Structural Engineering and Mechanics

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Concerning the tensor-based flexural formulation: Applications

  • Alhassan, Mohammed A. (Al Ain University) ;
  • Al-Rousan, Rajai Z. (Department of Civil Engineering, Jordan University of Science and Technology) ;
  • Hejazi, Moheldeen A. (Department of Civil Engineering, Jordan University of Science and Technology)
  • Received : 2019.03.02
  • Accepted : 2021.02.04
  • Published : 2021.03.25
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Abstract

Recently, the plate bending analysis has been interpreted in terms of the tensor's components of curvatures and bending moments by presenting the conceptual perspectives of the Hydrostatic Method of Analysis (HM) and theoretical formulations that combine the continuum mechanics with the graphical statics analysis, the theory of thin orthotropic and isotropic plates, and the elasticity theory. In pursuance of uncovering a genuine formulation of the plate's flexural differential equations, that possess the general-covariance and coordinates-independency. This study had then, tackled various natural and structural problems in both solid and fluid branches of the continuum mechanics in a description of such theoretical and conceptual attainment in uncovering the dimensional independent diffeomorphism covariant partial differential laws.

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References

  1. Altekin, M. (2014), "Large deflection analysis of point supported super-elliptical plates", Struct. Eng. Mech., 51(2), 333-347. http://dx.doi.org/10.12989/sem.2014.51.2.333.
  2. Backus, G. (1966), "Potentials for tangent tensor fields on spheroids", Arch. Rat. Mech. Anal., 22, 210-252. https://doi.org/10.1007/BF00266477.
  3. Barozzi, G.S. and Angeli, D. (2014), "A note on capillary rise in tubes", Energy Procedia, 45, 548-557. https://doi.org/10.1016/j.egypro.2014.01.059.
  4. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling Analysis of hybrid laminated composite Plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. http://dx.doi.org/10.12989/sem.2018.66.6.761
  5. Bramble, J.H. and Payne, L.E. (1962), "Some uniqueness theorems in the theory of elasticity", Arch. Rat. Mech. Anal., 9, 319-328. https://doi.org/10.1007/BF00253354
  6. Cauchy, A. (1900), "Oeuvres completes d'Augustin Cauchy", Serie 2, tome 1/publiees sous la direction scientifique de l'Academie des sciences et sous les auspices de M. le ministre de l'Instruction publique. Gauthier-Villars fils 1, 381-411.
  7. Dean, R.G. and Dalrymple, R.A. (1991), Water Wave Mechanics for Engineers and Scientists, Vol. 2, World Scientific Publishing Company.
  8. Eddy, H.T. (1913), The Theory of the Flexure and Strength of Rectangular Flat Plates Applied to Reinforced Concrete Floor Sabs, Rogers & Company, Minneapolis.
  9. Einstein, A. and Minkowski, H. (1920). "The foundation of the generalised theory of relativity", On a Heuristic Point of View about the Creation and Conversion of Light, 1, 22.
  10. Euler, L. (1766), "De motu vibratorio tympanorum (On the motion of vibrations in drums)", Novi Comment Acad Sci Petropolitanae, 10, 243-260.
  11. Germain, S. (1826), "Remarques sur la nature, les bornes et l'etendue de la question des surfaces elastiques et equation generale de ces surfaces", Impr de Huzard-Courcier, Paris 21.
  12. Gray, M. (1978), "Sophie Germain (1776-1831), Eds. Grinstein, L.S., Campbell, P., Women Math", A Bibliogr. Sourceb, 47-55.
  13. Greaves, G.N., Greer, A.L., Lakes, R.S. and Rouxel, T. (2011), "Poisson's ratio and modern materials", Nat. Mater., 10, 823-837. https://doi.org/10.1038/nmat3134
  14. Hejazi, M.A. (2018), "Innovative approach for analyzing thinthick plates considering non-linearity and plasticity with damage for various boundary conditions", Jordan university of Science and Technology.
  15. Huang, W.H. and Lin, C.C. (1998), "Negatively curved sets on surfaces of constant mean curvature in ℝ 3 are large", Arch. Rat. Mech. Anal., 141, 105-116. https://doi.org/10.1007/s002050050074.
  16. Huber, M.T. (1925), "uber die genaue Biegungsgleichung einer orthotropen Platte in ihrer Anwendung auf kreuzweise bewehrte Betonplatten", Der Bauingenieur, 6, 878-879.
  17. Huber, M.T. (1929), "Probleme der Statik technisch wichtiger orthotroper Platten", Akademia Nauk Technicznych, Warsaw.
  18. Jurin, J. (1728), "Disquisitio physicae de tubulis capillaribus", Comment Acad Sci Imp Petropolitana, 3, 281-292.
  19. Kirchhoff, G. (1897), Vorlesungen uber mechanik (Lectures on Mechanics), 4th Edition, Leipzig, B.G. Teubner, Leipzig.
  20. Love, A. (1888), "The small free vibrations and deformation of a thin elastic shell", Philos. Tran. R. Soc. London, 179, 491-546. https://doi.org/10.1098/rsta.1888.0016
  21. Mohr, O. (1906), Abhandlungen aus dem Gebiete der Technischen Mechanik mit Zahlreichen Textabbildungen, Wilhelm Ernst & Sohn, Berlin.
  22. Munson, B.R., Rothmayer, A.P., Okiishi, T.H. and Huebsch, W.W. (2013), Fundamentals of Fluid Mechanics, John Wiley & Sons, Inc.
  23. Navier, C.L.M.H. (1826), "Resume des lecons donnees a l'ecole royale des ponts et chaussees sur l'application de la mecanique a l'etablissement des constructions et des machines", Ler Partie: Lecons sur la resistance des materiaux et sur l'etablissement des constructions en terre, Firmin Didot pere et fils, Paris.
  24. Navier, C.L.M.H. (1828), "Remarques sur l'article de M. Poisson, insere dans le cahier d'août, Annales de chimie et de physique", Landmarks II, Sci J., 39, 145-151
  25. Norton, J.D. (1993), "General covariance and the foundations of general relativity: eight decades of dispute", Rep. Prog. Phys., 56, 791458 https://doi.org/10.1088/0034-4885/56/7/001
  26. O'Mathuna, D. (1994), Jacques II Bernoulli and The Problem of the Vibrating Plate, Dublin Institute for Advanced Studies.
  27. Poisson, S.D. (1829), "Memoire sur l'equilibre et le mouvement des corps elastique", Academie des Sciences, Ed. Memoires l aCTM Academie des Sci. l aCTM Inst. Fr. Gauthier-Villars, Paris.
  28. Rad, A.B., Farzan-Rad, M.R. and Majd, K.M. (2017), "Static analysis of non-uniform heterogeneous circular Plate with porous material resting on a gradient hybrid foundation involving friction force", Struct. Eng. Mech., 64(5), 591-610. http://dx.doi.org/10.12989/sem.2017.64.5.591.
  29. Sather, D. (1965), "Maximum properties of Cauchy's problem in three-dimensional space-time", Arch. Rat. Mech. Anal., 18(1), 14-26. http://dx.doi.org/10.1007/BF00253979.
  30. Schade, H.H. (1940), "The orthogonally stiffened plate under uniform lateral load", J. Appl. Mech., 7(4), A143-A146. https://doi.org/10.1115/1.4009063.
  31. Soedel, W. (2004), Vibration of Shells and Plates, Marcel Dekker, Inc., New York.
  32. Szilard, R. (2004), "Theories and applications of plate analysis: Classical, numerical and engineering methods", Appl, Mech, Rev., 57(6), B32-B33. https://doi.org/10.1115/1.1849175.
  33. Timoshenko, S. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, 2nd Edition, McGraw-Hill, NewYork
  34. Timoshenko, S.P. (1953), History of Strength of Materials. With a Brief Account of the History of Theory of Elasticity and Theory of Structures, McGraw-Hill, NewYork.
  35. Troitsky, M.S. and Hoppmann, W.H. (1977), "Stiffened plates: Bending, stability and vibrations", J. Appl. Mech., 44, 516. https://doi.org/10.1115/1.3424122
  36. Tu, T.M., Quoc, T.H. and Long, N.V. (2017), "Bending analysis of functionally graded plates using new eight-unknown higher order shear deformation theory", Struct. Eng. Mech., 62(3), 311-324. http://dx.doi.org/10.12989/sem.2017.62.3.311.
  37. ugural, A.C. (2010), Stresses in Beams, Plates, and Shells, CRC Press Taylor Fr Gr.
  38. Ventsel, E. and Krauthammer, T. (2001), "Thin plates and shells: theory: Analysis, and applications", Appl. Mech. Rev., 55(4), B72-B73. https://doi.org/10.1201/9780203908723.
  39. Yahia, S.A., Amar, L.H.H., Belabed, Z. and Tounsi, A. (2018), "Effect of homogenization models on stress analysis of functionally graded plates", Struct. Eng. Mech., 67(5), 527-544. http://dx.doi.org/10.12989/sem.2018.67.5.527.