The novelty and main contributions of this research are to investigate simultaneously static bending, free vibration, and buckling responses of a sandwich beam composed of a five-layer beam using sinusoidal shear deformation theory (SSDT). In this work, five layers of a sandwich beam including a honeycomb core, carbon nanotubes reinforced composite (Matrix and Resin) (CNTRC) at the top and bottom of the core, and also, shape memory alloy (SMA) in the form of nanoscale particles with matrix in top and bottom of CNTRC are derived. In this study, the governing equations of equilibrium are obtained using the principle of minimum potential energy for deflection and buckling analyses, while Hamilton's principle is employed to obtain the governing equations of motion. Then, based on Navier's type method for simply supported boundary conditions, the deflection, critical buckling load, and the natural frequency for a sandwich beam composed of five layers are obtained. To validate the results, they are compared with existing literature, and there is a good agreement between them. Also, the effects of the thickness of the core, volume fraction of carbon nanotubes, and volume fraction of SMA are analyzed. The results reveal that changing the volume fraction from 0 to 0.01 results in a 30% decrease in deflection. It is concluded that with an enhancement in thickness ratio, the heat flux decreases due to the increase in the thickness of the core, while the thickness of face sheets decreases because the conductivity coefficient for CNT is higher than the core. Moreover, increasing temperature softens the material, leading to a decrease in the critical buckling load.

In this paper, layerwise theory (LT) along with the first, second and third-order shear deformation theories (FSDT, SSDT and TSDT) are used to determine the stress distribution in a simply supported square sandwich plate subjected to a uniformly distributed load. Two functionally graded (FG) face sheets encapsulate an elastomeric core while two epoxy adhesive layers adhere the core to the face sheets. The sandwich plate is assumed to be symmetric with respect to its core mid-plane. First, second and third-order shear deformation theories are used to model shear distribution in the adhesive layers as well as others. Results obtained from the three theories are compared with those of finite element solution. Results indicate that finite element analysis (FEA) and LT based on the first, second and third-order shear deformation theories give almost the same estimations on planar stresses. Moreover, the out-of-plane shear stresses obtained by FEA, are slightly different from those of LT based on FSDT. The differences are decreased on using LT based on SSDT or TSDT. Additionally, SSDT and TSDT predict almost the same distribution for the two planer stress and out-of-plane shear stress components along the face sheet thickness. Furthermore, third-order shear deformation theory seems to be more appropriate for prediction of out-of-plane shear stress at lower values of a/h ratio.

In this study, the dynamic buckling of the embedded laminated nanocomposite plates is investigated. Theplates are reinforced with the single-walled carbon nanotubes (SWCNTs), and the Mori-Tanaka model isapplied to obtain the equivalent material properties of them. Based on the sinusoidal shear deformationtheory (SSDT), the motion equations are derived using the energy method and Hamilton's principle. TheNavier’ s method is used in conjunction with the Bolotin's method for obtaining the dynamic instabilityregion (DIR) of the structure. The effects of different parameters such as the volume percentage ofSWCNTs, the number and orientation angle of the layers, the elastic medium, and the geometricalparameters of the plates are shown on DIR of the structure. Results indicate that by increasing the volumepercentage of SWCNTs the resonance frequency increases, and DIR shifts to right. Moreover, it is foundthat the present results are in good agreement with the previous researches.

The seismic response of the smart layer is studied in this article based on mathematical modeling and numerical solution. The structure is modeled by sinusoidal shear deformation (SSDT) and the motion equations are derived by energy method and virtual work. The concrete beam is covered by a piezoelectric layer for smart control of the structure. The differential quadrature (DQ) and Newark methods are applied for numerical solution and dynamic response of the smart concrete beam under the earthquake load. The influences of boundary conditions; external voltage, and geometrical parameters of the beam are studied on the seismic response of the smart concrete beam. The results indicate that by applying an external negative voltage, the dynamic deflection of the smart concrete beam is reduced, which is important for smart control of the system while this phenomenon is converse for positive external voltage.