MATLAB: Una herramienta para la didáctica del Método de los Elementos Finitos

• Autores: Emilio Martínez Pañeda
• Localización: Unión: revista iberoamericana de educación matemática, ISSN-e 1815-0640, Nº. 45, 2016, págs. 242-268
• Idioma: español
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    El método de los elementos finitos (MEF) es a día de hoy el método numérico más utilizado en aplicaciones de ciencia e ingeniería. Sin embargo, el desarrollo de procedimientos efectivos para la enseñanza del mismo continúa siendo un desafío para los docentes de todo el mundo. En el presente trabajo se plantea el uso del software matemático MATLAB para el desarrollo de códigos con orientación docente. Los ejemplos presentados revelan la idoneidad del enfoque adoptado para reducir la brecha existente entre el sustento matemático del método y la sencillez de uso de los potentes programas comerciales.

  • English

    The finite element method (FEM) is nowadays the most widely used numerical method in science and engineering applications. However, the development of effective ways to teach it remains a challenge for teachers worldwide. In the present work, the use of the mathematical software MATLAB is proposed for the development of teaching-oriented codes. The examples presented reveal the suitability of the suggested approach to close the gap between the mathematical theory of the method and the ease of use of the powerful commercial programs.

  • português

    O método dos elementos finitos (FEM) é hoje o método numérico mais amplamente utilizado em aplicações científicas e de engenharia. No entanto, o desenvolvimento de maneiras eficazes de ensinar continua a ser um desafio para os professores em todo o mundo. No presente trabalho, é proposta a utilização do software MATLAB para o desenvolvimento de códigos orientada para o ensino. Os exemplos apresentados revelam a aptidão da abordagem sugerida para fechar o espaço entre a teoria matemática do método e a facilidade de utilização dos programas comerciais.

• Referencias bibliográficas
  • Alberty, J., Cartensen, C., Funken, S.A., & Klose, R. (2002). MATLAB implementation of the finite element method...
  • Baaser, H. (2010). Development and Application of the Finite Element Method based on MatLab. Springer.
  • Backer, J.R., Capece, V.R., & Lee J.R. (2001). Integration of finite element software in undergraduate engineering ...
  • Connell, H., Blyth, B., May, R., & Zorzan, C. (1999). Teaching the finite element method using software. Proceedings of the Delta’99...
  • Earley, R.D. (1998). Use of FEA in an introductory strength of materials course. ASEE Annual Conference Proceedings, Session 3648.
  • Ferreira, A.J.M. (2009). MATLAB Codes for Finite Element Analysis. Solid Mechanics and its Applications, Springer.
  • Howard, W.E., Musto, J.C., & Prantil, V. (2001). Finite element analysis in a mechanics course sequence. ASEE Annual Conference...
  • Jiang, Y., & Wang, C. (2008). On teaching finite element method in plasticity with Mathematica. Computer Applications in Engineering Education,...
  • Jolley, W.O., Rencis J.J., & Grandin H.T. (2003). A module for teaching fundamentals of finite-element theory and practice...
  • Kattan, P.I. (2007). MATLAB Guide to finite elements, an interactive approach. Springer, Berlin, 2nd ed.
  • Kosashi, P.B. (2010). Learning finite element methods by building applications. International Journal of Mechanical Engineering Education,...
  • Kwon, Y. W., & Bang H. (1996). Finite element method using MATLAB. CRC Press, Boca Raton, FL.
  • Lissenden, C.J., Wagle, G.S., & Salamon, N.J. (2002). Applications of finite element analysis for undergraduates. ASEE...
  • Logue, L.J., & Hall, K.A. (2001). Introducing finite element analysis in an MET strength of materials course. ASEE Annual Conference Proceedings,...
  • Martínez-Pañeda, E., & Betegón, C., (2015). Modeling damage and fracture within strain- gradient plasticity. International...
  • Martínez-Pañeda, E., & Gallego, R., (2015). Numerical analysis of quasi-static fracture in functionally graded materials. International...
  • Martínez-Pañeda, E., & Niordson, C., (2015). On fracture in finite strain gradient plasticity. International Journal of Plasticity,...
  • Oñate, E. (1995). Cálculo de estructuras por el método de elementos finitos. Centro Internacional de Métodos Numéricos en Ingeniería,...
  • Pike, M. (2001). Introducing Finite Element Analysis in Statics. Proceedings of the 2001 American Society for Engineering Education...
  • Rahman, T., & Valdman, J. (2013). Fast MATLAB assembly of FEM matrices in 2D and 3D: Nodal elements. Applied Mathematics and Computation,...
  • Teh, K., & Morgan, L. (2005). The application of Excel in teaching finite element analysis to final year engineering students. Proceedings...
  • Zecher, J. (2002). Teaching finite element analysis in an MET program. ASEE Annual Conference Proceedings, Session 3448