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CONTENTS
Volume 90, Number 3, May10 2024
 

Abstract
In current study, for the first time, Nonlinear Bending of a skew microplate made of a laminated composite strengthened with graphene nanosheets is investigated. A mixture of mechanical and thermal stresses is applied to the plate, and the reaction is analyzed using the First Shear Deformation Theory (FSDT). Since different percentages of graphene sheets are included in the multilayer structure of the composite, the characteristics of the composite are functionally graded throughout its thickness. Halpin-Tsai models are used to characterize mechanical qualities, whereas Schapery models are used to characterize thermal properties. The microplate's non-linear strain is first calculated by calculating the plate shear deformation and using the Green-Lagrange tensor and von Karman assumptions. Then the elements of the Couple and Cauchy stress tensors using the Modified Coupled Stress Theory (MCST) are derived. Next, using the Hamilton Principle, the microplate's governing equations and associated boundary conditions are calculated. The nonlinear differential equations are linearized by utilizing auxiliary variables in the nonlinear solution by applying the Frechet approach. The linearized equations are rectified via an iterative loop to precisely solve the problem. For this, the Differential Quadrature Method (DQM) is utilized, and the outcomes are shown for the basic support boundary condition. To ascertain the maximum values of microplate deflection for a range of circumstances—such as skew angles, volume fractions, configurations, temperatures, and length scales-a parametric analysis is carried out. To shed light on how the microplate behaves in these various circumstances, the resulting results are analyzed.

Key Words
frechet differential; functionally graded; GDQM; graphene nanosheets; hamilton principle; large deformation; MCST; Von-Karman assumptions

Address
J. Jenabi, A.R. Nezamabadi: Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran
M. Karami Khorramabadi: Department of Mechanical Engineering, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran

Abstract
This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

Key Words
bi-directional functionally graded beam; exponential power-law; finite element formulation; free vibration; higher-order shear deformation theory

Address
Zakaria Belabed: Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, Institute of Technology, University Center of Naama, BP 66, 45000 Naama, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Abdeldjebbar Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Industrial Engineering and Sustainable Development Laboratory, University of Rélizane, Algeria
Abdelmoumen Anis Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, Faculty of Science & Technology, Mechanical Engineering Department, Université de Sidi Bel Abbés, Algeria
Abdelouahed Tounsi: Department of Civil and Environmental Engineering, Lebanese American University, 309 Bassil Building, Byblos, Lebanon; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
Mohamed Bourada: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Mohammed A. Al-Osta: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals,
31261 Dhahran, Eastern Province, Saudi Arabia; Interdisciplinary Research Center for Construction and Building Materials, KFUPM, 31261 Dhahran, Saudi Arabia

Abstract
This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

Key Words
bi-directional functionally graded beam; exponential power-law; finite element formulation; free vibration; higher-order shear deformation theory

Address
Y.C. Huang: Information Technology Faculty, Duy Tân University, 254 Nguyen Van Linh, Danang, Vietnam
M.D. TuMuli Lulios: Princess Margaret Hospital, Funafuti Island, Private Mail Bag, Tuvalu
Chu-Ho Chang: College of Electrical Engineering and Computer Science, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan
M. Nasir Noor: College of Maritime, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan
Jen-Chung Shao: 3ollege of Electrical Engineering and Computer Science, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan
Chien-Liang Chiu: Department of Electronic Engineering, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan
Tsair-Fwu Lee: Department of Electronic Engineering, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan; Medical Physics and Informatics Laboratory of Electronics Engineering, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan
Renata Wang: Information and Research Center of China, 1/9, Road: 2, Block: D, Section: 15, Dhaka 1216, Bangladesh

Abstract
This research deals with the study of two-dimensional deformation in transversely isotropic thermoelastic diffusion medium. This investigation integrates the effect of diffusion and thermal effects in transversely isotropic thermoelastic solids under inclined load. Inclined load is taken as linear combination of normal load and tangential load. Laplace and Fourier transformation techniques are employed to transform the physical domain and then transformed solutions are inverted with the aid of numerical inversion techniques. Concentrated and distributed load are considered to exemplify its utility. Graphical representation of variation in displacement, stresses, temperature and concentration distribution with distance is depicted by taking inclination at different angles. Some particular cases are studied.

Key Words
inclined load; Laplace and Fourier transform; thermoelastic diffusion; transversely isotropic

Address
Parveen Lata and Heena: Department of Mathematics, Punjabi University, Patiala, Punjab, India

Abstract
Tapered girders emerged as an economical remedy for the challenges associated with constructing long-span buildings. From an economic standpoint, these systems offer significant advantages, such as wide spans, quick assembly, and convenient access to utilities between the beam's shallow sections and the ceiling below. Elastic-local buckling is among the various failure modes that structural designers must account for during the design process. Despite decades of study, there remains a demand for efficient and comprehensive procedures to streamline product design. One of the most pressing requirements is a better understanding of the tapered web plate girder's local buckling behavior. This paper conducts a comprehensive numerical analysis to estimate the critical buckling coefficient for simply supported tapered steel web plates, considering loading conditions involving compression and bending stresses. An eigenvalue analysis was carried out to determine the natural frequencies and corresponding mode shapes of tapered web plates with varying geometric parameters. Additionally, the study highlights the relative significance of various parameters affecting the local buckling phenomenon, including the tapering ratio of the panel, normalized plate length, and ratio of minimum to maximum compressive stresses. The regression analysis and optimization techniques were performed using MATLAB software for the results of the finite element models to propose a separate formula for each load case and a unified formula covering different compression and bending cases of the elastic local buckling coefficient. The results indicate that the proposed formulas are applicable for estimating the critical buckling coefficient for simply supported tapered steel web plates.

Key Words
local buckling coefficient; optimization technique; stress gradient; tapered plate

Address
Saad A. Yehia, Ramy I. Shahin: Department of Civil Engineering, Higher Institute of Engineering and Technology, Kafrelsheikh, Egypt
Bassam Tayeh: Civil Engineering Department, Faculty of Engineering, Islamic University of Gaza, P.O. Box 108, Gaza Strip, Palestine

Abstract
Composite skew plates are aesthetically appealing light weight structural units finding wide applications in floors and roofs of commercial buildings. Although bending and vibration characteristics of these units have received attention from researchers but the domain of first and progressive failure has not been explored. Confident use of these plates necessitates comprehensive understanding of their failure behavior. With this objective, the present paper uses an eight noded isoparametric finite element together with von-Kármán's approach of nonlinear strains to study first ply and progressive failure up to ultimate damage of skew plates being subjected to uniform surface pressure. Parameters like skew angles, laminations and boundary conditions are varied and the results are practically analyzed. The novelty of the paper lies in the fact that the stiffness matrix of the damaged plate is calculated by considering material degradation locally only at failed points at each stage of first and progressive failure and as a result, the present outputs are so close to experimental findings. Interpretation of results from practical angles and proposing the relative performances of the different plate combinations in terms of ranks will be of much help to practicing engineers in selecting the best suited plate option among many combinations.

Key Words
finite element method (FEM); first ply failure; laminated composite; progressive failure; skew plate; von- Kármán nonlinearity

Address
Dona Chatterjee: Department of Civil Engineering, Heritage Institute of Technology, Kolkata, 700107, India
Arghya Ghosh: Department of Civil Engineering, Netaji Subhas University of Technology, New Delhi, 110078, India
Dipankar Chakravorty: Department of Civil Engineering, Jadavpur University, Kolkata, 700032, India

Abstract
Different methods have been proposed in the literature for splicing the reinforcing bars in the construction of concrete structures, which are alternatively used depending on design requirements. The most common approach is the lap splicing which is known as a cost-effective method although, its main disadvantages including congestion of bars at the lap zone and consequently, material wastage has motivated utilization of the other techniques such as mechanical splices (couplers). To better evaluate the performance of the couplers, 6 reinforced concrete (RC) beams whose difference is only the type and location of splices have been experimentally studied in this paper. Based on the results, the mechanical connection of the bars did not markedly affect the load-carrying capacity of the specimens. Moreover, it was observed that after applying the loads and failure of the specimens, none of the bars ruptured at the splice location and all couplers remained undamaged.

Key Words
coupler; mechanical splice; RC beam; Reinforced Concrete (RC) structures; splicing

Address
Sadegh Hashemi, Ali Kheyroddin: Department of Civil Engineering, University of Semnan, Semnan, Iran
Ghasem Pachideh: Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

Abstract
Most of existing buildings in Mexico City are made of reinforced concrete (RC), however, it has been shown that they are very susceptible to narrow-band long duration ground motions. In recent years, the use of dual systems composed by Buckling Restrained Braces (BRB) has increased due to its high energy dissipation capacity under reversible cyclical loads. Therefore, in this work the behavior of RC buildings with BRB is studied in order to know their performance, specifically, the energy distribution through height and response transformation factors between the RC and simplified systems are estimated. For this propose, seven RC buildings with different heights were designed according to the Mexico City Seismic Design Provisions (MCSDP), in addition, equivalent single degree of freedom (SDOF) systems were obtained. Incremental dynamic analyses on the buildings under 30 narrow-band ground motions in order to compute the relationship between normalized hysteretic energy, maximum inter-story drift and roof displacement demands were performed. The results shown that the entire structural frames participate in energy dissipation and their distribution is independent of the global ductility. The results let propose energy distribution equations through height. Finally, response transformation factors between the SDOF and multi degree of freedom (MDOF) systems were developed aimed to propose a new energy-based approach of BRB reinforced concrete buildings.

Key Words
buckling restrained braces; dual systems; energy distribution; hysteretic energy; transformation factors

Address
Herian A. Leyva: Facultad de Ingeniería, Arquitectura y Diseño, Universidad Autónoma de Baja California, Ensenada 22860, México
Edén Bojórquez, Juan Bojórquez, Alfredo Reyes: 2acultad de Ingeniería, Universidad Autónoma de Sinaloa, Culiacán 80040, México
Fabrizio Mollaioli: Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy
Omar Payán: Department of Mechanical and Mechatronic Engineering, Tecnológico Nacional de México Campus Culiacán, México
Leonardo Palemón: Departamento de Ingeniería Civil, Universidad Autónoma del Carmen, Cd. del Carmen, Campeche 24180, México
Manual A. Barraza: Facultad de Ingeniería, Arquitectura y Diseño, Universidad Autónoma de Baja California, Ensenada 22860, México

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