The nonlinear buckling and post-buckling response of imperfect porous plates is investigated analytically in this paper. The porous materials with elastic moduli are assumed to vary through the thickness of the plate according to two different distribution types. Governing equations are derived based on the classical shell theory taking into account Von Karman nonlinearity and initial geometrical imperfection. Explicit relations of load–deflection curves for rectangular porous plates are determined by applying stress function and Galerkin’s method. The accuracy of present theoretical formulation is verified by comparing it with available results in the literature. The effects of varying porosity distribution, porosity coefficient, boundary condition and imperfection on post-buckling behavior of the porous plate are studied in detail. A parametric study is carried out to investigate the effects of varying porosity distribution, porosity coefficient, boundary condition and imperfection on post-buckling behavior of the porous plate. The results show that the critical buckling loads decrease with increasing porosity coefficient and the post-buckling curves for nonlinear symmetric porosity distribution are always higher than those for nonlinear non-symmetric porosity.
This paper analyzes the nonlinear buckling and post-buckling characteristics of the porous eccentrically stiffened functionally graded sandwich truncated conical shells resting on the Pasternak elastic foundation subjected to axial compressive loads. The core layer is made of a porous material (metal foam) characterized by a porosity coefficient which influences the physical properties of the shells in the form of a harmonic function in the shell’s thickness direction. The physical properties of the functionally graded (FG) coatings and stiffeners depend on the volume fractions of the constituents which play the role of the exponent in the exponential function of the thickness direction coordinate axis. The classical shell theory and the smeared stiffeners technique are applied to derive the governing equations taking the von Kármán geometrical nonlinearity into account. Based on the displacement approach, the explicit expressions of the critical buckling load and the post-buckling load-deflection curves for the sandwich truncated conical shells with simply supported edge conditions are obtained by applying the Galerkin method. The effects of material properties, core layer thickness, number of stiffeners, dimensional parameters, semi vertex angle and elastic foundation on buckling and post-buckling behaviors of the shell are investigated. The obtained results are validated by comparing with those in the literature.
This paper studies the free vibration behavior of a sandwich beam resting on Winkler elastic foundation. The sandwich beam is composed of two FGM face layers and a functionally graded (FG) porous core. A common general form of different beam theories is proposed and the equations of motion are formulated using Hamilton's principle. The result of the general form is validated against those of a particular case and shows a good agreement. The effect of different parameters on the fundamental natural frequency of the sandwich beam is investigated.
Article history: Received 02 March 2018, Revised 26 March 2018, Accepted 27 April 2018
This paper presents the free vibration analysis of laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates. The CNTRC layer consists of single-walled carbon nanotubes (SWCNTs) as reinforcement and polymer as a matrix. The material properties are determined according to the extended rule of mixture. Four different patterns of SWCNTs distribution across the thickness of individual layers are considered. Based on the first-order shear deformation theory (FSDT), the equations of motion are derived and then solved by employing the pb2-Ritz method. The accuracy of the present approach is verified by comparing the obtained results with those available in the literature and commercial ANSYS software. The significant influences of CNT volume fractions, CNT distribution patterns, plate aspect ratio, plate width-to-thickness ratio, and boundary conditions on the non-dimensional fundamental frequency of symmetric and anti-symmetric laminated FG-CNTR plates has been proven through the numerical examples. Furthermore, the influence of lamination schemes, CNT fiber orientation and the number of layers is also investigated.
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