A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation

Abdelouahed Tounsi,S.U. Al-Dulaijan,Mohammed A. Al-Osta,Abdelbaki Chikh,M.M. Al-Zahrani,Alfarabi Sharif,Abdeldjebbar Tounsi 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.34 No.4

In this research, a simple four-variable trigonometric integral shear deformation model is proposed for the static behavior of advanced functionally graded (AFG) ceramic-metal plates supported by a two-parameter elastic foundation and subjected to a nonlinear hygro-thermo-mechanical load. The elastic properties, including both the thermal expansion and moisture coefficients of the plate, are also supposed to be varied within thickness direction by following a power law distribution in terms of volume fractions of the components of the material. The interest of the current theory is seen in its kinematics that use only four independent unknowns, while first-order plate theory and other higher-order plate theories require at least five unknowns. The "in-plane displacement field" of the proposed theory utilizes cosine functions in terms of thickness coordinates to calculate out-of-plane shear deformations. The vertical displacement includes flexural and shear components. The elastic foundation is introduced in mathematical modeling as a two-parameter Winkler-Pasternak foundation. The virtual displacement principle is applied to obtain the basic equations and a Navier solution technique is used to determine an analytical solution. The numerical results predicted by the proposed formulation are compared with results already published in the literature to demonstrate the accuracy and efficiency of the proposed theory. The influences of "moisture concentration", temperature, stiffness of foundation, shear deformation, geometric ratios and volume fraction variation on the mechanical behavior of AFG plates are examined and discussed in detail.

Impact of viscoelastic foundation on bending behavior of FG plate subjected to hygro-thermo-mechanical loads

Ismail M. Mudhaffar,Abdelbaki Chikh,Abdelouahed Tounsi,Mohammed A. Al-Osta,Mesfer M. Al-Zahrani,Salah U. Al-Dulaijan 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.86 No.2

This work applies a four-known quasi-3D shear deformation theory to investigate the bending behavior of a functionally graded plate resting on a viscoelastic foundation and subjected to hygro-thermo-mechanical loading. The theory utilizes a hyperbolic shape function to predict the transverse shear stress, and the transverse stretching effect of the plate is considered. The principle of virtual displacement is applied to obtain the governing differential equations, and the Navier method, which comprises an exponential term, is used to obtain the solution. Novel to the current study, the impact of the viscoelastic foundation model, which includes a time-dependent viscosity parameter in addition to Winkler’s and Pasternak parameters, is carefully investigated. Numerical examples are presented to validate the theory. A parametric study is conducted to study the effect of the damping coefficient, the linear and nonlinear loadings, the power-law index, and the plate width-tothickness ratio on the plate bending response. The results show that the presence of the viscoelastic foundation causes an 18% decrease in the plate deflection and about a 10% increase in transverse shear stresses under both linear and nonlinear loading conditions. Additionally, nonlinear loading causes a one-and-a-half times increase in horizontal stresses and a nearly two-times increase in normal transverse stresses compared to linear loading. Based on the article’s findings, it can be concluded that the viscosity effect plays a significant role in the bending response of plates in hygrothermal environments. Hence it shall be considered in the design.

Buckling analysis of functionally graded hybrid composite plates using a new four variable refined plate theory

A. Fekrar,A. Tounsi,N. El Meiche,A. Bessaim,E. A. Adda Bedia 국제구조공학회 2012 Steel and Composite Structures, An International J Vol.13 No.1

In this research, mechanical buckling of hybrid functionally graded plates is considered using a new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. The effectiveness of the theories is brought out through illustrative examples.

A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis

Miloud Kaddari,Abdelhakim Kaci,Abdelmoumen Anis Bousahla,Abdelouahed Tounsi,Fouad Bourada,AbdeldjebbarTounsi,E.A. Adda Bedia,Mohammed A. Al-Osta 사단법인 한국계산역학회 2020 Computers and Concrete, An International Journal Vol.25 No.1

This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.

Structural performance of submerged ring support FG shell using numerical ananlysis

Mohamed A. Khadimallah,Muzamal Hussain,Ahmad Yahya,Khaled Mohamed Khedher,Faisal Al-Thobiani,Shauket Ali Tahir,Abdelouahed Tounsi 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.80 No.3

In this study, the cylindrical shell submerged in a fluid and surrounded by ring supports. The use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel’s functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. Shell motion equations are framed first order shell theory due to Love. These equations are partial differential equations which are usually solved by approximate technique. The transverse constraints produced ring supports are assumed by the polynomial functions possessing degree equal to the number of ring supports. The frequencies with ring supports against wave number, length-to-radius ratio and height-to-radius ratio are investigated. The frequency analysis versus wave number for simply supported cylindrical shells submerged in a fluid with ring supports is given for different types of configuration. The variations of frequencies against the positions of the ring supports are furnished for not submerged and submerged cylindrical shells. It is observed that vibration frequencies increase and decreases as the positions of a ring support is increased. Programming is written in MATLAB codes to solve the frequency equation for the computation of frequencies of shells submerged in a fluid along with ring supports. The frequency result of submerged cylindrical shell is less than with the results of not submerged cylindrical shell. Robust and efficient technique produced the valid results.

Free vibration investigation of functionally graded plates with temperaturedependent properties resting on a viscoelastic foundation

Abdeldjebbar Tounsi,Adda Hadj Mostefa,Amina Attia,Abdelmoumen Anis Bousahla,Fouad Bourada,Abdelouahed Tounsi,Mohammed A. Al-Osta 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.86 No.1

The free vibration of temperature-dependent functionally graded plates (FGPs) resting on a viscoelastic foundation is investigated in this paper using a newly developed simple first-order shear deformation theory (FSDT). Unlike other first order shear deformation (FSDT) theories, the proposed model contains only four variables’ unknowns in which the transverse shear stress and strain follow a parabolic distribution along the plates’ thickness, and they vanish at the top and bottom surfaces of the plate by considering a new shape function. For this reason, the present theory requires no shear correction factor. Linear steadystate thermal loads and power-law material properties are supposed to be graded across the plate’s thickness. Uniform, linear, non-linear, and sinusoidal thermal rises are applied at the two surfaces for simply supported FGP. Hamilton’s principle and Navier’s approach are utilized to develop motion equations and analytical solutions. The developed theory shows progress in predicting the frequencies of temperature-dependent FGP. Numerical research is conducted to explain the effect of the power law index, temperature fields, and damping coefficient on the dynamic behavior of temperature-dependent FGPs. It can be concluded that the equation and transformation of the proposed model are as simple as the FSDT.

Large deformation analysis for functionally graded carbon nanotube-reinforced composite plates using an efficient and simple refined theory

K. Bakhti,A. Tounsi,A. Kaci,A.A. Bousahla,M.S.A. Houari,E. A. Adda Bedia 국제구조공학회 2013 Steel and Composite Structures, An International J Vol.14 No.4

In this paper, the nonlinear cylindrical bending behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) is studied using an efficient and simple refined theory. This theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The fundamental equations for functionally graded nanocomposite plates are obtained using the Von-Karman theory for large deflections and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtainedas comparators.

Mechanical behaviour analysis of FGM plates on elastic foundation using a new exponential-trigonometric HSDT

Fatima Z. Zaoui,Djamel Ouinas,Abdelouahed Tounsi,Belkacem Achour,Jaime A. Viña Olay,Tayyab A. Butt 국제구조공학회 2023 Steel and Composite Structures, An International J Vol.47 No.5

In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori– Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.

Shear correction factors of a new exponential functionally graded porous beams

Mohammed Sid Ahmed Houari,Aicha Bessaim,Tarek Merzouki,Ahmed Amine Daikh,Aman Garg,Abdelouahed Tounsi,Mohamed A. Eltaher,Mohamed-Ouejdi Belarbi 국제구조공학회 2024 Structural Engineering and Mechanics, An Int'l Jou Vol.89 No.1

This article introduces a novel analytical model for examining the impact of porosity on shear correction factors (SCFs) in functionally graded porous beams (FGPB). The study employs uneven and logarithmic-uneven modified porositydependent power-law functions, which are distributed throughout the thickness of the FGP beams. Additionally, a modified exponential-power law function is used to estimate the effective mechanical properties of functionally graded porous beams. The correction factor plays a crucial role in this analysis as it appears as a coefficient in the expression for the transverse shear stress resultant. It compensates for the assumption that the shear strain is uniform across the depth of the cross-section. By applying the energy equivalence principle, a general expression for static SCFs in FGPBs is derived. The resulting expression aligns with the findings obtained from Reissner’s analysis, particularly when transitioning from the two-dimensional case (plate) to the onedimensional case (beam). The article presents a convenient algebraic form of the solution and provides new case studies to demonstrate the practicality of the proposed formulation. Numerical results are also presented to illustrate the influence of porosity distribution on SCFs for different types of FGPBs. Furthermore, the article validates the numerical consistency of the mechanical property changes in FG beams without porosity and the SCF by comparing them with available results.

The nano scale buckling properties of isolated protein microtubules based on modified strain gradient theory and a new single variable trigonometric beam theory

Alwabli, Afaf S.,Kaci, Abdelhakim,Bellifa, Hichem,Bousahla, Abdelmoumen Anis,Tounsi, Abdelouahed,Alzahrani, Dhafer A.,Abulfaraj, Aala A.,Bourada, Fouad,Benrahou, Kouider Halim,Tounsi, Abdeldjebbar,Mah Techno-Press 2021 Advances in nano research Vol.10 No.1

Microtubules (MTs) are the main part of the cytoskeleton in living eukaryotic cells. In this article, a mechanical model of MT buckling, considering the modified strain gradient theory, is analytically examined. The MT is assumed as a cylindrical beam and a new single variable trigonometric beam theory is developed in conjunction with a modified strain gradient model. The main benefit of the present formulation is shown in its new kinematic where we found only one unknown as the Euler-Bernoulli beam model, which is even less than the Timoshenko beam model. The governing equations are deduced by considering virtual work principle. The effectiveness of the present method is checked by comparing the obtained results with those reported by other higher shear deformation beam theory involving a higher number of unknowns. It is shown that microstructure-dependent response is more important when material length scale parameters are closer to the outer diameter of MTs. Also, it can be confirmed that influences of shear deformation become more considerable for smaller shear modulus and aspect ratios.