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.

A mechanical approach for mosquito fascicle under the influence of mechanical forces with medical applications

Naser Alkenani,S.R. Mahmoud,Ahmed M. Metwally,Afaf S. Alwabli,Habeeb M. Al-Solami 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.79 No.6

In the present paper, an analysis of elastic stability for mosquito fascicle with the elastic foundation is investigated by the variational iteration method. A mathematical model is established for the mosquito fascicle for the associated clamped and free boundary conditions. Results attained expert the stability condition of mosquito fascicle for given parameters. Design guidelines for the dynamically stable microneedle are developed and critically debated. A uniform homogeneous mosquito fascicle is considered to be restrained by labium along its length. The restraint considered in this work is an elastic foundation model by labium, and it is of great interest to bioengineering and foundation engineers. An analytical solution is not a simple procedure since the equations are highly nonlinear. This study presents the application of the variational iteration method for obtaining exact solutions for continuously restrained mosquito fascicle. The research proves that the variational iteration method is a very efficient and promising approach to understand the probing behavior of mosquitoes and the process of penetration.

Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory

Kada Draiche,Abdelmoumen Anis Bousahla,Abdelouahed Tounsi,Afaf S. Alwabli,Abdeldjebbar Tounsi,S.R. Mahmoud 사단법인 한국계산역학회 2019 Computers and Concrete, An International Journal Vol.24 No.4

This paper aims to present an analytical model to predict the static analysis of laminated reinforced composite plates subjected to sinusoidal and uniform loads by using a simple first-order shear deformation theory (SFSDT). The most important aspect of the present theory is that unlike the conventional FSDT, the proposed model contains only four unknown variables. This is due to the fact that the inplane displacement field is selected according to an undetermined integral component in order to reduce the number of unknowns. The governing differential equations are derived by employing the static version of principle of virtual work and solved by applying Navier’s solution procedure. The non-dimensional displacements and stresses of simply supported antisymmetric cross-ply and angle-ply laminated plates are presented and compared with the exact 3D solutions and those computed using other plate theories to demonstrate the accuracy and efficiency of the present theory. It is found from these comparisons that the numerical results provided by the present model are in close agreement with those obtained by using the conventional FSDT.

A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations

Amina Attia,Abdelmoumen Anis Bousahla,Abdelouahed Tounsi,S. R. Mahmoud,Afaf S. Alwabli 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.4

In this paper, an efficient higher-order shear deformation theory is presented to analyze thermomechanical bending of temperature-dependent functionally graded (FG) plates resting on an elastic foundation. Further simplifying supposition are made to the conventional HSDT so that the number of unknowns is reduced, significantly facilitating engineering analysis. These theory account for hyperbolic distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Nonlinear thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from the principle of virtual displacements. Analytical solutions for the thermomechanical bending analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier’s method). Non-dimensional results are compared for temperature-dependent FG plates and validated with those of other shear deformation theories. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature field on the thermomechanical bending characteristics. It can be concluded that the present theory is not only accurate but also simple in predicting the thermomechanical bending responses of temperature-dependent FG plates.

A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations

Attia, Amina,Bousahla, Abdelmoumen Anis,Tounsi, Abdelouahed,Mahmoud, S.R.,Alwabli, Afaf S. Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.4

In this paper, an efficient higher-order shear deformation theory is presented to analyze thermomechanical bending of temperature-dependent functionally graded (FG) plates resting on an elastic foundation. Further simplifying supposition are made to the conventional HSDT so that the number of unknowns is reduced, significantly facilitating engineering analysis. These theory account for hyperbolic distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Nonlinear thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from the principle of virtual displacements. Analytical solutions for the thermomechanical bending analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent FG plates and validated with those of other shear deformation theories. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature field on the thermomechanical bending characteristics. It can be concluded that the present theory is not only accurate but also simple in predicting the thermomechanical bending responses of temperature-dependent FG plates.

The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory

Benmansour, Djazia Leila,Kaci, Abdelhakim,Bousahla, Abdelmoumen Anis,Heireche, Houari,Tounsi, Abdelouahed,Alwabli, Afaf S.,Alhebshi, Alawiah M.,Al-ghmady, Khalid,Mahmoud, S.R. Techno-Press 2019 Advances in nano research Vol.7 No.6

In this investigation, dynamic and bending behaviors of isolated protein microtubules are analyzed. Microtubules (MTs) can be considered as bio-composite structures that are elements of the cytoskeleton in eukaryotic cells and posses considerable roles in cellular activities. They have higher mechanical characteristics such as superior flexibility and stiffness. In the modeling purpose of microtubules according to a hollow beam element, a novel single variable sinusoidal beam model is proposed with the conjunction of modified strain gradient theory. The advantage of this model is found in its new displacement field involving only one unknown as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. The equations of motion are constructed by considering Hamilton's principle. The obtained results are validated by comparing them with those given based on higher shear deformation beam theory containing a higher number of variables. A parametric investigation is established to examine the impacts of shear deformation, length scale coefficient, aspect ratio and shear modulus ratio on dynamic and bending behaviors of microtubules. It is remarked that when length scale coefficients are almost identical of the outer diameter of MTs, microstructure-dependent behavior becomes more important.

Discrimination and bifurcation analysis of tumor immune interaction in fractional form

Taj, Muhammad,Khadimallah, Mohamed A.,Hussain, Muzamal,Rashid, Yahya,Ishaque, Waqas,Mahmoud, S.R.,Din, Qamar,Alwabli, Afaf S.,Tounsi, Abdelouahed Techno-Press 2021 Advances in nano research Vol.10 No.4

A tumor immune interaction is a main topic of interest in the last couple of decades because majority of human population suffered by tumor, formed by the abnormal growth of cells and is continuously interacted with the immune system. Because of its wide range of applications, many researchers have modeled this tumor immune interaction in the form of ordinary, delay and fractional order differential equations as the majority of biological models have a long range temporal memory. So in the present work, tumor immune interaction in fractional form provides an excellent tool for the description of memory and hereditary properties of inter and intra cells. So the interaction between effector-cells, tumor cells and interleukin-2 (IL-2) are modeled by using the definition of Caputo fractional order derivative that provides the system with long-time memory and gives extra degree of freedom. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Furthermore, existence and local stability of fixed points are investigated for discrete model. Moreover, it is proved that two types of bifurcations such as Neimark-Sacker and flip bifurcations are studied. Finally, numerical examples are presented to support our analytical results.

Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory

Sadoun, Mohamed,Houari, Mohammed Sid Ahmed,Bakora, Ahmed,Tounsi, Abdelouahed,Mahmoud, S.R.,Alwabli, Afaf S. Techno-Press 2018 Geomechanics & engineering Vol.16 No.2

In this current work a quasi 3D "trigonometric shear deformation theory" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical "higher order shear deformation theories" (HSDT) and the "first shear deformation theory" (FSDT), the constructed theory utilizes a new displacement field which includes "undetermined integral terms" and presents only three "variables". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse "normal deformation". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of "flexural mode", mode of shear and mode of thickness stretch impact of dynamic of simply supported "orthotropic" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.

An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions

Hadj Henni Abdelaziz,Mohamed Ait Amar Meziane,Abdelmoumen Anis Bousahla,Abdelouahed Tounsi,S.R. Mahmoud,Afaf S. Alwabli 국제구조공학회 2017 Steel and Composite Structures, An International J Vol.25 No.6

In this research, a simple hyperbolic shear deformation theory is developed and applied for the bending, vibration and buckling of powerly graded material (PGM) sandwich plate with various boundary conditions. The displacement field of the present model is selected based on a hyperbolic variation in the in-plane displacements across the plate‟s thickness. By splitting the deflection into the bending and shear parts, the number of unknowns and equations of motion of the present formulation is reduced and hence makes them simple to use. Equations of motion are obtained from Hamilton‟s principle. Numerical results for the natural frequencies, deflections and critical buckling loads of several types of powerly graded sandwich plates under various boundary conditions are presented. The accuracy of the present formulation is demonstrated by comparing the computed results with those available in the literature. As conclusion, this theory is as accurate as other theories available in the literature and so it becomes more attractive due to smaller number of unknowns.