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Exact solution of the harmonic problem for a rectangular plate in flat deformation by the method of initial functions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A wide range of applications is based nowadays on analytical developments which allow a precise and effective approach and short time of computations compared with the time required for numerical methods; in this way these developments are suitable for calculations in real time. This work proposes an approach for solving a two-dimensional harmonic problem of a rectangular plate under local surface loading using Vlasov’s symbolic method of initial functions and a general solution of the harmonic equation for a rectangle. Substituting the harmonic functions in symbolic form for the corresponding solutions allows us to give the exact solution of the problem in trigonometric form.
Rocznik
Strony
349--361
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Polytechnic School of Abomey-Calavi (EPAC) Department of Civil Engineering, University of Abomey-Calavi 01BP2009 Cotonou, BENIN
  • International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi (UAC) 072 BP 50 Cotonou, BENIN
  • International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi (UAC) 072 BP 50 Cotonou, BENIN
Bibliografia
  • [1] Soldatenkov I.A. (2016): The three-dimensional problem on the mutual wear of a thin elastic layer and punch sliding on it. – Journal of Applied Mathematics and Mechanics, vol.80, No.1, pp.117-137.
  • [2] Saidi A.R., Jomehzadeh E. and Atashipour S.R. (2009): Exact analytical solution for bending analysis of functionally graded annular sector plates. – International Journal of Engineering, Translation B: Applications, vol.22, No.3, pp.307-316.
  • [3] Jomehzadeh E., Saidi A.R. and Atashipour S.R. (2009): Analytical approach for stress analysis of functionally graded annular sector plates. – Materials and Design, vol.30, No.9, pp.3679-3685.
  • [4] Yang B., Ding H.J. and Chen W.Q. (2009): Elasticity solutions for a uniformly loaded rectangular plate of functionally graded materials with opposite edges simply supported. – Acta Mechanica, vol.207, No.3, pp.245-258.
  • [5] Maliev A.S. (1951): Some problems of the bending theory of rectangular plates. – Abstract of doctor of science thesis -Leningrad.
  • [6] Vlasov V.Z. (1955): The method of initial functions in problems of theory of elasticity. – Bulletin of the Academy of Science of the USSR, vol.7, pp.49-69.
  • [7] Kellog O.G. (1951): On the derivatives of harmonic functions on the boundary. – Transaction of American Mathematical Society, vol.39, pp.406-510.
  • [8] Faraji S., Lowell and Archer R.R. (1989): Method of initial functions for thick transversely isotropic shells. – Archive of Applied Mechanics, vol.60, No.1, pp.1-9.
  • [9] Sargand S.M., Chen N.N. and Das Y.C. (1992): Method of initial functions for axially symmetric elastic bodies. – International Journal of Solids and Structures, vol.29, No.6, pp.711-719.
  • [10] Chandrashekhara K. and Nanjunda Rao K.S. (1998): Method of initial functions for the analysis of laminated circular cylindrical shell under axisymmetric load. – Mechanics of Composite Materials and Structures, vol.5, No.2, pp.187-201.
  • [11] Patel R., Dubey S.K. and Pathak K.K. (2012): Analusis of Composite beams using method of initial functions. – International Journal of Advanced Structures and Geotechnical Engineering, vol.1, No.02,
  • [12] Patel R., Dubey S.K. and Pathak K.K. (2013): Analysis of flexural members using an alternative approach. – Research Journal of Engineering Science, vol.2,N.4, pp.40-42.
  • [13] Matrosov V.A. (2012): Convergence of power series in the method of initial functions. – Bulletin of S.-Petersburg University, Applied Mathematics Series, vol.10, No.1, pp.41-51.
  • [14] Vlasov V.Z. and Leontiev U.N. (1966): Beams, plates and shells on elastic foundation. – Jerusalem: Izrael Program for Scientific Translations.
  • [15] Zeldovich Y.B. (1977): Elements of Applied Mathematics. – Amazon.
  • [16] Polianin A.D. (2001): Spravochnik po lineinym uravneniiam matematicheskoy fiziki. – M.: Fizmatlit. (In Russian).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-882ef5c5-99b6-43b6-8974-5c9290633a26
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