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CONTENTS
Volume 11, Number 4, October 2021
 


Abstract
Functionally graded materials (FGMs) are designed for specific purpose and applications. Functionally graded materials for bi-layered cylindrical shell was discussed for different boundary conditions. Functionally graded materials (FGMs) are that kind of material in which function and formation may deviate continuously. Cylindrical shells are mainly significant in various fields of science as well as advanced technology of engineering like aerospace engineering, mechanical engineering and civil engineering. Wide applications of cylindrical shell in different fields like aircraft, aerospace and pressure vessels etc. Bi-layered cylindrical shells consist of two layers and in this work, one layer is of FGM material whose constituents are nickel (Ni) and zirconia (Zr) and other is of isotropic material whose constituent is stainless steel. In this work, effect of trigonometric volume fraction law on cantilever FGM bi-layered cylindrical shell with internal pressure has analyzed by using Rayleigh-Ritz technique and Love's shell theory. Present results of FGM bi-layered cylindrical shell are compared with FGM cylindrical shell. Validity of present technique has verified by way of comparisons with current conclusions and those obtained in the past studies.

Key Words
bi-layered; clamped boundary condition; FGMs; Rayleigh-Ritz technique; trigonometric volume fraction law

Address
Madiha Ghamkhar and Muhammad Zafer Iqbal: Department of Mathematics and Statistics, University of Agriculture, Faisalabad,38000, Pakistan

Mohamed A. Khadimallah and Muhammad N. Naeem: Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department, Al-Kharj, 11942, Saudi Arabia

Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

Ahmad Yahya: Nuclear Engineering Department, King Abdulaziz University, Jeddah, Saudi Arabia

Khaled Mohamed Khedher: Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia/ Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia

Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea/ Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia


Abstract
This paper investigates dynamic behavior of porous functionally graded beams under various boundary conditions using State-space approach. The material parameters of FG beams change continuously along the thickness direction according to the power-law function (PFGM) or sigmoid function (SFGM). The porous FG beams are assumed to have even and uneven distributions of porosities over the beam cross-section. The classical beam theory, first-order and higher-order shear deformation theories are employed to consider beams of various boundary conditions. Hamilton's principle are employed for derivation of the equations of motion. Fundamental frequencies are calculated numerically for different boundary conditions, gradient index, volume fraction of porosity, distribution shape of porosity, and span-to-depth ratios. The results show that the variation of the distribution shape of porosity has an effect on the fundamental frequencies.

Key Words
dynamic analysis; FG beams; porosity; state-space approach

Address
Youcef Tlidji: Department of Civil Engineering, University of Tiaret, Algeria

Rabia Benferhat and Hassaine Daouadji Tahar: Department of Civil Engineering, University of Tiaret, Algeria/ Laboratory of Geomatics and Sustainable Development, University of Tiaret, Algeria

Tounsi Abdelouahed: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea/ 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, Civil Engineering Department, Algeria


Abstract
Natural frequency analysis of functionally graded porous joined truncated conical–cylindrical shell reinforced by graphene platelet is investigated in this paper. The structure is consisting of a layered model with five kinds of distribution of graphene platelets in a metallic matrix containing open-cell interior pores. To calculate the effective properties of the porous nanocomposite joined shell, the generalized rule of mixture and the modified Halpin-Tsai equations are employed. Four different porosity distributions are assumed along the shell thickness: two kinds of symmetric functionally graded distributions, non-symmetric functionally graded distributions and uniform distribution of porosity. Graded finite element method (GFEM) based on Rayleigh-Ritz energy formulation has been used to solve 2D- axisymmetric elasticity equations. A parametric study is also conducted to show the effects of different geometric parameters, boundary conditions, weight fraction of graphene platelets, porosity coefficient, distribution of porosity and dispersion pattern of graphene platelets on the natural frequencies and mode shapes of the structure.

Key Words
FG porous; graded finite element method; graphene platelets; joined truncated conical–cylindrical shell; natural frequency analysis

Address
Faraz Kiarasi and Masoud Babaei: Department of Mechanical Engineering, University of Eyvanekey, Eyvanekey, Semnan, Iran

Somayeh Mollaei: Department of Civil Engineering, University of Bonab, Bonab, East Azerbaijan, Iran

Mokhtar Mohammadi: Department of Information Technology, College of Engineering and Computer Science, Lebanese French University, Kurdistan Region, Iraq

Kamran Asemi: Department of Mechanical Engineering, Islamic Azad University, North Tehran Branch, Tehran, Iran

Abstract
This paper is devoted to investigate the nonlinear free vibrations of multi-phase piezoelectric doubly-curved microshells in the context of modified strain gradient elastic (MSGT). The microshell has been made from two constituents for which different compositions have been considered by defining a piezoelectric phase percentage. The microscale effects have been described with the incorporation of three scale coefficients involved in MSGT. With the use of suitable Fourier series and the concept of Galerkin's method, the solution for the governing equations of double-curvature microshell have been provided. The calculated frequencies are dependent on the piezoelectric phase percentage, scale coefficients, curvature radius and applied electric voltage.

Key Words
doubly-curved shell; modified strain gradient theory; multi-phase material; nonlinear vibration; piezoelectric material

Address
Dongxuan Wang: College of science and technology, Hebei Agricultural University, Huanghua 061100, Hebei, China

Yazhou Xing and Su Zhang: College of Mechanical and Electrical Engineering, Hebei Agricultural University, Baoding 071001, Hebei China

Abstract
By using differential quadrature method (DQM), a numerical investigation was provided for nonlinear stability behavior of magneto-electro-elastic (MEE) cylindrical shells at microscale. It is assumed that the cylindrical shell has been subjected to compressive loads leading to buckling phenomena in geometrically nonlinear regime. The non-uniformity of strain field has been inserted in the formulation for considering the microscale effects. The material properties of the shell are considered to be inhomogeneous with graded distribution. After solving the governing equations using DQM, it is realized that if the nanoscale shell is subjected to electrical and magnetic fields, the post-buckling path may be changed with the value of electrical voltage and magnetic potential. Also, strain gradient effects have remarkable influence on post-buckling curves and critical voltages.

Key Words
classic shell theory; magneto-electro-elastic materials; nonlinear stability; smart material; strain gradient theory

Address
By using differential quadrature method (DQM), a numerical investigation was provided for nonlinear stability behavior of magneto-electro-elastic (MEE) cylindrical shells at microscale. It is assumed that the cylindrical shell has been subjected to compressive loads leading to buckling phenomena in geometrically nonlinear regime. The non-uniformity of strain field has been inserted in the formulation for considering the microscale effects. The material properties of the shell are considered to be inhomogeneous with graded distribution. After solving the governing equations using DQM, it is realized that if the nanoscale shell is subjected to electrical and magnetic fields, the post-buckling path may be changed with the value of electrical voltage and magnetic potential. Also, strain gradient effects have remarkable influence on post-buckling curves and critical voltages.

Abstract
This paper explores the size–dependent vibration response of porous functionally graded (FG) micro/nanobeams based on an integrated nonlocal-couple stress continuum model (NLCS). The mutual effect of the microstructure local rotation and nonlocality are modelled using the modified couple stress theory and Eringen nonlocal elasticity theory, respectively, into the classical Euler–Bernoulli beam model. All the material properties of the bulk continuum including the microstructure material length scale parameter (MLSP) are assumed to be graded along the thickness according to a power law. For the first time, the effect of the porosity and voids on the modulus of elasticity and MLSP is taken as a ratio of the mass density with porosity-to-that without porosity. Accounting for the physical neutral axis concept and generalized elasticity theory, Hamilton's principle is utilized to formulate the equations of motion and boundary conditions for the FG porous micro/nanobeams. The analytical solution using Navier method is applied to solve the governing equations and obtain the results. The impact of different parameters such as the gradation index, porosity pattern, porosity parameter, nonlocal parameter, and MLSP on the free vibration characteristics of simply supported FG nanobeams are presented discussed in detail. The current model is efficient in many applications used porous FGM, such as aerospace, nuclear, power plane sheller, and marine structures.

Key Words
analytical solutions; functionally graded structure; modified porosity model; nonlocal–modified couple stress model; size-dependent nanobeams

Address
Emad E. Ghandourah: Nuclear Engineering Dept., Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia

Haitham M. Ahmed: Mining Engineering Dept., Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mohamed A. Eltaher: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia/ Mechanical Design & Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt

Azza M. Abdraboh: Physics Department, Faculty of Science, Banha University, Banha, Egypt


Abstract
Use of additives/supplementary materials in partial substitution of cement is gaining widespread attention across the world due to the sustainability issue with production of cement. With their pozzolanic activity & filler effect, use of nano-pozzolans such as nano-silica has been proved as quite promising & cost-effective for use as supplementary cementitious materials. This study is aimed at highlighting the effect of partial substitution of cement/addition of various nano-pozzolans on the hydration, strength and microstructure of the cementitious materials. Further, the effect of incorporation of other pozzolans has also been discussed. Comparative account of pozzolanic activity of different pozzolans has also been critically analyzed. It has been found that the cement matrix gets improved in terms of its microstructure by partial substitution of cement/addition of pozzolan in appropriate amount resulting in enhancement of the bulk properties by consumption of portlandite. The improved compressive strength of cementitious materials not only results in enhancement of the durability but also the service life of the construction structures and results in reduction of the cost incurred in maintenance and repair. Thus, the cement demand can be decreased by the partial substitution of cement/addition of such materials. It will result in an ultimate reduction of the green-house effect and lead to sustainable development.

Key Words
cementitious materials; durability; nano-pozzolans; microstructure; strength

Address
Rishav Garg: Department of Civil Engineering, Galgotias College of Engineering and Technology, Greater Noida, Uttar Pradesh 201310, India

Rajni Garg: Department of Chemistry, Rayat Bahra University, Mohali, Punjab, 140301, India

Nnabuk Okon Eddy: Department of Pure and Industrial Chemistry, University of Nigeria, Nsukka, Enugu State, 410001, Nigeria

Abstract
Static analysis of microstructures, including bending and buckling, is widely practiced in the fabrication and creation of applications such as actuation, sensing, and energy recovery. This article aims to inquire about the static behavior of non-uniform and imperfect microtubes through a numerical solution. Based on the modified couple stress theory, the first-order shear deformation theory and Von-Karman nonlinear theory, and employing the energy conservation method, the linear and nonlinear governing equations are derived. The porosity-dependent material in both ceramic and metal phases makes the functionally graded materials which are varied along tube length, moreover, cross-sections are also considered uniform and nonuniform via three valuable functions. Finally, the linear and nonlinear equations are solved utilizing the generalized differential quadrature method (GDQM) coupled with the numerical iteration method.

Key Words
axially functionally graded material; buckling; nonlinear effect; non-uniform section; porosity

Address
Xiaohuan Li, Tian Wang and Fang Liu: School of Mechanical Engineering, Tianjin University, Tianjin 300072, Tianjin, China

Zhiwen Zhu: Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin 300072, Tianjin, China


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