Calculation of thin, isotropic circular Plates subject to constant loading by the Generalized Equations of Finite Difference Method

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-2
Year of Publication : 2020
Authors : Seydou Youssoufa, Moussa Sali, Nkongho Anyi Joeph, Abdou Njifenjou
  10.14445/22315373/IJMTT-V66I2P520

MLA

MLA Style:Seydou Youssoufa, Moussa Sali, Nkongho Anyi Joeph, Abdou Njifenjou   "Calculation of thin, isotropic circular Plates subject to constant loading by the Generalized Equations of Finite Difference Method" International Journal of Mathematics Trends and Technology 66.2 (2020):163-176. 

APA Style: Seydou Youssoufa, Moussa Sali, Nkongho Anyi Joeph, Abdou Njifenjou (2020). Calculation of thin, isotropic circular Plates subject to constant loading by the Generalized Equations of Finite Difference Method International Journal of Mathematics Trends and Technology, 163-176.

Abstract
For calculation of circular plates under bending, we used generalized equations of Finite difference method. The algorithm allows taking into consideration finite breaks of required function, her first derivative and the right part of the differential equation without using surrounding points and a special condensation of grid. The shown examples here illustrate the simplicity of the algorithm because the results obtained are satisfactory; compared to those of other researchers, the error is less than 5%.

Reference
[1] B. Z. BLASSOV, N. N. LEONTIV, “Plates and shells on anelastic base”, Ed. GIFML, Moscow, (1960) 208 p.
[2] N. N. LEONTIV, А. N. LEONTIV, D. N. SOBOLEV, N. N. ANOHIN, “Fundamentals of the theory of beams and plates on a deformed base”, Ed. MISI, Moscow, (1982) 119 p.
[3] E. B. KORENEVA, “Analytical methods for calculating variable thickness plates and their practical applications”, Ed. ABS publisher, Moscow, (2009) 238 p.
[4] P.M. PINSKY, R.V JASTI. A mixed finite element formulation for Reissner–Mindlin plates based on the use of bubble functions. International Journal for Numerical Methods in Engineering, (28) (1989) 1677 – 1702
[5] D. J. ARGUIRIS, “Recent advances in methods for the calculation of structures from matrices”, Ed. Stroyizdat, Moscow,(1968) 241p.
[6] YVES DEBARD: RDM- éléments finis, manuels d‟exercices, IUT du mans, département de génie mécanique et productique 26 Juin 2006 – 20 Novembre 2017
[7] C. A. IVANOV, Analysis of bent plates by the finite element method, EdМarsi, (4) (1972) 25 – 31
[8] S. TIMOSHENKO, S. WOINOWSKY-KRIEGER „„Theory of Plates and Shells‟‟. Ed. McGRAW-HILL, (1966)
[9] MOUSSA SALI : « Le calcul des poutres et plaques de rigidité variable soumises à l‟action des charges : Le résumé de la thèse pour l‟obtention du Ph. D. MOSCOU 2002
[10] R. F. GABBASSOV, S. MOUSSA, Generalized Equations of FiniteDifferenceMethod and their Application for Calculation of Variable StiffnessCurved Plates, Ed. News of Higher Educational
[11] MARCO SUTTI, Elastic Theory of Plates, EcolePolytechniqueFederale de Lausane, Suisse,(2015) 17P.
[12] V. V. FILATOV, To the calculation of bending and compressed beams and plates on the non homogenous foundation, Thesis of Ph.D. – Moscow, (2000) 160 p.

Keywords
circular Plate, generalized equations, Finite difference method, edge conditions, discontinuity, finite breaks, surroundings points, convergence, constant loading.