Abstract
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 (rz),
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 (rx) 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.
Address
Wubin Shan: College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, China
Zipan Yang: Hunan Vocational Institute of Technology, Xiangtan 411104, China
Kuineng Chen: Xiangtan Hengxin Industrial Co., Ltd., Xiangtan, 411300, China
Abstract
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 highorder-
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.
Key Words
FG sandwich beam; free vibratio; functionallyy graded materia; porosity distributio; powerr
law
Address
Messaoud Baazouzi: Department of Civil Engineering, Faculty of Sciences & Technology, Abbes Laghrour University,
Khenchela, 40000, Algeria;
Civil Engineering Research Laboratory LRGC, Biskra University, 07000 Biskra, Algeria
Rachid Slimani: University of Tamanghasset, Faculty of Sciences & Technology, Sciences & Technology Department, BP
10034, Sersouf Tamanghasset 11000, Algeria
Mourad Chitour: Department of Mechanical Engineering, Faculty of Sciences & Technology, Abbes Laghrour University,
Khenchela, 40000, Algeria
Abdelhakim Bouhadra and Abderrahmane Menasria: University of Tamanghasset, Faculty of Sciences & Technology, Sciences & Technology Department, BP
10034, Sersouf Tamanghasset 11000, Algeria;
Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria
Khawla Boudiaf: University of Tamanghasset, Faculty of Sciences & Technology, Sciences & Technology Department, BP
10034, Sersouf Tamanghasset 11000, Algeria;
Civil Engineering Research Laboratory LRGC, Biskra University, 07000 Biskra, Algeria
Abstract
The present work focuses on the flexural behaviour of multi-layered composite panels under hygrothermo-
elastic conditions. Here, various geometrical configurations, such as skewed, cylindrical and sinusoidallycorrugated
panels, are modelled using geometry transformation and curvature effects via the higher-order sheardeformation
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.
Key Words
deformation; higher-order kinematics; hygro-thermo-elastic constitutive model; multi-layered
composites; sinusoidal corrugation; 2D Lagrange elements
Address
Vinod Kumar Shukla, Vishesh Ranjan Kar: Department of Mechanical Engineering, National Institute of Technology Jamshedpur,
Jamshedpur 831014, Jharkhand, India
Abstract
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.
Key Words
multilayered CNTRC plates; Navier
Address
Ahmed Amine Daikh, Loubna Nadji: Mechanical Engineering Department, Faculty of Technology, University of Naama, Naama, Algeria
Aicha Bessaim: Laboratoire d
Abstract
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.
Address
Djilalli Mokhefi, Ali Belhocine, Mohammed Sid Ahmed Houari: Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil,
Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P. 29000 Mascara, Algérie
Ahmed Bakoura: Département de Génie Civil, Faculté d'Architecture et de Génie Civil,
Université des Sciences et de la Technologie d'Oran, BP 1505 El M'naouer, USTO, Oran, Algeria;
Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology,
University of Sidi Bel Abbes, Algeria
Fouad Kherbouche: Laboratory of Science and Technology of Water (LSTE), Department of Electrical Engineering,
University of Mustapha Stambouli, Mascara, BP 305, Algeria
Ahmed Amine Daikh: Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil,
Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305,
R.P. 29000 Mascara, Algérie;
Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil,
University Centre of Naama, Naama, Algeria
