Salim Belouettar

Analysis of FGM Beams by Means of Classical and Advanced Theories

This paper proposes several axiomatic refined theories for the linear static analysis of beams made of materials whose properties are graded along one or two directions. Via a unified formulation, a generic N-order approximation is assumed for the displacement unknown variables over the beam cross-section. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. A Navier type, closed form solution is adopted. Classical beam theories, such as Euler-Bernoullis and Timoshenkos, are obtained as particular cases. Beams that undergo bending and torsional loadings are investigated. Several values of the span-to-height ratio are considered. Slender as well as deep beams are, therefore, investigated. Comparisons with elasticity solutions and three-dimensional finite element models are given. The numerical investigation shows that the proposed unified formulation yields the complete three-dimensional displacement and stress fields as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and the loading conditions.

Thermo-Mechanical Analysis Of Functionally Graded Shells

The thermo-mechanical analysis of a simply supported, functionally graded shell is considered in this work. Refined shell theories are considered to account for grading material variation in the thickness direction. The governing thermodynamical equations are derived from the Principle of Virtual Displacements. The distribution of the temperature field T(z) is not assumed linear in the thickness direction of the layered shells and Fouriers heat conduction equation is solved to provide T(z). Classical and higher order shell theories are implemented in cases of both an equivalent single layer and layer-wise variable description by referring to Carreras Unified Formulation. The numerical results show temperature, displacement and stress distributions along the thickness direction. Different volume fractions of the metallic and ceramic constituents as well as different shell thickness ratios and orders of expansion are analyzed. These are in good agreement with the quasi-3D solution obtained considering mathematical layers with constant properties in the FGM layer and using high orders of expansion.

Analysis of thin-walled beams via a one-dimensional unified formulation through a navier-type solution

A unifying approach to formulate several axiomatic theories for beam structures is addressed in this paper. A N-order polynomials approximation is assumed on the beam cross-section for the displacement unknown variables, N being a free parameter of the formulation. Classical beam theories, such as Euler–Bernoullis and Timoshenkos, are obtained as particular cases. According to the proposed unified formulation, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The linear static analysis of thin-walled beams is carried out through a closed form, Navier-type solution. Simply supported beams are, therefore, presented. Box, C- and I-shaped cross-sections are accounted for. Slender and deep beams are investigated. Bending and torsional loadings are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and the loading conditions.

Hygrothermal effects on the free vibration and buckling of laminated composites with cutouts

Abstract The effect of moisture concentration and the thermal gradient on the free flexural vibration and buckling of laminated composite plates are investigated. The effect of a centrally located cutout on the global response is also studied. The analysis is carried out within the framework of the extended finite element method. A Heaviside function is used to capture the jump in the displacement and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The formulation takes into account the transverse shear deformation and accounts for the lamina material properties at elevated moisture concentrations and temperature. The influence of the plate geometry, the geometry of the cutout, the moisture concentration, the thermal gradient and the boundary conditions on the free flexural vibration is numerically studied.

Evaluation of Kinematic Formulations for Viscoelastically Damped Sandwich Beam Modeling

For efficiently simulating static and dynamic behaviors of sandwich structures, an accurate kinematic model is essential. This study presents analytical and numerical evaluations of kinematics and theories proposed in the literature. Several types of assumed displacement fields are considered. This article compares and addresses the efficiency, the applicability, and the limits of classical models, higher order models (CLT, FSDT, and HSDT), and zig-zag theories. To achieve this, a comparative study with a finite element based solution free of any kinematic assumptions as well as a qualitative and quantitative assessment of displacement, stress fields, and modal parameters (natural frequency and loss factor) are conducted. The results are presented and discussed for several sandwich beam configurations where the faces and the cores are both isotropic. For these purposes, static (three-point bending test) and dynamic (free vibration) problems are considered.

A Thermo-Mechanical Analysis of Isotropic and Composite Beams via Collocation with Radial Basis Functions

In this article, the mechanical behavior of beams subjected to thermal loads is investigated. The temperature field is obtained by exactly solving Fouriers heat conduction equation and it is considered as an external load within the mechanical analysis. Several higher-order beam models as well as Timoshenkos classical theory are derived thanks to a compact notation for the a priori approximation of the displacement field upon the cross-section. The governing differential equations and boundary conditions are obtained in a compact nucleal form that does not depend upon the displacements’ expansion order. The latter can be regarded as a free parameter of the formulation. A meshless strong-form solution based upon collocation with Wendlands radial basis functions is adopted. Isotropic and laminated orthotropic beams are investigated. Results are validated toward an analytical Navier-type solution and three-dimensional FEM results. It is shown that good accuracy can be obtained.

A Shell Finite Element for Active-Passive Vibration Control of Composite Structures with Piezoelectric and Viscoelastic Layers.

This paper presents an accurate shell finite element (FE) formulation to model composite shell structures with embedded viscoelastic and piezoelectric layers and an integrated active damping control mechanism. The five-layered finite element introduced in this paper uses the first order shear deformation theory in the viscoelastic core and Kirchoff theory for the elastic and piezoelectric layers. The corresponding coupled FE formulation is derived starting from the shell kinematic and electromechanical governing equations. Assuming a linear strain field through each layer and exactly the same transverse displacement and the rotations in the elastic and piezoelectric layers, the number of degree of freedoms (dof) per node is reduced to 8. All the eight of these dofs are mechanical in nature. Constant velocity and constant displacement feedback control algorithms are used to actively control the dynamic response of the adaptive structure. Based on this formulation, a finite element code is implemented and the obtained results are compared to those in the literature analytical model and to the numerical results obtained using a commercial finite element code.

Coupling of hierarchical piezoelectric plate finite elements via Arlequin method

Coupling of piezoelectric plate elements based on different through-the-thickness expansions and variational principles through the Arlequin method is proposed in this article. Computational cost is reduced assuming refined models only in those zones of the structure where high accuracy is needed. Piezoelectric finite elements are formulated on the basis of a unified formulation. Higher order, layer-wise and mixed finite elements are easily obtained via unified formulation. This formulation is extended to the Arlequin method in the piezoelectric context to derive matrices related to coupling zones. Two electro-mechanical coupling operators are proposed. Multilayered plates are investigated. Numerical results show that the Arlequin method in the context of unified formulation couples sub-domains having different piezoelectric finite elements effectively.

Diffusion and viscosity of liquid tin: Green-Kubo relationship-based calculations from molecular dynamics simulations

Molecular dynamics (MD) simulations of liquid tin between its melting point and 1600 °C have been performed in order to interpret and discuss the ionic structure. The interactions between ions are described by a new accurate pair potential built within the pseudopotential formalism and the linear response theory. The calculated structure factor that reflects the main information on the local atomic order in liquids is compared to diffraction measurements. Having some confidence in the ability of this pair potential to give a good representation of the atomic structure, we then focused our attention on the investigation of the atomic transport properties through the MD computations of the velocity autocorrelation function and stress autocorrelation function. Using the Green-Kubo formula (for the first time to our knowledge for liquid tin) we determine the macroscopic transport properties from the corresponding microscopic time autocorrelation functions. The selfdiffusion coefficient and the shear viscosity as functions of temperature are found to be in good agreement with the experimental data.

On high-cycle fatigue of 316L stents

This paper deals with fatigue life prediction of 316L stainless steel cardiac stents. Stents are biomedical devices used to reopen narrowed vessels. Fatigue life is dominated by the cyclic loading due to the systolic and diastolic pressure and the design against premature mechanical failure is of extreme importance. Here, a life assessment approach based on the Dang Van high cycle fatigue criterion and on finite element analysis is applied to explore the fatigue reliability of 316L stents subjected to multiaxial fatigue loading. A finite element analysis of the stent vessel subjected to cyclic pressure is performed to carry out fluctuating stresses and strain at some critical elements of the stent where cracks or complete fracture may occur. The obtained results show that the loading path of the analysed stent subjected to a pulsatile load pressure is located in the safe region concerning infinite lifetime.