An Accurate Solution Method for the Static and Vibration Analysis of Functionally Graded Reissner-Mindlin Rectangular Plate with General Boundary Conditions

This paper presents an accurate solution method for the static and vibration analysis of functionally graded Reissner-Mindlin plate with general boundary conditions on the basis of the improved Fourier series method. In the theoretical formulations, the governing equations and the general elastic bo...

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Bibliographic Details
Published in:Shock and vibration 2018-01, Vol.2018 (2018), p.1-21
Main Authors: Du, Yuan, Pang, Fuzhen, Liu, Ning, Li, Haichao, Li, Shuo
Format: Article
Language:English
Subjects:
Boundary conditions
Carbon
Convergence
Cosine series
Displacement
Engineering
Finite element analysis
Formulations
Fourier series
Functionally gradient materials
Mathematical analysis
Mathematical problems
Mindlin plates
Nuclear reactors
Rectangular plates
Studies
Theory
Trigonometric functions
Vibration analysis
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Summary:This paper presents an accurate solution method for the static and vibration analysis of functionally graded Reissner-Mindlin plate with general boundary conditions on the basis of the improved Fourier series method. In the theoretical formulations, the governing equations and the general elastic boundary equations are obtained by using Hamilton’s principle. The components of admissible displacement functions are expanded as an improved Fourier series form which contains a 2D Fourier cosine series and auxiliary function in the form of 1D series. The major role of the auxiliary function is to remove the potential discontinuities of the displacement function and its derivatives at the edges and ensure and accelerate the convergence of the series representation. The characteristic equations are easily obtained via substituting admissible displacement functions into governing equations and the general elastic boundary equations. Several examples are made to show the excellent accuracy and convergence of the current solutions. The results of this paper may serve as benchmark data for future research in related field.
ISSN:1070-9622
1875-9203
DOI:10.1155/2018/4535871