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Mahsa Najafi,Isa Ahmadi 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.40 No.1
In this study, a nonlocal Layerwise theory is presented for free vibration analysis of nanobeams resting on an elastic foundation. Eringen’s nonlocal elasticity theory is used to consider the small-scale effect on behavior of nanobeam. The governing equations are obtained by employing Hamilton’s principle and Layerwise theory of beams and Eringen’s nonlocal constitutive equation. The presented theory takes into account the in-plane and transverse normal and shear strain in the modeling of the nanobeam and can predict more accurate results. The governing equations of the beam are solved by Navier's method for Simple-Simple boundary conditions and semi-analytical methods to obtain the natural frequency for various boundary conditions including Clamped-Simple (C-S), Clamped-Clamped (C-C) and Free-Free (F-F) boundary conditions. Predictions of the present theory are compared with benchmark results in the literature. Effects of nonlocal parameter, Pasternak shear coefficient, Winkler spring coefficient, boundary conditions, and the aspect ratio on the free vibration of nanobeams are studied. The flexural mode and thickness mode natural frequencies of the nanobeam are predicted. It is shown that the predictions of present method are more accurate than the equivalent single layer theories. The theoretical developments and formulation presented herein should also be served to analyze the mechanical behavior of various nanostructures with various loading and boundary conditions.
Three-dimensional stresses analysis in rotating thin laminated composite cylindrical shells
Isa Ahmadi,Mahsa Najafi 국제구조공학회 2016 Steel and Composite Structures, An International J Vol.22 No.5
In this paper, the 3D stress state and inter-laminar stresses in a rotating thin laminated cylinder shell are studied. The thickness of the cylinder is supposed to be thin and it is made of laminated composite material and can have general layer stacking. The governing equations of the cylindrical shell are obtained by employing the Layerwise theory (LWT). The effect of rotation is considered as rotational body force which is induced due to the rotation of the cylinder about its axis. The Layerwise theory (LWT), is used to discrete the partial differential equations of the problem to ordinary ones, in terms of the displacements of the mathematical layers. By applying the Free boundary conditions the solution of the governing equations is completed and the stress state, the inter-laminar stresses, and the edge effect in the rotating cylindrical shells are investigated in the numerical results. To verify the results, LWT solution is compared with the results of the FEM solution and good agreements are achieved. The inter-laminar normal and shear stresses in rotating cylinder are studied and effects of layer stacking and angular velocity is investigated in the numerical results.