A posteriori error estimates for beams with inexact flexural stiffness representation

• Autorzy: Torii André J. , Gracite Paula M.A. , Miguel Leandro F.F. , Lopez Rafael H.

Identyfikatory

DOI

10.17512/jamcm.2023.2.06

• Języki publikacji: EN

Abstrakty

EN

In this work, we present a posteriori error estimates for the Euler-Bernoulli beam theory with inexact flexural stiffness representation. This is an important subject in practice because beams with non-uniform flexural stiffness are frequently modeled using a mesh of elements with constant stiffness. The error estimates obtained in this work are validated by means of two numerical examples. The estimates presented here can be employed for adaptive mesh refinement.

Słowa kluczowe

EN

beam; error estimate; inexact stiffness

PL

belka; oszacowanie błędów

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2023
• Tom: Vol. 22, nr 2
• Strony: 62--74
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Torii André J.

• Latin-American Institute of Technology, Infrastructure and Territory, Federal University for Latin-American Integration (UNILA) Foz do Iguaҫu, Brazil

autor

Gracite Paula M.A.

• Latin-American Institute of Technology, Infrastructure and Territory, Federal University for Latin-American Integration (UNILA) Foz do Iguaҫu, Brazil

autor

Miguel Leandro F.F.

• Department of Civil Engineering, Federal University of Santa Catarina (UFSC) Florianópolis, Brazil

autor

Lopez Rafael H.

• Department of Civil Engineering, Federal University of Santa Catarina (UFSC) Florianópolis, Brazil

Bibliografia

• [1] Cook, R.D., Malkus, D.S., Plesha, M.E., & Witt, R.J. (2002). Concepts and Applications of Finite Element Analysis. 4th ed. Hoboken: John Wiley & Sons.
• [2] Hutton, D.V. (2004). Fundamentals of Finite Element Analysis. McGraw-Hill.
• [3] Dong, Y., Yuan, S., & Xing, Q. (2019). Adaptive finite element analysis with local mesh refinement based on a posteriori error estimate of element energy projection technique. Engineering Computations, 36(6), 2010-2033.
• [4] Grätsch, T., & Bathe, K.-J. (2005). A posteriori error estimation techniques in practical finite element analysis. Computers & Structures, 83(4), 235-265.
• [5] Sun, H., & Yuan, S. (2023). An improved local error estimate in adaptive finite element analysis based on element energy projection technique. Engineering Computations, 40(1), 246-264.
• [6] Wang, Y. (2023). Finite element mesh refinement for in-plane and out-of-plane vibration of variable geometrical Timoshenko beams based on superconvergent vibration modes. Engineering Computations, 40(1), 22-40.
• [7] Zienkiewicz, O.C. (2006). The background of error estimation and adaptivity in finite element computations. Computer Methods in Applied Mechanics and Engineering, 195(4), 207-213.
• [8] Bauer, A.M., Wüchner, R., & Bletzinger, K.-U. (2020). Weak coupling of nonlinear isogeometric spatial Bernoulli beams. Computer Methods in Applied Mechanics and Engineering, 361, 112747.
• [9] Dvořáková, E., & Patzák, B. (2020). Isogeometric Bernoulli beam element with an exact representation of concentrated loadings. Computer Methods in Applied Mechanics and Engineering, 361, 112745.
• [10] Lestringant, C., Audoly, B., & Kochmann, D.M. (2020). A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams. Computer Methods in Applied Mechanics and Engineering, 361, 112741.
• [11] Peres, N., Gonҫalves, R., & Camotim, D. (2021). A geometrically exact beam finite element for curved thin-walled bars with deformable cross-section. Computer Methods in Applied Mechanics and Engineering, 381, 113804.
• [12] Wei, D., & Liu, Y. (2012). Analytic and finite element solutions of the power-law Euler-Bernoulli beams. Finite Elements in Analysis and Design, 52, 31-40.
• [13] Hibbeler, R.C. (2022). Mechanics of Materials. 11th ed. Pearson.
• [14] Maple (2016). Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).