Abdelmalek Zine

Wave Finite Element Method Based on Reduced Model for One-Dimensional Periodic Structures

In this paper, an efficient numerical approach is proposed to study free and forced vibration of complex one-dimensional (1D) periodic structures. The proposed method combines the advantages of component mode synthesis (CMS) and wave finite element method. It exploits the periodicity of the structure since only one unit cell is modelled. The model reduction based on CMS improves the computational efficiency of unit cell dynamics, avoiding ill-conditioning issues. The selection of reduced modal basis can reveal the influence of local dynamics on global behavior. The effectiveness of the proposed approach is illustrated via numerical examples.

Computation of the filtration laws through porous media for a non-Newtonian fluid obeying the power law

We consider a stationary flow of an incompressible non-Newtonian flow through a porous medium, induced by an injection velocity when inertial effects are negligible. At the pore scale, the governing equations are based on a nonlinear relation between the stress and the rate of deformation. In such a situation, the limit problem obtained when the pore size tends to zero, is called the homogenized problem that leads to the filtration law. This filtration law is given by a non-linear system coupling a local problem on a typical cell of the porous medium to a global problem at the scale of the whole porous medium. We propose, in this work, a numerical method to solve this homogenized problem and apply this method when the velocity dependent viscosity is given by the power law. Finally, we propose some numerical experiments to illustrate our approach.

Decoupled approach for the problem of viscoelastic fluid flow of PTT model I: continuous stresses

We present in this work a numerical analysis of a decoupled approach with continuous stresses for the viscoelastic fluid flows obeying the PTT model. The Streamline Upwind Petrov–Galerkin is used to treat the transport part of the equations. This model introduces supplementary difficulties linked to the non-linearities of the exponential type present in the constitutive equation. In exchange, it seems to be more realistic and gives best numerical results. The method is tested on the classical benchmark problem: Stick–Slip flow. Numerical results show that our method is remarkably stable and no upper Weissenberg limit number was encountered for reasonable values of ϵ, a material-depending parameter.

Multi-Scale Homogenization of Transversal Waves in Periodic Composite Beams

This paper deals with the deduction of new homogenized models for the flexural wave in bi-periodic beams. According to the homogenization theory, the long-wave assumption is used and the valid frequency range of homogenized models is limited to the first Bragg band gap. However, the classical homogenization method, whose idea is taking the component’s mean values as effective material properties, has limitations in mimicking the dispersive behavior and the real valid frequency range is far less than the limit. Thus, enriched homogenized models, derived by the multi-scale asymptotic homogenization method, are proposed to provide more accurate homogenization models with larger real valid frequency range. The new homogenized models are validated by investigating the dispersion relation in the infinite case and the frequency response function in the finite case. Wave finite element method (WFEM) are used to provide associated references. A parametric study is carried out in the infinite case while two different boundary conditions are considered in the finite case.

A mixed finite element method for a Ladyzhenskaya model

We study a mixed finite element approximation of a model proposed by Ladyzhenskaya for stationary incompressible viscous flow. We give existence and uniqueness results for the continuous problem and its approximation and we prove error bounds which improve the existing ones. Finally, some numerical results are presented.

Wave Finite Element Formulation of the Acoustic Transmission Through Complex Infinite Plates

A finite element-based derivation of the transmission loss (TL) of anisotropic layered infinite plates is presented in this paper. The wave-finite element method (WFE) is used to represent the plate with a finite element model of a single unit cell. The incident acoustic field is a known plane wave, and the reflected and transmitted pressures are supposed to be plane waves with unknown amplitudes and phases. The periodicity conditions on the unit cell allow to find a simple matrix equation linking the amplitudes of the transmitted and reflected fields as a function of the incident one. This approach is validated for several cases against classical analytical models for thin plates and sandwich constructions, where the results agree perfectly for a reasonable mesh size. The method is then used to study the effect of stacking order in a laminated composite plate. The main interest of the method is the use of finite elements, which enables a relative easy modelling since most packages readily include different formulations, compared to analytical models, where different formulations have to be implemented for every kind of material.

Reflectance spectra based skin and non-skin classification

Face recognition systems have been widely studied and integrated in various applications. Under certain spoofing attacks such as displaying high-resolution photos/videos or wearing masks made up of non-skin materials, they fail. In this work, we propose a new approach of skin and non-skin classification, based on spectral reflectance, providing more discriminative signatures. This approach allows synthesis of biological skin features based on photo-biophysics model. Here, a simple 2-layered skin model is applied which is proofed to be effective in skin and non-skin classification both from theoretical explanations and experimental results. This approach is compared to direct spectral reflectance analysis and classification. Experimental results can reach a classification rate up to 96.4%.

Demographic Classification Using Skin RGB Albedo Image Analysis

Age, gender and skin type classification of demographics using common imaging techniques is costly and does not provide good performance. We propose an approach based on skin RGB albedo image analysis for demographic classification. The diffuse albedo uses inherent skin properties which prevail over illumination conditions variation despite being based on visual perception. The method was tested using skin samples from multiple facial regions to evaluate their performance for classification. Moreover, the application of a fusion algorithm using albedo data from each of the facial regions improved the overall performance resulting in rates above 90% accuracy in age, gender and skin type categories.

A dual-mixed finite element method for quasi-Newtonian flows whose viscosity obeys a power law or the Carreau law

The aim of this work is a construction of a dual mixed finite element method for a quasi-Newtonian flow obeying the Carreau or power law. This method is based on the introduction of the stress tensor as a new variable and the reformulation of the governing equations as a twofold saddle point problem. The derived formulation possesses local (i.e. at element level) conservation properties (conservation of the momentum and the mass) as for finite volume methods. Based on such a formulation, a mixed finite element is constructed and analyzed. We prove that the continuous problem and its approximation are well posed, and derive error estimates.