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Scientific paper - Original scientific paper
Derivation matrix in mechanics – data approach
Engineering Review : Međunarodni časopis namijenjen publiciranju originalnih istraživanja s aspekta analize konstrukcija, materijala i novih tehnologija u području strojarstva, brodogradnje, temeljnih tehničkih znanosti, elektrotehnike, računarstva i građevinarstva, 43 (2023), 1; 1-8. https://doi.org/10.30765/er.1892
Kožar, Ivica; Plovanić, Marina; Sulovsky, Tea

Institutional repository: Repository of the University of Rijeka, Faculty of Civil Engineering

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Kožar, I., Plovanić, M. & Sulovsky, T. (2023). Derivation matrix in mechanics – data approach. Engineering Review : Međunarodni časopis namijenjen publiciranju originalnih istraživanja s aspekta analize konstrukcija, materijala i novih tehnologija u području strojarstva, brodogradnje, temeljnih tehničkih znanosti, elektrotehnike, računarstva i građevinarstva, 43. (1), 1-8. doi: 10.30765/er.1892

Kožar, Ivica, et al. "Derivation matrix in mechanics – data approach." Engineering Review : Međunarodni časopis namijenjen publiciranju originalnih istraživanja s aspekta analize konstrukcija, materijala i novih tehnologija u području strojarstva, brodogradnje, temeljnih tehničkih znanosti, elektrotehnike, računarstva i građevinarstva, vol. 43, no. 1, 2023, pp. 1-8. https://doi.org/10.30765/er.1892

Kožar, Ivica, Marina Plovanić and Tea Sulovsky. "Derivation matrix in mechanics – data approach." Engineering Review : Međunarodni časopis namijenjen publiciranju originalnih istraživanja s aspekta analize konstrukcija, materijala i novih tehnologija u području strojarstva, brodogradnje, temeljnih tehničkih znanosti, elektrotehnike, računarstva i građevinarstva 43, no. 1 (2023): 1-8. https://doi.org/10.30765/er.1892

Kožar, I., Plovanić, M. and Sulovsky, T. (2023) 'Derivation matrix in mechanics – data approach', Engineering Review : Međunarodni časopis namijenjen publiciranju originalnih istraživanja s aspekta analize konstrukcija, materijala i novih tehnologija u području strojarstva, brodogradnje, temeljnih tehničkih znanosti, elektrotehnike, računarstva i građevinarstva, 43(1), pp. 1-8. doi: 10.30765/er.1892

Kožar I, Plovanić M, Sulovsky T. Derivation matrix in mechanics – data approach. Engineering Review : Međunarodni časopis namijenjen publiciranju originalnih istraživanja s aspekta analize konstrukcija, materijala i novih tehnologija u području strojarstva, brodogradnje, temeljnih tehničkih znanosti, elektrotehnike, računarstva i građevinarstva [Internet]. 2023 [cited 2024 November 28];43(1):1-8. doi: 10.30765/er.1892

I. Kožar, M. Plovanić and T. Sulovsky, "Derivation matrix in mechanics – data approach", Engineering Review : Međunarodni časopis namijenjen publiciranju originalnih istraživanja s aspekta analize konstrukcija, materijala i novih tehnologija u području strojarstva, brodogradnje, temeljnih tehničkih znanosti, elektrotehnike, računarstva i građevinarstva, vol. 43, no. 1, pp. 1-8, 2023. [Online]. Available at: https://urn.nsk.hr/urn:nbn:hr:157:582722. [Accessed: 28 November 2024]

Metadata
Title (english)Derivation matrix in mechanics – data approach
AuthorIvica Kožar
MBZ: 146206
AuthorMarina Plovanić
MBZ: 392856
AuthorTea Sulovsky
MBZ: 392860
Author's institutionUniversity of Rijeka
Faculty of Civil Engineering
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Civil Engineering
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract (english)
Existence of data allows use of solution methods for differential equations that would otherwise be inapplicable. The solution process for this is formalized by using derivation matrices that reduce the time necessary for derivation and solving of differential equations. Derivation matrices are formulated by applying numerical methods in matrix notation, like finite difference schemes. In this work, a novel formulation is developed based on Lagrange polynomials with special care taken at boundary points in order to persevere a uniform precision. The main advantage of the approach is straightforward formulation, clear engineering insight into the process and (almost) arbitrary precision through choice of the interpolation order. The result of this procedure is the derivation matrix of the dimension [n×n], where 'n' is the number of data points. The resulting matrix is singular (of rank 'n-1') until boundary/initial conditions are introduced. However, that does not prevent the user to successfully differentiate its unknown function represented with the recorded data points. Derivation matrix approach is easily applicable to a wide range of engineering problems. This methodology could be extended to dynamic systems with multiple degrees of freedom and adapted when velocities or accelerations are recorded instead of displacements.
Keywords (english)
Languageenglish
Publication typeScientific paper - Original scientific paper
Publication statusPublished
Peer reviewPeer review - international
Publication versionPublished version
Journal titleEngineering Review : Međunarodni časopis namijenjen publiciranju originalnih istraživanja s aspekta analize konstrukcija, materijala i novih tehnologija u području strojarstva, brodogradnje, temeljnih tehničkih znanosti, elektrotehnike, računarstva i građevinarstva
Numberingvol. 43, no. 1, pp. 1-8
p-ISSN1330-9587
e-ISSN1849-0433
DOIhttps://doi.org/10.30765/er.1892
URN:NBNurn:nbn:hr:157:582722
Publication2023
ProjectNumber: IP-2019-04-7926
Title (croatian): Razdvajanje uticaja parametara u inžinjerskom modeliranju s parametarskom identifikacijom
Title (english): Separation of Parameter Influence in Engineering Modelling and Parameter Identification
Acronym: SEPAEMPI
Leader: Ivica Kožar
Jurisdiction: Croatia
Funding stream: IP
Document URLhttps://hrcak.srce.hr/295818
Type of resourceText
Access conditionsOpen access
Terms of useLicence Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) icon
Created on2023-10-30 11:26:06