:19:00