In this paper a high order implicit algorithm is developed for solving instationary non-linear problems. This generic numerical method combines four mathematical techniques: a time discretization, a homotopy transformation, a perturbation... more
In this paper a high order implicit algorithm is developed for solving instationary non-linear problems. This generic numerical method combines four mathematical techniques: a time discretization, a homotopy transformation, a perturbation technique and a space discretization. The time integration is performed by classical implicit schemes (Euler implicit for problems with a first order time derivative and Newmark for second order). The timediscretization leads to non-linear equations. In this paper a new technique is proposed to solve iteratively the latter equations. The key points in this approach are, first a high order solver based on perturbation techniques, second the possibility of choosing the iteration operator, which limits the number of matrices to be triangulated. To illustrate the performance of the proposed algorithm two examples are considered: the Korteweg-de Vries equation (KdV) and the non-linear oscillations of a 2D elastic pendulum.
In the framework of the cellular bifurcation theory, we investigate the effect of distributed and/or localized imperfections on the buckling of long cylindrical shells under axial compression. Using a double scale perturbative approach... more
In the framework of the cellular bifurcation theory, we investigate the effect of distributed and/or localized imperfections on the buckling of long cylindrical shells under axial compression. Using a double scale perturbative approach including modes interaction, we establish that the evolution of amplitudes of instability patterns is governed by a nonhomogeneous second order system of three non-linear complex equations. The localized imperfections are included by employing jump conditions for their amplitude and permitting discontinuous derivatives. By solving these amplitude equations, we show the influence of distributed and/or localized imperfections on the reduction of the critical load. To assess the validity of the present method, our results are compared to those given by two finite element codes.
- by Noureddine DAMIL and +1
- •
- Engineering, Mathematical Sciences
In this paper a high order implicit algorithm is developed for solving instationary non-linear problems. This generic numerical method combines four mathematical techniques: a time discretization, a homotopy transformation, a perturbation... more
In this paper a high order implicit algorithm is developed for solving instationary non-linear problems. This generic numerical method combines four mathematical techniques: a time discretization, a homotopy transformation, a perturbation technique and a space discretization. The time integration is performed by classical implicit schemes (Euler implicit for problems with a first order time derivative and Newmark for second order). The timediscretization leads to non-linear equations. In this paper a new technique is proposed to solve iteratively the latter equations. The key points in this approach are, first a high order solver based on perturbation techniques, second the possibility of choosing the iteration operator, which limits the number of matrices to be triangulated. To illustrate the performance of the proposed algorithm two examples are considered: the Korteweg-de Vries equation (KdV) and the non-linear oscillations of a 2D elastic pendulum.
Nous développons dans cet article quelques nouveaux algorithmes implicites pour la résolution de problèmes non linéaires instationnaires. Les algorithmes proposés sont des variantes des Méthodes Asymptotiques Numériques (MAN), obtenus en... more
Nous développons dans cet article quelques nouveaux algorithmes implicites pour la résolution de problèmes non linéaires instationnaires. Les algorithmes proposés sont des variantes des Méthodes Asymptotiques Numériques (MAN), obtenus en associant la méthode de perturbation, la technique d'homotopie et des procédures classiques de discrétisation en temps et en espace. La performance de ces algorithmes est testée sur un modèle classique des phénomènes de propagation d'ondes non linéaires, décrit par l'équation de Fisher. Les résultats obtenus attestent d'une économie notable en temps CPU par comparaison à d'autres méthodes de résolution de problèmes non linéaires. ABSTRACT. In this paper, we develop some new implicit algorithms for solving instationary non-linear problems. The proposed algorithms are variants of Asymptotic Numerical Methods (ANM). They are obtained by coupling the perturbation method, the homotopy technique and classical time-space discretization procedures. The efficiency of these algorithms is tested on a model for non-linear wave propagation phenomena typified by the Fisher equation. The obtained results prove a computational cost save in comparison with other algorithms for non-linear problems. MOTS-CLÉS : non linéaire, instationnaire, algorithmes implicites, homotopie, perturbation, Méthode Asymptotique Numérique, ondes non linéaires.
- by Bouazza Braikat and +1
- •
- Numerical Method
ABSTRACT On développe dans ce travail quelques solveurs temporels implicites d'ordre élevé pour la résolution des problèmes dynamiques non linéaires des structures élastiques en transformations finies. Ces solveurs se basent sur... more
ABSTRACT On développe dans ce travail quelques solveurs temporels implicites d'ordre élevé pour la résolution des problèmes dynamiques non linéaires des structures élastiques en transformations finies. Ces solveurs se basent sur la méthode de perturbation, la transformation homotopique et sur des techniques de discrétisation temporelle et spatiale. On montre que l'efficacité de ces algorithmes augmente par l'introduction des approximants de Padé. La performance et la comparaison de ces algorithmes avec d'autres solveurs classiques sont testées sur la vibration non linéaire d'une poutre élastique 2D et d'une plaque élastique.
- by Bouazza Braikat and +1
- •
An approach is developed for solving linear structural dynamic problems. This alternative is based on the classical finite element procedure and time power series expansion. The time integration is carried out without time discretization... more
An approach is developed for solving linear structural dynamic problems. This alternative is based on the classical finite element procedure and time power series expansion. The time integration is carried out without time discretization procedure. The solution of the structural dynamic problem is sought in the form of an integro-power series expansion with respect to time. The Padé Approximants and Shanks transformation techniques are introduced for improving the range of validity of the series. The example of forced linear vibration of a beam is given to illustrate the use of the proposed method. Results obtained by this approach are compared to those computed by a direct integration with an implicit Newmark scheme.
- by Bouazza Braikat and +1
- •
On développe dans ce travail quelques solveurs temporels implicites d'ordre élevé pour la résolution des problèmes dynamiques non linéaires des structures élastiques en transformations finies. Ces solveurs se basent sur la méthode de... more
On développe dans ce travail quelques solveurs temporels implicites d'ordre élevé pour la résolution des problèmes dynamiques non linéaires des structures élastiques en transformations finies. Ces solveurs se basent sur la méthode de perturbation, la transformation homotopique et sur des techniques de discrétisation temporelle et spatiale. On montre que l'efficacité de ces algorithmes augmente par l'introduction des approximants de Padé. La performance et la comparaison de ces algorithmes avec d'autres solveurs classiques sont testées sur la vibration non linéaire d'une poutre élastique 2D et d'une plaque élastique.
- by Bouazza Braikat and +1
- •
Background: Polycystic ovary syndrome (PCOS) is a common cause of infertility, especially in the morbidly obese. We evaluated the long-term effects of Roux-en-Y gastric bypass on PCOS and infertility. Methods: A total of 566 morbidly... more
Background: Polycystic ovary syndrome (PCOS) is a common cause of infertility, especially in the morbidly obese. We evaluated the long-term effects of Roux-en-Y gastric bypass on PCOS and infertility. Methods: A total of 566 morbidly obese women underwent Roux-en-Y gastric bypass from 2000 to 2009. A total of 31 patients (5.5%) had a history of PCOS. Of the 31 patients, 6 were postmenopausal and 5 lost to follow-up and were excluded. Telephone interviews were conducted with the 20 eligible patients. Results: The mean age and body mass index was 32 Ϯ 5.8 years (range 22-42) and 52.8 Ϯ 9.08 kg/m 2 (range 37-76) before surgery. All 20 patients had Ն2 of 3 diagnostic criteria for PCOS, including clinical or biochemical evidence of hyperandrogenism, anovulation, or polycystic ovaries. Of these, 85% had oligomenorrhea, 70% had hirsutism, and 45% had type 2 diabetes mellitus with medication. Before surgery, 8 patients conceived with or without hormonal treatment, 2 did not desire pregnancy, and 10 did not conceive. The mean follow-up was 46.7 months. After surgical weight loss, menstruation was corrected in 82%, hirsutism had resolved in 29%, and 77.8% of those with diabetes had complete remission. Of the 10 patients who did not conceive before surgery, 4 no longer desired pregnancy, and the remaining 6 patients had become pregnant within 3 years of surgery-5 without any hormonal treatment and 1 with in utero insemination. Conclusion: Surgical weight loss after Roux-en-Y gastric bypass achieves excellent amelioration of PCOS manifestations and the postoperative conception rate in infertile PCOS subjects desiring pregnancy was 100%. (Surg Obes Relat Dis 2011;xx:xxx.)
A numerical mesh-free model applied to a strong formulation for simulating elasto-plastic structures with contact is developed in the context of large deformation. This numerical mesh-free model is based on the Asymptotic Numerical Method... more
A numerical mesh-free model applied to a strong formulation for simulating elasto-plastic structures with contact is developed in the context of large deformation. This numerical mesh-free model is based on the Asymptotic Numerical Method (ANM) which is used in the meshless collocation framework to extend its application field to elasto-plastic problems with contact. The efficiency of this model is to take into account of large deformations and to avoid the meshing distortion problem. According to (ANM) techniques, the development in Taylor series is performed to obtain a sequence of linear systems to be solved. These linear systems are then discretized by a collocation meshless approach by using the Moving Least Squares (MLS) functions and a continuation method is adopted to evaluate the solution. The unilateral contact problem is identified to boundary conditions which are replaced by force-displacement relations through a regularization technique. The performance of the proposed approach is tested on several elasto-plastic bi-dimensional examples without and with contact. The obtained results are compared to those computed by the Newton–Raphson method.
- by jamal mohammad and +1
- •
In this paper, we propose a new explicit analytical formula of the critical buckling load of double-walled carbon nanotubes (DWCNT) under axial compression. This formula takes into account van der Waals interactions between adjacent tubes... more
In this paper, we propose a new explicit analytical formula of the critical buckling load of double-walled carbon nanotubes (DWCNT) under axial compression. This formula takes into account van der Waals interactions between adjacent tubes and the effect of terms involving tube radii differences generally neglected in the derived expressions of the critical buckling load published in the literature. The elastic multiple Donnell shells continuum approach is employed for modelling the multi-walled carbon nanotubes. The validation of the proposed formula is made by comparison with a numerical solution. The influence of the neglected terms is also studied. r é s u m é Cet article a pour objectif la proposition d'une formule analytique explicite de la charge critique de flambage des nantubes de carbone à double parois (DWCNT) soumis à une compression axiale. Cette formule prend en compte les interactions de van der Waals entre les tubes adjacents et l'influence des rayons, généralement negligée dans les formules donnant la charge critique de flambage publiées dans la littérature. L'approche continue des coques multiples de Donnell est utilisée pour la modélisation des nanotubes de carbone multi-parois. La validation de la formule proposée est faite par une comparaison avec une solution numérique. L'effet des termes négligés a aussi été étudié.
- by jamal mohammad and +1
- •
In this paper we propose bifurcation indicators for linear or nonlinear eigenvalue problems. These indicators are the determinants of a reduced stiffness matrix. They measure the intensity of the response of the system to perturbation... more
In this paper we propose bifurcation indicators for linear or nonlinear eigenvalue problems. These indicators are the determinants of a reduced stiffness matrix. They measure the intensity of the response of the system to perturbation forces. The numerical computation of the indicators is done by a direct method and by an Asymptotic Numerical Method.
In this paper we propose bifurcation indicators for linear or nonlinear eigenvalue problems. These indicators are the determinants of a reduced stiffness matrix. They measure the intensity of the response of the system to perturbation... more
In this paper we propose bifurcation indicators for linear or nonlinear eigenvalue problems. These indicators are the determinants of a reduced stiffness matrix. They measure the intensity of the response of the system to perturbation forces. The numerical computation of the indicators is done by a direct method and by an Asymptotic Numerical Method.
On développe dans ce travail quelques solveurs temporels implicites d'ordre élevé pour la résolution des problèmes dynamiques non linéaires des structures élastiques en transformations finies. Ces solveurs se basent sur la méthode de... more
On développe dans ce travail quelques solveurs temporels implicites d'ordre élevé pour la résolution des problèmes dynamiques non linéaires des structures élastiques en transformations finies. Ces solveurs se basent sur la méthode de perturbation, la transformation homotopique et sur des techniques de discrétisation temporelle et spatiale. On montre que l'efficacité de ces algorithmes augmente par l'introduction des approximants de Padé. La performance et la comparaison de ces algorithmes avec d'autres solveurs classiques sont testées sur la vibration non linéaire d'une poutre élastique 2D et d'une plaque élastique. ABSTRACT. We develop in this work, some implicit temporal high order solvers for solving non linear elastic structural dynamic problems involvingfinite deformations. These solvers are based on the perturbation method, the homotopical transformation and time space discretization techniques. Their accuracy is improved by the introduction of Padé approximants. Numerical calculations, compared with others classical solvers, are illustrated on forced nonlinear vibration problems of a 2D elastic beam and an elastic plate. MOTS-CLÉS : solveurs implicites d'ordre élevé, dynamique non linéaire des structures, homotopie, perturbation.
In this paper a high order implicit algorithm is developed for solving instationary non-linear problems. This generic numerical method combines four mathematical techniques: a time discretization, a homotopy transformation, a perturbation... more
In this paper a high order implicit algorithm is developed for solving instationary non-linear problems. This generic numerical method combines four mathematical techniques: a time discretization, a homotopy transformation, a perturbation technique and a space discretization. The time integration is performed by classical implicit schemes (Euler implicit for problems with a first order time derivative and Newmark for second order). The timediscretization leads to non-linear equations. In this paper a new technique is proposed to solve iteratively the latter equations. The key points in this approach are, first a high order solver based on perturbation techniques, second the possibility of choosing the iteration operator, which limits the number of matrices to be triangulated. To illustrate the performance of the proposed algorithm two examples are considered: the Korteweg-de Vries equation (KdV) and the non-linear oscillations of a 2D elastic pendulum.
Response of 17 sugarcane varieties was observed in 3 plant and 3 ratoon stages from 1996-97 to 1998-99. The analysis of mean values revealed that varieties Bannu-1, Naurang-98, 5-84-I-351 and S-82-US-624 possessed better cane yield and... more
Response of 17 sugarcane varieties was observed in 3 plant and 3 ratoon stages from 1996-97 to 1998-99. The analysis of mean values revealed that varieties Bannu-1, Naurang-98, 5-84-I-351 and S-82-US-624 possessed better cane yield and sugar recovery. Varieties Bannu-1 and S-84-I-351 exhibited higher stalk yield and considerable sugar recovery. Variety COL-75 although, produced highest cane yield in plant crop, 1998-99 but poor in sugar contents. While, S-82-US-624 and S-88-US-402 showed better cane yield and the highest sugar recovery. Varieties Bannu-1 and Naurang-98 have already been approved for general cultivation in the area. While varieties S-84-I-351, S-82-US-624 and S-88-US-402 are the candidates varieties and are under consideration for commercial cultivation in the area. Short title: Response of distinct sugarcane varieties.