Abstract
This manuscript investigates the impact of porosity and micromechanical models on the flexural behavior of functionally graded plates employing a refined higher order shear and deformation theory. The plate's material properties are supposed to be varying gradually through the direction of the plate's thickness according to different micromechanical models namely: Voigt's model often used in furthermost functionally graded plates researches, Mori Tanaka's, Reuss's and LRVE's models. Virtual works principle is employed to determine the equations of equilibrium and some numerical results are exhibited to validate the accuracy and effectiveness of the present theory for flexural behavior of functionally graded plates. A parametric investigation is conducted to assess the influence of various parameters on the displacements and stresses of the plate including micromechanical models', porosity distribution shape and geometry of the plate. In light of this study we conclude that the present refined theory is efficient accurate and reliable for predicting the flexural behavior of functionally graded plates considering different porosity distribution shapes and various micromechanical models.
Key Words
flexural behavior; functionally graded plates; micromechanical models; porosity distribution shapes; shear stresses and strains
Address
Belkacem Adim: Civil, Mechanical and Transportation Engineering Department, Tissemsilt University, Tissemsilt 38000, Algeria; Geomatics and Sustainable Development Laboratory, Ibn Khaldoun University, Tiaret 14000, Algeria
Tahar Hassaine Daouadji: Geomatics and Sustainable Development Laboratory, Ibn Khaldoun University, Tiaret 14000, Algeria; Civil Engineering Department, Ibn Khaldoun University, Tiaret14000, Algeria
Kheira Bekda: Civil, Mechanical and Transportation Engineering Department, Tissemsilt University, Tissemsilt 38000, Algeria
Abstract
This paper presents a unified solution approach to investigate the bending and free vibration behaviors of laminated composite cylindrical shells with varying radii of curvature and simply supported edges, using a new refined shear deformation shell theory (RSDST). The theoretical formulation of the proposed approach is based on a new displacement model that incorporates undetermined integral terms to account for the effects of transverse shear deformation. It also meets the shear stress-free boundary conditions on the upper and lower surfaces of the cylindrical shell. The governing equations are derived from the principle of virtual work and are resolved using Navier-type closed form solutions. The effects of material properties and geometric parameters on the static bending and free vibration of laminated composite cylindrical shells are presented and discussed in detail. Convergence and validation studies clearly indicate that the values for displacements and stresses derived from the present theory are highly consistent with those of previous higher-order shell theories. Furthermore, a satisfactory convergence was observed when compared with 3D elasticity solutions (the percentage errors for transverse shear stresses are a maximum of 1.38%, 3.19% and 21.33% for isotropic, orthotropic and laminated composite cylindrical shells, respectively). It is shown that the present model with only four variables is able to accurately predict the stress distributions and natural frequencies, with less computational effort compared to conventional HSDST models.
Key Words
bending; free vibration; laminated cylindrical shells; new displacement model; RSDST
Address
Ali Meksi: University Mustapha Stambouli of Mascara, BP 305, 29000 Mascara, Algeria
Kada Draiche: Department of Civil Engineering, University of Tiaret, BP 78 Zaaroura, 14000 Tiaret, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Emrah Madenci: Department of Civil Engineering, Necmettin Erbakan University, 42090, Konya, Turkey; Department of Technical Sciences, Western Caspian University, Baku 1001, Azerbaijan
Abdelouahed Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; 6Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia; Department of Civil and Environmental Engineering, Lebanese American University, 309 Bassil Building, Byblos, Lebanon
Abstract
The buckling behavior of advanced sandwich composite beams is critical to their performance and stability, and understanding this behavior is essential for optimizing their design. This research aims to develop a new theory to investigate the buckling behavior of isotropic and functionally graded (FG) sandwich beams under various boundary conditions. The proposed theory eliminates the necessity of employing shear correction factors as it considers the parabolic variation of the shear stress distribution along the thickness. Based on Galerkin's method, a novel analytical solution is applied to solve the governing equilibrium equations. Considering that the material properties of functionally graded sandwich beams are graded in thickness according to a power-law distribution. A key aspect of this approach is to compare results obtained from the proposed theory with those derived from established higher-order shear deformation beam theories, intending to validate the accuracy and reliability of the new theory by comparing it with existing literature. In addition, the effects of different boundary conditions, FG material distribution, face-to-core thickness ratio, length-to-thickness ratio and volume fraction index on the critical buckling of FG sandwich beams are studied and discussed in detail. Our study showed that the shear deformation effect is remarkably significant for the case of thick or moderately thick beams. However, it is negligible in the case of slender beams. Finally, the presented findings and benchmark results offer a foundation for future research and design considerations within the domain of composite materials and structural engineering.
Key Words
advanced sandwich; beams; elastic buckling; functionally graded; shear deformation beam theory
Address
Mohammed Sid Ahmed Houari: Laboratoired'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
Ali Belhocine: Laboratoired'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
Abderahman Younsi: Medea University, Medea, 26000, Algeria
Ahmed Amine Daikh: Laboratoired'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, P.O. Box 66, Naama 45000, Algeria
Mohamed-Ouejdi Belarbi: Laboratoire de Recherche en Génie Civil, LRGC, Université de Biskra, B.P. 145, R.P. 07000, Biskra, Algeria
Abdelkrim Aid: Department of Mechanical Engineering, Faculty of Science and Technology, University Mustapha Stambouli of Mascara, Mascara, Algeria
Abstract
Beam-like structural members and components manufactured by functionally graded materials are widely applied in up-to-date aeronautical and aerospace engineering. Being parts of various flying apparatuses (helicopters, aircrafts, spacecrafts, etc.) these structural members very often are involved in different types of nonuniform spatial motion in the time of their service. This fact indicates the importance of studying the fracture behavior of the structural members and components with taking into account the inertia loading in the conditions of spatial motion. The present paper analyzes the effects of spatial translational motion on lengthwise fracture in functionally graded beams with non-linear elastic behavior. The beams under consideration are executing spatial translational motion with acceleration along the three axes in the space. The law of motion of the beams is known. The paper is focused particularly on deriving the strain energy release rate (SERR) in the beams acted upon by the inertia loading. The content of this paper is presented in the following consequence. First, the SERR problem in beams executing spatial translational motion is treated generally. Determination of accelerations and inertia loads along the three axes of the beam is considered. Then solution of an example is presented in detail. Finally, results illustrating the effects of spatial translational motion, material inhomogeneity and distribution of material density in the beam structure on the SERR are displayed in various graphs. A comparison in terms of the SERR between plane translation and spatial translation motion is presented. In context of this comparison, the effect of thickness to width ratio of the beam is evaluated.
Address
Victor I. Rizov: Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy,
1 Chr. Smirnensky Blvd., 1046-Sofia, Bulgaria
Holm Altenbach: Lehrstuhl für Technische Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Deutschland
Abstract
This study explores the influence of porosity on the stability behavior of shear-deformable auxetic-core
sandwich-structured toroidal shell segments (TSSs) with porous carbon nanotube (CNT)-reinforced face sheets
supported by a Kerr-type elastic foundation and subjected to external pressure. The CNTs are embedded in a polymer
matrix throughout the face sheet thickness, with three distinct porosity distribution patterns examined: uniform,
symmetric, and asymmetric. The metamaterial core features an arc-type auxetic design inspired by the traditional reentrant honeycomb structure, with curved ribs that facilitate a smooth transition between adjacent unit cells, reducing stress concentrations. The Kerr elastic foundation is modeled with three parameters: a shear layer in the middle and spring layers at the top and bottom. The governing equations for the TSSs are derived using Reddy's third-order shear deformation theory (TSDT), accounting for von Kármán-type geometric nonlinearity. A three-term deflection solution, based on simply supported boundary conditions, is employed, and the Galerkin method is used to establish the nonlinear load-deflection relationship. The validity of the approach is confirmed through a comparative analysis with existing literature, showing good agreement with theoretical results. Numerical findings provide a detailed analysis of how porosity parameters, including coefficient and distribution type, influence the stability of sandwich TSSs.
Address
Mohammadhossein Goudarzfallahi, Ali Alinia Ziazi: Department of Mechanical Engineering, SR.C., Islamic Azad University, Tehran, Iran
Farzad Ebrahimi: Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran
