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Curved and Layered Structures

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2353-7396
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Static-kinematic duality in beams, plates, shells and its central role in the finite element method

Alberto Carpinteri
  • Politecnico di Torino, Department of Structural, Geotechnical and Building Engineering, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
  • Other articles by this author:
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Published Online: 2017-05-03 | DOI: https://doi.org/10.1515/cls-2017-0005

Abstract

Static and kinematic matrix operator equations are revisited for one-, two-, and three-dimensional deformable bodies. In particular, the elastic problem is formulated in the details in the case of arches, cylinders, circular plates, thin domes, and, through an induction process, shells of revolution. It is emphasized how the static and kinematic matrix operators are one the adjoint of the other, and then demonstrated through the definition of stiffness matrix and the application of virtual work principle. From the matrix operator formulation it clearly emerges the identity of the usual Finite Element Method definition of elastic stiffness matrix and the classical definition of Ritz-Galerkin matrix.

References

  • [1] Bathe, K.J. and Wilson, E.L. (1976) Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar

  • [2] Carpinteri, A. (1992) Scienza delle Costruzioni, Vol. 1 and 2, Pitagora, Bologna.Google Scholar

  • [3] Carpinteri, A. (1997) Structural Mechanics: A Unified Approach, Chapman & Hall, London.Google Scholar

  • [4] Carpinteri, A. (2014) Structural Mechanics Fundamentals, CRC (Taylor & Francis Group), New York.Google Scholar

  • [5] Carpinteri, A. (2017) Advanced Structural Mechanics, CRC (Taylor & Francis Group), New York.Google Scholar

  • [6] Carpinteri, A. and Cornetti, P. (1997) Lastre a doppia curvatura, in: Carpinteri, A., Calcolo Automatico delle Strutture, Pitagora, Bologna, 159-215.Google Scholar

  • [7] Di Pasquale, S. (1975) Scienza delle Costruzioni: Introduzione alla Progettazione Strutturale, Tamburini, Milan.Google Scholar

  • [8] Di Tommaso, A. (1981) Fondamenti di Scienza delle Costruzioni, Vol. 1, Patron, Bologna.Google Scholar

  • [9] Novozhilov, V.V. (1970) Thin Shell Theory, Noordhoff, Groningen.Google Scholar

  • [10] Zienkiewicz, O.C. (1971) The Finite Element Method in Engineering Science, McGraw-Hill, London.Google Scholar

About the article

Received: 2016-11-16

Accepted: 2016-11-28

Published Online: 2017-05-03

Published in Print: 2017-01-26


Citation Information: Curved and Layered Structures, Volume 4, Issue 1, Pages 38–51, ISSN (Online) 2353-7396, DOI: https://doi.org/10.1515/cls-2017-0005.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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