This study investigates the nonlinear dynamic behavior of bi-directional functionally graded material (BDFG) plates under moving loads, with a focus on material gradient effects and geometric imperfection. The material properties follow a symmetric power-law distribution across both in-plane and thickness dimensions. In accordance with the first-order shear deformation theory (FSDT), the displacement fields of the nonlinear dynamic behavior of BDFG plates under moving loads are obtained. In accordance with the Hamilton's principle, the governing equations for the dynamics of a system are deduced. By systematically adjusting the gradient profile, significant enhancements in dynamic stability and structural performance are achieved. The fourth-order Runge-Kutta method is developed to evaluate mechanical responses under varying boundary conditions and load velocities. Key findings show: (a) Forced vibration sees a monotonic rise in deflection with material gradient parameter (r_z), while free vibration shows a non-monotonic pattern due to response shift from load to stiffness-damping dominance. Forced vibration deflection increases with in-plane gradient parameter (r_x) from enhanced lateral disturbance, but free vibration exhibits a fluctuating pattern governed by structural properties. (b) Higher initial geometric imperfections amplify deflection in both stages by reducing stiffness and increasing load sensitivity and initial energy.

In this study, a free-vibration- analysis of sandwich beams featuring functionally graded face sheets and a functionally graded porosity- (FGP) core (either ceramic for Type A- or metal for Type B-)is presented using high-order- beam theory. In this study, three different porosity distributions (PDs) were employed, assuming that the elastic moduli and mass density of the material varied with thickness. This study analyzed the effects of the slenderness ratio and porosity volume fraction on the natural frequency of porous sandwich beams, considering two different boundary conditions and a fixed set of parameters. The governing equations are derived using Hamilton's principle. The effects of varying porosity distributions (PD) on the structural properties have also been highlighted to showcase the impact of porosity design on free vibration. The numerical results of the natural frequency obtained using the present theory are compared with those obtained using higher-order shear deformation beam theories in 2D and 3D. This study presents the effects of the power-law factor, boundary conditions, aspect ratio, and lamination schemes on the dynamic response of FGM sandwich beams.

The present work focuses on the flexural behaviour of multi-layered composite panels under hygro-thermo-elastic conditions. Here, various geometrical configurations, such as skewed, cylindrical and sinusoidally-corrugated panels, are modelled using geometry transformation and curvature effects via the higher-order shear-deformation mid-plane kinematics with nine degrees-of-freedom. The hygro-thermo-elastic constitutive model is considered to include the moisture and temperature effects in the present analysis. For this purpose, the moisture and temperature-dependent elastic properties of composite lamina are considered to ensure the accurate behaviour. The governing equations for the hygro-thermo-elastic analysis of multi-layered skewed/cylindrical/corrugated panels, the minimum total potential energy principle is expressed and solved further using a homemade robust finite element model based on quadratic Lagrange quadrilateral 2D-elements. Here, the mesh-refinement followed by the verification tests are executed, which demonstrate the precision and accuracy of the developed model. Furthermore, various test conditions are executed, including skewness, corrugation, curvature, etc., to illustrate the deformation characteristics of multi-layered skewed/cylindrical/corrugated panels under hygro-thermo-elastic loadings. These results exhibit that the present comprehensive investigation is vital for the multi-layered composite exposed to a complex environment, and towards the benefit of real-life applications.

The thermodynamic bending behavior of multilayered functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates has received limited attention in the existing literature, despite their promising applications in advanced aerospace, mechanical, and nano-engineering structures. To address this gap, the present study develops, for the first time, an analytical model to investigate the thermodynamic bending response of multilayered FG-CNTRC plates subjected to thermal loading. The formulation is based on the higher-order shear deformation theory (HSDT), while the governing equations and boundary conditions are derived using Hamilton's principle. An analytical solution for simply supported plates is obtained by employing Navier's method. The material properties are assumed to be temperature-dependent and are evaluated according to the Touloukian principle. In addition, the volume fraction of carbon nanotubes (CNTs) is considered to vary through the thickness according to several distribution patterns, namely uniform distribution (UD) and four functionally graded distributions (FG-X, FG-O, FG-V, and FG-A). A comprehensive parametric investigation is performed to examine the effects of CNT distribution patterns, CNT volume fraction, temperature difference, and number of layers on the bending response of the plates. The numerical results reveal that the FG-X distribution exhibits the highest stiffness and consequently the lowest deflection among all the considered distributions. Furthermore, increasing the CNT volume fraction and the number of layers enhances the structural stiffness, whereas increasing the temperature difference leads to a significant reduction in stiffness and an increase in deflection. The proposed model provides new insights into the thermodynamic bending behavior of multilayered FG-CNTRC plates and may serve as an efficient analytical tool for the design and optimization of advanced nanocomposite structures.

This study introduces a refined and computationally efficient hyperbolic Shear-Order Shear Deformation Theory (HypSDT) with only four displacement variables for the buckling analysis of functionally graded transparent (FGT) doubly curved shells. By reducing the number of unknowns compared with conventional FSDT formulations, the proposed model achieves high accuracy while improving computational efficiency. The analysis focuses on shells made of sapphire and soda lime glass, and the governing equations are derived using Minimum Total Potential Energy's principle before being solved analytically through the Navier approach for simply supported boundary conditions. The numerical results show that the critical buckling load is highly sensitive to the material gradation index, with higher values of k leading to lower stiffness and reduced buckling resistance. The study also reveals that spherical shells provide the greatest structural stability because of their balanced double curvature, whereas biaxial loading and larger radius-to-side ratios significantly decrease the buckling capacity. Overall, the proposed formulation provides an accurate and efficient tool for the design and analysis of lightweight, transparent shell structures intended for modern architectural and advanced aerospace applications.