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Original Article

Use of the integration by part to derive beam/plate equilibrium equations from elasticity with applications to beams

Received 14 Jul 2024, Accepted 15 Jul 2024, Published online: 08 Aug 2024

References

  • R. Ballarini, The da vinci–euler–bernoulli beam theory mechanical engineering magazine, 2003. Available from http://www.memagazine.org/ retrieved 18 April 2003.
  • Timoshenko, S.P. Donovan, and H. Young, Theory of Structures Paperback, 2nd eds., McGraw-Hill Inc., New York, NY, 1968.
  • Washizu K, Variational Methods in Elasticity and Plasticity, Pergamon Press, Oxford, 1982.
  • V.V. Novozhilov, Theory of Elasticity, Pergamon Press Book, Oxford, 1961.
  • J.N. Reddy, Theory and Analyses of Elastic Plates and Shells, CRC Press, Boca Raton, FL, 2006.
  • R.M. Rivello, Theory and Analysis of Flight Structures, McGraw-Hill College, New York, NY, 1968.
  • A. Öchsner, Classical Beam Theories of Structural Mechanics, Springer, Berlin, Germany, 2021.
  • O.C. Zienkiewics, and K. Morgan, Finite Element Approximations, (Dover Book on Engineering), Dover Publications, Mineola, NY, 1983.
  • E. Carrera, M. Cinefra, M. Petrolo, and E. Zappino, Finite Element Analysis Of Structures Through Unified Formulation, Wiley, Hoboken, NJ, 2015.
  • E. Carrera, G. Giunta, and M. Petrolo, Beam Structures: Classical and Advanced Theories, Wiley, Hoboken, NJ, 2011.
  • E. Carrera, Stress resultants governing equations of any beam theory by direct manipulation of 3D equilibrium, Mech. Adv. Mater. Struct., pp. 1–12, 2023. DOI: 10.1080/15376494.2023.2250543.
  • E. Carrera, Governing equations of plate theories by direct manipulation of three-dimensional elasticity equilibrium, Mech. Adv. Mater. Struct., pp. 1–13, 2024. DOI: 10.1080/15376494.2024.2353897.
  • E. Carrera, A Class of Two-Dimensional Theories for Anisotropic Multilayered Plates Analysis, Accademia delle Scienze, Torino, Italy, pp. 19–20, 1–39, 1995–1996.
  • E. Carrera, Developments, ideas, and evaluations based upon reissner’s mixed variational theorem in the modeling of multilayered plates and shells, Appl. Mech. Rev., vol. 54, no. 4, pp. 301–329, 2001. DOI: 10.1115/1.1385512.
  • E. Carrera, Historical review of Zig-Zag theories for multilayered plates and shells, Appl. Mech. Rev., vol. 56, no. 3, pp. 287–308, 2003. DOI: 10.1115/1.1557614.

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