Lahcen Azrar

Micromechanical modeling of magnetoelectroelastic composite materials with multicoated inclusions and functionally graded interphases

In this article, micromechanical modeling of magnetoelectroelastic composites with multicoated inclusions and functionally graded interphases are elaborated. The integral equation taking into account the continuously varying interphase properties as well as the multifunctional coating effects is introduced based on Green’s tensors and interfacial operators. Magnetoelectroelastic composites with functionally graded interphases are analyzed, and the effective properties are derived. Based on the Mori–Tanaka, Self-Consistent, and Incremental Self-Consistent models, the numerically predicted effective properties of magnetoelectroelastic composites are presented with respect to the volume fractions, shapes of the multicoated inclusions, and the thickness of the coatings. The multicoating and functionally graded interphase concepts can be used to optimize the effective properties of multifunctional composites. This can be used to design new multifunctional composite materials with higher coupling coefficients.

Time response of structures with uncertain parameters under stochastic inputs based on coupled polynomial chaos expansion and component mode synthesis methods

ABSTRACT This article presents a numerical procedure to compute the stochastic dynamic response of large finite element models with uncertain parameters based on polynomial chaos and component mode synthesis methods. Polynomial chaos expansions at higher orders are used to derive the statistical solution of the dynamic response as well as the Monte Carlo simulation procedure. Based on various component mode synthesis methods, the size of the model is reduced. These methods are coupled with polynomial chaos expansion and the explicit mathematical formulations are given. Numerical results illustrating the accuracy and efficiency of the proposed coupled methodological procedures are presented.

Analytical and numerical modeling of higher order free vibration characteristics of single-walled carbon nanotubes

ABSTRACT In this article, analytical and numerical investigations of small, higher, and asymptotic order vibration eigenmodes and natural eigenfrequencies of single-walled carbon nanotubes (CNT) are elaborated. The nonlocal elasticity theory is used and the numerical simulation is based on the differential quadrature method. Due to numerical instability, the common analytical forms of eigenmodes can be only used for the first 12 modes or so. New mathematical models for higher eigenmodes and associated eigenfrequencies of CNT are developed. The obtained eigenmodes are well conditioned and numerically stable and may be used as modal bases at any required frequency range.

Viscomagnetoelectroelastic effective properties’ modeling for multi-phase and multi-coated magnetoelectroelastic composites

In this article, the effective properties of new active–passive multifunctional viscomagnetoelectroelastic composite materials are modeled and numerically predicted. The correspondence principle, extended to linear viscomagnetoelectroelasticity, and the Carson transform are coupled to the Mori–Tanaka micromechanical mean field approach. Based on the viscomagnetoelectroelastic convolution integral equations and the interfacial operators, the concentration tensors are derived for multi-phase and multi-coated viscomagnetoelectroelastic composites. The effective properties are derived in the frequency domain and then inverted numerically to the time domain using the inverse transform. The effective properties are thus obtained in both frequency and time domains. The obtained hybrid multifunctional coefficients can be used for their active and passive properties. The resulting visco-magneto-electro-elastic effects can be enhanced by a proper choice of the shape and volume fraction of reinforcements as well as by coating thickness.

Analytical and semi-analytical modeling of effective moduli bounds: Application to transversely isotropic piezoelectric materials

In this article, analytical and semi-analytical models of upper and lower bounds for the effective moduli of transversely isotropic piezoelectric heterogeneous materials based on the generalized Hashin–Shtrikman variational principle are presented. Compact matrix formulations are used to derive closed-form bound expressions for coupled and uncoupled effective moduli. Analytical models are given for some uncoupled coefficients and simplified formulations for the others. For more narrow bounds, downstream and upstream bounds are developed based on an incremental procedure. Numerical predictions are performed based on the developed methodological approaches, and the obtained results showed the applicability and effectiveness of the proposed models for transversely isotropic elastic and piezoelectric composite materials with ellipsoidal reinforcements of different types and shapes.

Steady Flow of Couple-Stress Fluid in Constricted Tapered Artery: Effects of Transverse Magnetic Field, Moving Catheter, and Slip Velocity

Steady flow of a couple-stress fluid in constricted tapered artery has been studied under the effects of transverse magnetic field, moving catheter, and slip velocity. With the help of Bessel’s functions, analytic expressions for axial velocity, flow rate, impedance, and wall shear stress have been obtained. It is of interest to note that these solutions can be used for different types of fluid flow in tubes and not only the case of blood. The effects of various geometric parameters, the parameters arising out of the fluid considered and the magnetic field, are discussed by considering the slip velocity, the catheter velocity, and tapering angle. The study of the above model is very important as it has direct applications in the treatment of cardiovascular diseases.

Numerical Procedures for Random Differential Equations

Some methodological approaches based on generalized polynomial chaos for linear differential equations with random parameters following various types of distribution laws are proposed. Mainly, an internal random coefficients method ‘IRCM’ is elaborated for a large number of random parameters. A procedure to build a new polynomial chaos basis and a connection between the one-dimensional and multidimensional polynomials are developed. This allows handling easily random parameters with various laws. A compact matrix formulation is given and the required matrices and scalar products are explicitly presented. For random excitations with an arbitrary number of uncertain variables, the IRCM is couplet to the superposition method leading to successive random differential equations with the same main random operator and right-hand sides depending only on one random parameter. This methodological approach leads to equations with a reduced number of random variables and thus to a large reduction of CPU time and memory required for the numerical solution. The conditional expectation method is also elaborated for reference solutions as well as the Monte-Carlo procedure. The applicability and effectiveness of the developed methods are demonstrated by some numerical examples.

Nonlinear vibrations of large structures with uncertain parameters

The effects of uncertainties on the nonlinear dynamics of complex structures remain poorly mastered and most methods deal with the linear case. This article deals with a model of a large and complex structure with uncertain parameters for the nonlinear dynamic case, and the reduction in the model discretized by the finite element method is obtained by reducing the degrees of freedom in the numerical model. This is achieved by the development of the unknown displacement vector on the basis of the eigenmodes; a particular attention is paid to the calculation of the nonlinear stiffness coefficients of the model. The method combines the stochastic finite element methods with a modal reduction class based on sub-structuring the component mode synthesis method. The reference method is the Monte Carlo simulation which consists in making several simulations for different values of the uncertain parameters. The simulation of complex and nonlinear structures is costly in terms of memory and computation time. To solve this problem, the perturbation method combined with the component mode synthesis reduction method significantly reduces the computational cost by preserving the physical content of the original structure. The numerical integration by the Newmark schema is used; the first statistical moments (mean and variance) of the nonlinear dynamic response are computed. Numerical simulations illustrate the accuracy and effectiveness of the proposed methodology.