Métodos analíticos y numéricos para el análisis de placas delgadas
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oct 30, 2024
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https://doi.org/10.36677/rici.v2i3.24425
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Jaime de la Colina Martínez
http://orcid.org/0000-0002-1588-3550
http://orcid.org/0000-0002-1588-3550
Resumen
Las placas son elementos estructurales planos que se emplean comúnmente en varias ramas de la ingeniería. A diferencia de los problemas de estados planos, los cuales pueden tener geometrías similares, las cargas en una placa son normales a su superficie media. El presente trabajo presenta de forma general la teoría general de placas delgadas así como algunos de los métodos analíticos y numéricos más usados para su análisis. Se describe el método de Rayleigh-Ritz, el método de diferencias finitas y el método del elemento finito. Se incluye un ejemplo de una placa con geometría atípica, la cual se analiza con ayuda de Matlab.
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DE LA COLINA MARTÍNEZ, Jaime.
Métodos analíticos y numéricos para el análisis de placas delgadas.
Ideas en Ciencias de la Ingeniería, [S.l.], v. 2, n. 3, p. 89-104, oct. 2024.
ISSN 2992-7447.
Disponible en: <https://ideasencienciasingenieria.uaemex.mx/article/view/24425>. Fecha de acceso: 10 oct. 2026
doi: https://doi.org/10.36677/rici.v2i3.24425.
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Esta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial-SinObrasDerivadas 4.0.
Citas
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[2] S. Timoshenko and S. Woinowsky-Krieger. Theory of Plates and Shells. 2nd ed., McGraw-Hill, 1959.
[3] R. Szilard. Theories and Applications of Plate Analysis – Classical, Numerical and Engineering Methods. John Wiley and Sons, 2004.
[4] J. N. Reddy. Theory and Analysis of Elastic Plates and Shells. 2nd ed., CRC Press, 2006.
[5] E. Ventsel and T. Krauthammer. Thin Plates and Shells – Theory, Analysis and Applications. Marcel Dekker and CRC Press, 2001.
[6] L. Rayleigh. Theory of Sound. Vol. 1, 2nd ed., Macmillan, 1894.
[7] H. L. Langhaar. Energy Methods in Applied Mechanics. John Wiley, 1962.
[8] Y. Kumar. The Rayleigh-Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review. Journal of Vibration and Control, I-23, 2017. doi: 10.1177/077546317694724.
[9] K. Liew and C. Wang. Pb-2 Rayleigh-Ritz method for general plate analysis. Engineering Structures, 15(1), 1993. doi: https://doi.org/10.1016/0141-0296(93)90017-X.
[10] F. Manzanares. Análisis de Placas Delgadas con Geometrías Atípicas. Tesis de Licenciatura, Universidad Autónoma del Estado de México, 2017.
[11] T. Liszka and J. Orkisz. The finite difference method at arbitrary irregular grids and its application in applied mechanics. Computers & Structures, 11, pp. 83–95, 1980. doi: https://doi.org/10.1016/0045-7949(80)90149-2.
[12] R. D. Cook, D. S. Malkus, M. E. Plesha, and R. J. Witt. Concepts and Applications of the Finite Element Analysis. 4th ed., John Wiley and Sons, 2002.
[13] O. C. Zienkiewicz, R. L. Taylor, and D. D. Fox. The Finite Element Method for Solid and Structural Mechanics. 7th ed., Elsevier, 2014.
[14] R. L. Burden, J. D. Faires, and A. M. Burden. Numerical Analysis. 10th ed., Cengage, 2015.
[15] S. C. Chapra and R. P. Canale. Numerical Methods for Engineers. 8th ed., McGraw-Hill, 2020.
[16] K. P. Chong, A. P. Boresi, S. Saigal, and J. D. Lee. Numerical Methods in Mechanics and Materials. 3rd ed., CRC Press, 2018.
[17] A. Gilat. MATLAB: An Introduction with Applications. 6th ed., John Wiley and Sons, 2017.
[18] B. D. Hahn and D. T. Valentine. Essential MATLAB for Engineers and Scientists. 8th ed., Academic Press, 2022.
[19] MathWorks. Partial Differential Equation Toolbox – User Guide MATLAB. R2022b, 2022.
[20] Autodesk. https://www.tinkercad.com, 2024.