Métodos analíticos y numéricos para el análisis de placas delgadas
Article Sidebar
Publicado
oct 30, 2024
##plugins.pubIds.doi.readerDisplayName##
https://doi.org/10.36677/rici.v2i3.24425
Main Article Content
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.
Article Details
Como citar
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: 26 ago. 2026
doi: https://doi.org/10.36677/rici.v2i3.24425.
Sección
Artículos
Esta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial-SinObrasDerivadas 4.0.
Citas
[1] International Code Council. International Building Code. International Code Council, 2021.
[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.
[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.