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    A comprehensive study on the size-dependent analysis of strain gradient multi-directional functionally graded microplates via finite element model
    (Elsevier France-Editions Scientifiques Medicales Elsevier, 2021) Karamanli, Armagan; Aydogdu, Metin; Vo, Thuc P.
    This paper presents a comprehensive study on bending, vibration and buckling behaviours of the multi-directional FG microplates. The material properties vary continuously both in-plane and through-thickness directions. Based on a quasi-3D shear and normal deformation plate theory and the modified strain gradient theory, a finite element model is proposed and employed to solve the problems of the multi-directional FG microplates with various boundary conditions. The verification is performed by comparing the numerical results with those from the previous studies. A number of numerical examples on the multi-directional FG microplates with nine boundary conditions and power-law index have been carried out. The effects of three material length scale parameters, aspect ratio, gradient indexes in spatial directions and boundary conditions on the displacements, natural frequencies and buckling loads of 1D, 2D and 3D-FG microplates are investigated in details. Some new results, which are not available in open literature, are provided as references for the future studies. (C) 2021 Elsevier Masson SAS. All rights reserved.
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    Free vibration of axially loaded composite beams using a four-unknown shear and normal deformation theory
    (Elsevier Sci Ltd, 2017) Vo, Thuc P.; Huu-Tai Thai; Aydogdu, Metin
    This paper presents free vibration of composite beams under axial load using a four-unknown shear and normal deformation theory. The constitutive equation is reduced from the 3D stress-strain relations of orthotropic lamina. The governing differential equations of motion are derived using the Hamilton's principle. A two-node C-1 beam element is developed by using a mixed interpolation with linear and Hermite-cubic polynomials for unknown variables. Numerical results are computed and compared with those available in the literature and commercial finite element software (ANSYS and ABAQUS). The comparison study illustrates the effects of normal strain, Jay-ups and Poisson's ratio on the natural frequencies and load-frequency curves of composite beams. (C) 2017 Elsevier Ltd. All rights reserved.