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CONTENTS
Volume 12, Number 4, August 2023
 

Abstract
This paper deals with delamination analysis of non-linear viscoelastic multilayered beam subjected to bending in the plane of the layers. For this purpose, first, a non-linear viscoelastic model is presented. In order to take into account the non-linear viscoelastic behaviour, a non-linear spring and a non-linear dashpot are assembled in series with a linear spring connected in parallel to a linear dashpot. The behaviours of the non-linear spring and dashpot are described by applying non-linear stress-strain and stress-rate of strain relationships, respectively. The constitutive law of the model is derived. Due to the non-linear spring and dashpot, the constitutive law is non-linear. This law is used for describing the time-dependent mechanical behaviour of the beam under consideration. The material properties involved in the constitutive law vary along the beam length due to the continuous material inhomogeneity of the layers. Solution of the strain energy release rate for the delamination is obtained by analyzing the balance of the energy with considering of the non-linear viscoelastic behaviour. The strain energy release rate is found also by using the complementary strain energy for verification. A parametric study is carried-out by using the solution obtained. The solutions derived and the results obtained help to understand the time-dependent delamination of non-linear viscoelastic beams under loading in the plane of layers.

Key Words
delamination; inhomogeneous material; multilayered beam; non-linear viscoelastic behaviour; stress-strain-time relationship

Address
Victor I. Rizov: Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky Blvd., 1046-Sofia, Bulgaria

Abstract
The building sector has seen a huge increase in the use of lightweight concrete recently, which might result in saving in both cost and time. As a result, the study has been done on various types of concrete, including lightweight (LC), heavyweight (HC), and ordinary concrete (OC), to understand how they react to earthquake loads. The comparisons between their responses have also been taken into account in order to acquire the optimal reaction for various materials in building work. The findings demonstrate that LWC building models are more earthquakeresistant than the other varieties due to the reduction in building weight which can be a curial factor in the resistance of earthquake forces. Another crucial factor that was taken into study is the combination of various types of concrete [HC, LC, and OC] in the structural components. On the other hand, the bending moments and shear forces of LC had reduced to 17% and 19%, respectively, when compared to OC. Otherwise, the bending moment and shear force demand responses in the HC model reach their maximum values by more than 34% compared to the reference model OC. In addition, the results show that the LCC-OCR (light concrete column and ordinary concrete roof) and OCC-LCR (ordinary concrete for the column and light concrete for the roof) models' responses have fewer values than the other types.

Key Words
dense concrete; heavyweight concrete; lightweight concrete; response spectrum analysis; seismic load

Address
Yasser A.S Gamal: Department of Civil Engineering, High Institute of Engineering Technology, EL-MINA, Egypt; Department of Civil Engineering, Faculty of Engineering, NUB University, Egypt
Mostafa Abd Elrazek: Department of Civil Engineering, High Institute of Engineering Technology, EL-MINA, Egypt

Abstract
The Rayleigh wave propagation is considered in the structure of the functionally graded piezoelectric material (FGPM) layer over the elastic substrate. The elastic substrate loosely bonds the layer through a corrugated interface, whereas its upper boundary is also corrugated but stress-free. Additionally, the solutions for the FGPM layer and substrate are derived using the fundamental variable separable approach to convert the partial differential equation to an ordinary differential equation. The results with boundary conditions lead to dispersion relations for the electrically open and electrically short cases in the determinant form. The outcomes have been numerically analyzed using a specific model. The findings were presented in the form of graphs, which were created using Mathematica 7. Graphs are plotted for variations in wavenumber and phase velocity. The outcomes may help measure interface defects and design Surface Acoustic Wave (SAW) devices.

Key Words
corrugation; functionally graded piezoelectric material; imperfect interface; Rayleigh wave

Address
K. Hemalatha, S. Kumar and A. Akshaya: Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur-603203, India

Abstract
Dynamic analysis of a typical concrete gravity dam-reservoir system is formulated by FE-(FE-TE) approach (i.e., Finite Element-(Finite Element-Truncation Element)). In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the H-W (i.e., Hagstrom-Warburton) high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model. The formulation is initially reviewed which was originally proposed in a previous study. Thereafter, the response of Pine Flat dam-reservoir system is studied due to horizontal and vertical ground motions for two types of reservoir bottom conditions of full reflective and absorptive. It should be emphasized that study is carried out under high order of H-W condition applied on the truncation boundary. The initial part of study is focused on the time harmonic analysis. In this part, it is possible to compare the transfer functions against corresponding responses obtained by FE-(FE-HE) approach (referred to as exact method). Subsequently, the transient analysis is carried out. In that part, it is only possible to compare the results for low and high normalized reservoir length cases. Therefore, the sensitivity of results is controlled due to normalized reservoir length values.

Key Words
absorbing boundary conditions; Hagstrom-Warburton condition; high-order condition; Pine Flat dam; truncation boundary

Address
Solmaz Dehghanmarvasty and Vahid Lotfi: Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract
This paper presents a static study of a rectangular functional graded material (FGM) plate, simply supported on its four edges, adopting a refined higher order theory that looks for, only, four unknowns, without taking into account any corrective factor of the deformation energy with the satisfaction of the zero shear stress conditions on the upper and lower faces of the plate. We will have determined the contribution of these stresses in the transverse deflection of the plate, as well as their effects on the axial stress within the interfaces between the layers (to avoid any problem of imperfections such as delamination) and on the top and bottom edges of the plate in order to take into account the fatigue phenomenon when choosing the distribution law of the properties used during the design of the plate. A numerical statement, in percentage, of the contribution of the shear effect is made in order to show the reliability of the adopted theory. We will also have demonstrated the need to add the shear effect when the aspect ratio is small or large. Code routines are programmed to obtain numerical results illustrating the validity of the model proposed in the theory compared to those available in the literature.

Key Words
deflection; FGM; form function; refined higher order theory; shear stress

Address
Ayoub El Amrani, Hafid Mataich, Bouchta El Amrani: Laboratory of Mathematics, Modeling and Applied Physics, High Normal School, Sidi Mohamed Ben Abbellah University, 30040 Fez, Morocco
Jaouad El-Mekkaoui: Laboratory of Technology and Innovations, High School of Technology, Sidi Mohamed Ben Abbellah University, 30040 Fez, Morocco

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