Aims/Objectives: In this work, we deal an elasticity model in 2D and 3D dimension for deformation under constraint by taking into account the deformation displacement orientation. This mathematical model can be used, for example, to describe the heart deformation taking into account the orientation of the fibers for estimating global and regional parameters of the left ventricular function. Place and Duration of Study: Department of Mathematics and Computer Science, Faculty of Sciences An Chok, University HassanII-Casablanca and C. Jordan UMR CNRS 5208 Institut- INSA Lyon, from June 2012 to July 2015. Methodology: In first, we start by studying a model of Poisson problem under constraint on a domain Ω ⊂ ℝn (n=2 or 3), considering a constraint on a part K of this domain. Secondly, we consider the proposed 2D and 3D elasticity model of deformation under constraint by taking into account the displacement orientation in the deformation. We treat only the case where the orientation of displacement is a given constant vector. The eigenvalues case is being finalized.
A major difficulty for those problems is to find a demonstration of existence and uniqueness of solution, which are given in both 2D and 3D dimension. A numerical approach of the solution using finite element method and its convergence is studied. Numerical simulations are performed with Free Fem software. Simulations results and comments are given in the end. Results: Existence and uniqueness results are established in Sobolev spaces for the proposed models. Convergence of the FEM approached solution is given and numerical simulations are performed with success.
Conclusion: This work has been devoted to study a problem of elasticity under constraint in order to take account the orientation of structure displacement. Both analytical and numerical study of the proposed problem are realized. The numerical simulations give good results.
This paper proves the existence of solution of wind speed equation of a point in air by fixed point theorem of periodic g-contrastive mapping. Further more, the solution of the wind speed equation is obtained by method of separating variables.
We define a general class of planar graphs called extended ladders and their corresponding extended ladder links. We then give some of the properties of the extended ladder graphs and corresponding extended ladder links. Finally, we count the number of components of some extended ladder links.
This paper presents a quantitative analysis on the nonlinear behavior of a forced and self-excited beam coupled with a positive position feedback controller PPF. Such that the external excitation is a harmonic motion on the support of the cantilever beam. Self-excitation is caused by fluid flow and modelled by a nonlinear damping with a negative linear part (Rayleigh’s function). Self-excitation can build up oscillations even in the absence of external forces. Also self-excitation can interact with the external excitation and lead system to vibrate with a quasi-periodic motion and to be unstable. This problem is treated here by using PPF controller. It is assumed that the beam vibrates in the presence of external harmonic excitation close to its natural frequency and one to one internal resonance. Multiple scales perturbation technique MSPT is used to get a first order approximate solution of this system. The stability of the steady state solution is investigated by using the frequency-response equations. The effects of different controller parameters on beam vibrations are studied and optimum conditions for system operation are deduced. Finally, all analytical results are validated by using numerical solution.
In this paper, we state the general Adomian Decomposition Method (ADM) for Fourth order linear differential equations. And applied it to obtain analytic solution in a rapidly convergent series to this class of equations. The concept of ADM was further applied to physical problems and the result showed excellent potentials of applying this method.
In this paper, For dual numbers in dual 3-space ID3, we define the new families of curves which are called dual similar curves in dual 3-space with variable transformation. Then, we prove some theorems and characterizations about this family, we show that a family of dual similar curves are formed the family of curves with wanishing curvatures in dual 3-space ID3.
In this work, cofinitely g-supplemented modules are defined and investigated some properties of these modules. It is shown that an arbitrary sum of cofinitely g-supplemented modules is cofinitely g-supplemented. In addition, amply cofinitely g-supplemented modules are also defined and given some equivalences.