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Free vibration of an axially loaded silicon microbeam in MEMS under electrostatic actuation is studied on the basis of a sinusoidal shear deformation theory. Based on the modified couple stress theory (MCST) and von Kármán geometric nonlinearity, a nonlinear finite element formulation is derived and employed to construct the discrete nonlinear governing equations for the microbeam. The deflection of the microbeam at a given DC voltage is firstly calculated using the Newton Raphson based iterative procedure, and used to evaluate the tangent stiffness matrix. The natural frequencies of the microbeam corresponding the DC voltage are then computed. The influence of the applied voltage, the axial force as well as the material length scale parameter on the frequencies of the microbeam is studied in detail and highlighted. The dependence of the pull-in voltage upon the material length scale and the axial force is also examined and discussed.

For the first time, postbuckling behavior of thick doubly curved panels made of carbon nanotube reinforced composite (CNTRC), under preexisting external pressure and subjected to uniform temperature rise is analyzed in this paper. Carbon nanotubes (CNTs) are reinforced into matrix through functionally graded (FG) distribution patterns, and effective properties of CNTRC are determined according to extended rule of mixture. Formulations are based on a higher order shear deformation theory including Von Karman-Donnell nonlinearity, initial geometrical imperfection and elasticity of tangential constraints of boundary edges. Analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is used to obtain nonlinear load-deflection relation. Taking into account temperature dependence of material properties, postbuckling temperature-deflection paths are traced through an iteration process. The effects of preexisting external pressure, CNT volume fraction, tangential edge constraints, initial geometrical imperfection and curvature ratios on thermal postbuckling behavior of CNTRC doubly curved panels are analyzed through numerical examples. The study reveals that thermally loaded panels experiences a quasi-bifurcation response due to the presence of preexisting external pressure. For the most part, perfect panels are deflected toward convex side at the onset of undergoing thermal load. Particularly, imperfect panels may exhibit a bifurcation type buckling response when imperfection size satisfy a special condition.

Free vibration of bidirectional functionally graded sandwich (BFGSW) beams is studied by using a first-order shear deformation finite element formulation. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in both the longitudinal and thickness directions by power gradation laws. The finite element formulation with the stiffness and mass matrices evaluated explicitly is efficient, and it is capable of giving accurate frequencies by using a small number of elements. Vibration characteristics are evaluated for the beams with various boundary conditions. The effects of the power-law indexes, the layer thickness ratio, and the aspect ratio on the frequencies are investigated in detail and highlighted. The influence of the aspect ratio on the frequencies is also examined and discussed. Keywords: BFGSW beam; first-order shear deformation theory; free vibration; finite element method.

The large displacements of functionally graded sandwich (FGSW) beams in thermal environment are studied using a finite element formulation. The beams are composed of three layers, a homogeneous core and two functionally graded face sheets with volume fraction of constituents following a power gradation law. The material properties of the beams are considered to be temperature-dependent. Based on Antman beam model and the total Lagrange formulation, a two-node nonlinear beam element taking the effect of temperature rise into account is formulated and employed in the study. The element with explicit expressions for the internal force vector and tangent stiffness matrix is derived using linear interpolations and reduced integration technique to avoid the shear locking. Newton-Raphson based iterative algorithm is employed in combination with the arc-length control method to compute the large displacement response of a cantilever FGSW beam subjected to end forces. The accuracy of the formulated element is confirmed through a comparison study. The effects of the material inhomogeneity, temperature rise and layer thickness ratio on the large deflection response of the beam are examined and highlighted.

Free vibration of functionally graded (FG) sandwich plates partially supported by a Pasternak elastic foundation is studied. The plates consist of three layers, namely a pure ceramic hardcore and two functionally graded skin layers. The effective material properties of the skin layers are considered to vary in the plate thickness by a power gradation law, and they are estimated by Mori--Tanaka scheme. The quasi-3D shear deformation theory, which takes the thickness stretching effect into account, is adopted to formulate a finite element formulation for computing vibration characteristics. The accuracy of the derived formulation is confirmed through a comparison study. The numerical result reveals that the foundation supporting area plays an important role on the vibration behavior of the plates, and the effect of the layer thickness ratio on the frequencies is governed by the supporting area. A parametric study is carried out to highlight the effects of material distribution, layer thickness ratio, foundation stiffness and area of the foundation support on the frequencies and mode shapes of the plates. The influence of the side-to-thickness ratio on the frequencies of the plates is also examined and discussed.

Dynamic analysis of an inclined functionally graded sandwich (FGSW) beam traveled by a moving mass is studied. The beam is composed of a fully ceramic core and two skin layers of functionally graded material (FGM). The material properties of the FGM layers are assumed to vary in the thickness direction by a power-law function, and they are estimated by Mori-Tanaka scheme. Based on the first-order shear deformation theory, a moving mass element, taking into account the effect of inertial, Coriolis and centrifugal forces, is derived and used in combination with Newmark method to compute dynamic responses of the beam. The element using hierarchical functions to interpolate the displacements and rotation is efficient, and it is capable to give accurate dynamic responses by small number of the elements. The effects of the moving mass parameters, material distribution, layer thickness ratio and inclined angle on the dynamic behavior of the FGSW beam are examined and highlighted.

Dynamic analysis of a functionally graded sandwich (FGSW) beam traversed by a moving mass is presented in the basis of a refined third-order shear deformation theory. The beam consists of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in the thickness direction by a power gradation law. Both Voigt and Mori-Tanaka micromechanical models are employed to evaluate the effective properties of the beam. A finite element formulation, taking into account the effect of inertial, Coriolis and centrifugal forces, is derived and used in combination with Newmark method to compute dynamic response of the beam. The accuracy and efficiency of the derived formulation are confirmed by comparing obtained results with the data of Refs. [3, 4, 6, 11]. The effects of the material gradation, the moving mass speed and the beam geometry on the dynamic behavior of the beam are studied in detail and highlighted. The influence of the micromechanical model on the dynamic response of the beam is also examined and discussed.

Free vibration and buckling of three-phase bidirectional functionally graded sandwich (BFGSW) plates are studied in this paper for the first time by using an efficient nine-node quadrilateral (Q9) element. The core of the sandwich plates is pure ceramic, while the two skin layers are of a three-phase bidirectional functionally graded material. The element is derived on the basis of the Mindlin plate theory and linked interpolations. Fundamental frequencies and buckling loads are computed for the plates with various boundary conditions. Numerical result shows that convergence of the linked interpolation element is faster compared to the conventional Lagrangian interpolation Q9 element. Numerical investigations are carried out to highlight the influence of the material gradation and the side-to-thickness ratio on the vibration and buckling behaviour of the plates.

A two-dimensional functionally graded sandwich (2D-FGSW) beam model\break formed from three constituent materials is proposed and its free vibration is studied for the first time. The beam consists of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in both the length and thickness directions by power gradation laws. Based on a third-order shear deformation theory, a beam element using the transverse shear rotation as an independent variable is formulated and employed in the study. The obtained numerical result reveals that the variation of the material properties in the length direction plays an important role on the natural frequencies and vibration modes of the beam. The effects of the material distribution and layer thickness ratio on the vibration characteristics are investigated in detail. The influence of the aspect ratio on the frequencies is also examined and discussed.

In this paper, numerical and experimental studies for crack detection of structures using "element stiffness index distribution" are presented. The element stiffness index distribution is defined as a vector of norms of sub-matrices corresponding to element stiffness matrices calculated from the reconstructed global stiffness matrix of the beam. When there is a crack at an element, the element stiffness index of that element will be changed. By inspecting the change in the element stiffness index distribution, the crack can be detected. A significant peak in the element stiffness index distribution is the indicator of the crack existence. The crack location is determined by the location of the peak and the crack depth can be determined from the height of the peak. The global stiffness matrix is calculated from the measured frequency response functions instead of mode shapes to avoid limitations of the mode shape-based methods for crack detection. Numerical simulation results for the cases of beam-like structures are provided. The experiment is carried out to justify the efficiency of the proposed method.

The effect of intermediate elastic support on the vibration of functionally graded Euler-Bernoulli beams excited by a moving point load is studied. The material properties of the beams are assumed ...

The elasto-plastic analysis of functionally graded (FG) metal-ceramic beams under mechanical loading by using the finite element method is presented. A bilinear stress-strain relation with isotropic hardening is assumed for elasto-plastic behaviour of metal, and the effective elasto-plastic properties of the functionally graded material are evaluated by using Tamura-Tomota-Ozawa (TTO) model. A nonlinear beam element based on the classical beam theory is formulated and employed in the analysis. The element employed nonlinear von K\'am\'an strain-displacement relationship is derived by using the neutral surface as reference plane. The layer beam approach, in which the plastic rate equation is solved at Gauss points, is adopted in updating the stress and evaluating the element nodal force vector and tangent stiffness matrix. Numerical examples are given to show the accuracy of the derived formulation and to illustrate the effect of the material distribution and plastic deformation on the behavior of the beams. The formation and propagation of plastic zone during the loading process is also examined and highlighted.