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CONTENTS
Volume 16, Number 3, March 2024
 

Abstract
This paper presents results of visual analysis of cracks formation and propagation of concretes made of quaternary binders (QBC). A composition of the two most commonly used mineral additives, i.e. fly ash (FA) and silica fume (SF) in combination with nanosilica (nS), has been proposed as a partial replacement of the cement. The principal objective of the present study is to achieve information about the effect of simultaneous incorporation of three pozzolans as partial replacement to the OPC on the fracture processes in concretes made from quaternary binders (QBC). The modern and precise non-contact measurement method (NCMM) via digital image correlation (DIC) technique was used, during the studies. In the course of experiments it was established that the substitution of OPC with three pozzolans including the nanoadditive in FA+SF+nS combination causes a clear change of brittleness and behavior during fractures in QBCs. It was found that the shape of cracks in unmodified concrete was quasi-linear. Substitution of the binder by SCMs resulted in a slight heterogeneity of the structure of the QBC, including only SF and nS, and clear heterogeneity for concretes with the FA additive. In addition, as content of FA rises throughout each of QBC series, material becomes more ductile and shows less brittle failure. It means that an increase in the FA content in the concrete mix causes a significant change in fracture process in this composite in comparison to concrete with the addition of silica modifiers only.

Key Words
cracking; fly ash (FA); nanosilica (nS); non-contact measurement method (NCMM); ordinary Portland cement (OPC); quaternary binder concrete (QBC); silica fume (SF); visual analysis

Address
Grzegorz Ludwik Golewski: Department of Structural Engineering, Faculty of Civil Engineering and Architecture, Lublin University of Technology,Nadbystrzycka 40 str., 20-618, Lublin, Poland


Abstract
When the amplitude of the vibrations is equivalent to that clearance, the vibrations for small amplitudes will really be significantly nonlinear. Nonlinearities will not be significant for amplitudes that are rather modest. Finally, nonlinearities will become crucial once again for big amplitudes. Therefore, the concrete panel system may experience a big amplitude in this work as a result of the high temperature. Based on the 3D modeling of the shell theory, the current work shows the influences of the von Kármán strain-displacement kinematic nonlinearity on the constitutive laws of the structure. The system's governing Equations in the nonlinear form are solved using Kronecker and Hadamard products, the discretization of Equations on the space domain, and Duffing-type Equations. Thermo-elasticity Equations. are used to represent the system's temperature. The harmonic solution technique for the displacement domain and the multiple-scale approach for the time domain are both covered in the section on solution procedures for solving nonlinear Equations. An effective data-driven solution is often utilized to predict how different systems would behave. The number of hidden layers and the learning rate are two hyperparameters for the network that are often chosen manually when required. Additionally, the data-driven method is offered for addressing the nonlinear vibration issue in order to reduce the computing cost of the current study. The conclusions of the present study may be validated by contrasting them with those of data-driven solutions and other published articles. The findings show that certain physical and geometrical characteristics have a significant effect on the existing concrete panel structure's susceptibility to temperature change and GPL weight fraction. For building construction industries, several useful recommendations for improving the thermo-mechanics' behavior of structural concrete panels are presented.

Key Words
efficient data-driven solution; nanocomposites; nonlinearities; thermo-elasticity; 3D-shell

Address
Hengbin Zheng: College of Water Conservancy and Civil Engineering, South China Agricultural University, Guangzhou, Guangdong, 510642, China

Wenjun Dai: Shenzhen Urban Transport Planning Center Co., Ltd, Shenzhen 518000, China

Zeyu Wang: School of Engineering and Technology, China University of Geosciences, Beijing, 100083, China

Adham E. Ragab: Industrial Engineering Department, College of Engineering, King Saud University, PO Box 800, Riyadh 11421, Saudi Arabia

Abstract
This article investigates the free vibration behavior of carbon nanotube reinforced composite (CNTRC) beams embedded using variational analytical methods and artificial neural networks (ANN). The material properties of layered functionally graded CNTRC (FG-CNTRC) beams are estimated using nonlocal parameters modified power-law with different types of CNT distributions through the thickness direction of the beam. Adopting Eringen's nonlocal elasticity theory to capture the small size effects, the nonlocal governing equations are derived and solved using the analytical method. And also, the problem was analyzed using the ANN method. The architecture of the proposed ANN model is 3-9-1. In the experiments, we used 112 different data to predict the natural frequency using ANN. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the beam are derived using Hamilton's principle. The classical beam theory is used to formulate a governing equation for predicting the free vibration of laminated CNTRC beams. According to the experimental results, the prediction ability of the ANN model is very good and the natural frequency can be predicted in ANN without attempting any experiments.

Key Words
artificial neural networks; carbon nanotube; composite beam; free vibration; nonlocal elasticity theory

Address
Emrah Madenci: Department of Civil Engineering, Necmettin Erbakan University, 42090 Konya, Türkiye

Şaban Gülcü: Department of Computer Engineering, Necmettin Erbakan University, 42090 Konya, Türkiye

Kada Draiche: Department of Civil Engineering, University of Tiaret, B.P. 78 Zaaroura, 14000 Tiaret, Algeria/ Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria


Abstract
In this paper, the problem of static bending of axially functionally graded (AFG) nanobeam is formulated with the local stress(Lσ)- and strain-driven(εD) two-phase local/nonlocal integral models (TPNIMs). The novelty of the present study aims to compare the size-effects of nonlocal integral models on bending deflections of AFG Euler–Bernoulli nano-beams. The integral relation between strain and nonlocal stress components based on two types nonlocal integral models is transformed unitedly and equivalently into differential form with constitutive boundary conditions. Purely LσD- and εD-NIMs would lead to ill-posed mathematical formulation, and Purely εD- and LσD-nonlocal differential models (NDM) may result in inconsistent size-dependent bending responses. The general differential quadrature method is applied to obtain the numerical results for bending deflection and moment of AFG nanobeam subjected to different boundary and loading conditions. The influence of AFG index, nonlocal models, and nonlocal parameters on the bending deflections of AFG Euler–Bernoulli nanobeams is investigated numerically. A consistent softening effects can be obtained for both LσD- and εD-TPNIMs. The results from current work may provide useful guidelines for designing and optimizing AFG Euler-Bernoulli beam based nano instruments.

Key Words
size-effect; axially functionally graded nanobeam; nonlocal integral model; general differential quadrature method

Address
Yuan Tang and Hai Qing: State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China


Abstract
The geometrical nonlinear vibrations of the gold nanoscale rod are investigated for the first time by considering the internal modals interactions using different nonlinear beam theories. This phenomenon is usually one of the important features of nonlinear vibration systems. For a more detailed analysis, the von-Kármán effects, preserving all the nonlinear terms in the strain-displacement relationships of gold nanoscale rods in three displacement directions, are considered to analyze the nonlinear axial vibrations of gold nanoscale rods. It uses highly accurate analytical-numerical solutions for the clamped-clamped and clamped-free boundary conditions of nanoscale gold rods. Also, with the help of Hamilton's principle, the governing equation and boundary conditions are derived based on Eringen's theory. The influence of nonlinear and nonlocal factors on axial vibrations was investigated separately for all three theories: Simple (ST), Rayleigh (RT) and Bishop (BT). Using different theories, the effects of inertia and shear on the internal resonances of gold nanorods were studied and compared in terms of two-to-one and three-to-one internal resonances. As the nonlocal parameter of the gold nanorod increases, the maximum nonlinear amplitude occurs. So, by adding nonlocal effects in a gold nanorod, the internal modal interactions resulting from the unique structure can be enhanced. It is worth noting that shear and inertial analysis have a significant effect on internal modal interactions in gold nanorods.

Key Words
gold nanoscale rod; internal modals interactions; nonlinear axial vibrations; nonlocal theory

Address
Somaye Jamali Shakhlavi: School of Engineering, Damghan University, Damghan, Iran/ School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

Reza Nazemnezhad: School of Engineering, Damghan University, Damghan, Iran

Abstract
In this work, an analytical model employing a new higher-order shear deformation beam theory is utilized to investigate the bending behavior of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams. A modified continuum nonlocal strain gradient theory is employed to incorporate both microstructural effects and geometric nano-scale length scales. The extended rule of mixture, along with molecular dynamics simulations, is used to assess the equivalent mechanical properties of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. Carbon nanotube reinforcements are randomly distributed axially along the length of the beam. The equilibrium equations, accompanied by nonclassical boundary conditions, are formulated, and Navier's procedure is used to solve the resulting differential equation, yielding the response of the nanobeam under various mechanical loadings, including uniform, linear, and sinusoidal loads. Numerical analysis is conducted to examine the influence of inhomogeneity parameters, geometric parameters, types of loading, as well as nonlocal and length scale parameters on the deflections and stresses of axially functionally graded carbon nanotubes reinforced composite (AFG CNTRC) nanobeams. The results indicate that, in contrast to the nonlocal parameter, the beam stiffness is increased by both the CNTs volume fraction and the length-scale parameter. The presented model is applicable for designing and analyzing microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) constructed from carbon nanotubes reinforced composite nanobeams.

Key Words
axially CNTs distribution; Navier's solution; nonlocal strain gradient higher order shear deformation theory; static bending and stress analyses

Address
Ahmed Amine Daikh: Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, University Centre of Naama, Naama, Algeria/ 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 Drai: Department of Mechanical Engineering, Mustapha STAMBOULI University of Mascara, 29000, Algeria/ LABAB Laboratory of ENPO, Oran, 31000, Algeria

Mohamed Ouejdi Belarbi: Laboratoire de Génie Energétique et Matériaux, LGEM, Université de Biskra, B.P. 145, R.P. 07000, Biskra, Algeria/ Department of Civil Engineering, Lebanese American University, Byblos, Lebanon

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

Benoumer Aour: LABAB Laboratory of ENPO, Oran, 31000, Algeria

Mohamed A. Eltaher: Faculty of Engineering, Mechanical Engineering Department, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia/ Faculty of Engineering, Mechanical Design and Production Department, Zagazig University, Zagazig, Egypt

Norhan A. Mohamed: Engineering Mathematics Department, Faculty of Engineering, Zagazig University, Zagazig Egypt

Abstract
This paper conducts a thorough economic evaluation of integrating nanoparticles into concrete structures within the construction industry, aiming to elevate the material properties of concrete. Employing the Halpin-Tsai micromechanics theory for deriving the effective material properties of the nanocomposite concrete structure, the research investigates the nuanced impact of nanoparticles on various mechanical properties, including the modulus of elasticity, compressive strength, and their indirect effects on the percentage of reinforcement. Implementing the Euler theory to formulate the governing equation based on Hamilton's principle, the study delves into the pricing dynamics of nanoparticles and their influence on the overall cost structure of concrete structures. Notably, the findings reveal that a measured increase in the volume percentage of nanoparticles, up to 1%, results in a remarkable 78% improvement in elastic modulus and a substantial 142% reduction in armature percentage. Remarkably, from an economic perspective, the incremental cost associated with the integration of nanoparticles is relatively modest (around $1 per ton of concrete), considering the substantial enhancements in mechanical properties achieved.

Key Words
concrete; dynamics; economic study; nanoparticles

Address
Taoqian Xie: School of Public Administration, Central China Normal University, Wuhan 430000, Hubei, China

Wei Han: Wanpu (Wuhan) Institute of Education, Wuhan 430000, Hubei, China

Haoqi Chang: College of Cities and environmental sciences, Central China Normal University, Wuhan 430000, Hubei, China/ Warner College of Natural Resources, Colorado State University, Fort Collins, CO 80523, USA

M.R. Motaghedfer: College of Engineering, Azad University, Iran

Abstract
The main aims of this study are to develop a new nonlocal quasi-3D theory for the free vibration behaviors of the functionally graded sandwich nanobeams. The sandwich beams consist of a ceramic core and two functionally graded material layers resting on elastic foundations. The two layers, linear spring stiffness and shear layer, are used to model the effects of the elastic foundations. The size-effect is considered using nonlocal elasticity theory. The governing equations of the motion of the functionally graded sandwich nanobeams are obtained via Hamilton's principle in combination with nonlocal elasticity theory. Then the Navier's solution technique is used to solve the governing equations of the motion to achieve the nonlocal free vibration behaviors of the nanobeams. A deep parametric study is also provided to demonstrate the effects of some parameters, such as length-to-height ratio, power-law index, nonlocal parameter, and two parameters of the elastic foundation, on the free vibration behaviors of the functionally graded sandwich nanobeams.

Key Words
functionally graded; nanobeams; nonlocal theory; quasi-3D theory; sandwich beam

Address
Mofareh Hassan Ghazwani and Ali Alnujaie: Mechanical Engineering Department, Faculty of Engineering, Jazan University, P. O. Box 45142, Jazan, Kingdom of Saudi Arabia

Pham Van Vinh:2Department of Solid Mechanics, Le Quy Don Technical University, Hoang Quoc Viet, Ha Noi, Viet Nam

Abdelouahed Tounsi: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia/ Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria/ Department of Civil and Environmental Engineering, Lebanese American University, 309 Bassil Building, Byblos, Lebanon


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