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ORIGINAL PAPER
Exact Solution of the Harmonic Problem for a Rectangular Plate in Flat Deformation by the Method of Initial Functions
1
Polytechnic School of Abomey-Calavi (EPAC) Department of Civil Engineering, University of Abomey-Calavi 01BP2009 Cotonou, BENIN
2
International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi (UAC) 072 BP 50 Cotonou, BENIN
Online publication date: 2017-06-09
Publication date: 2017-05-24
International Journal of Applied Mechanics and Engineering 2017;22(2):349-361
KEYWORDS
ABSTRACT
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.
FUNDING
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
CONFLICT OF INTEREST
The authors declare that they have no conflict of interest.
DATA AVAILABILITY
All data generated or analysed during this study are included in this published article.
REFERENCES (15)
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.
12.
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.
13.
Vlasov V.Z. and Leontiev U.N. (1966): Beams, plates and shells on elastic foundation. - Jerusalem: Israel Program for Scientific Translations.
15.
Polianin A.D. (2001): Spravochnik po lineinym uravneniiam matematicheskoy fiziki. - M.: Fizmatlit. (In Russian).
| eISSN: | 2353-9003 |
| ISSN: | 1734-4492 |
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