Abstract
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.
Highlights
The concept of functionally graded materials (FGMs) was firstly presented in 1987 by a group of material scientists in Sendai region of Japan during the first five-year project to study relaxation of thermal stress of materials in high speed aerospace vehicle [1, 2]
The research of static and vibration analysis of FG plate could provide the theoretical basis for practical engineering applications
The results of this paper could serve as the reference data in practical engineering applications in related field in future
Summary
The concept of functionally graded materials (FGMs) was firstly presented in 1987 by a group of material scientists in Sendai region of Japan during the first five-year project to study relaxation of thermal stress of materials in high speed aerospace vehicle [1, 2]. As a most common infrastructure, the functionally graded rectangular plate has been widely used in practical engineering applications, i.e., aerospace, naval vessels, nuclear reactor, automobile, robot, and civil industries. The research of static and vibration analysis of FG plate could provide the theoretical basis for practical engineering applications. The static and vibration analysis of the FG plate has been investigated by a large number of researches in the past decade. Among those available, Abrate [3] used the CPT to study the free vibration of FG thin rectangular plates with supported and clamped boundary conditions. Ferreira et al [8] employed the global collocation method and approximated the trial
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