L. Azrar - Academia.edu (original) (raw)

Papers by L. Azrar

Research paper thumbnail of Lateral post-buckling analysis of thin-walled open section beams

Thin-Walled Structures, 2002

Thin-walled beams with open sections are studied using a nonlinear model. This model is developed... more Thin-walled beams with open sections are studied using a nonlinear model. This model is developed in the context of large displacements and small deformations, by accounting for bending-bending and bending-torsion couplings. The warping and shortening effects are considered in the torsion equilibrium equation. The governing coupled equilibrium equations obtained from Galerkin's method are solved by a Newton-Raphson iterative process. It is established that the buckling loads are highly dependent on the pre-buckling deformations of the beam. The bifurcated branches are unstable and strongly influenced by shortening effects. Some comparisons are presented with the solutions commonly used in linear stability, like in the standard European steel code (Eurocode 3). The regular solutions appear to be very conservative, especially for I sections with large flanges. 

Research paper thumbnail of An amplitude equation for the non-linear vibration of viscoelastically damped sandwich beams

Journal of Sound and Vibration, 2004

... The goal of this paper is to establish the simplest consistent theory for the non-linear vibr... more ... The goal of this paper is to establish the simplest consistent theory for the non-linear vibration analysis of a viscoelastic sandwich beam. The non-linearity arises from axial stretching of theelastic face layers and the damping from the shear deformation of the viscoelastic core ...

Research paper thumbnail of A SEMI-ANALYTICAL APPROACH TO THE NON-LINEAR DYNAMIC RESPONSE PROBLEM OF BEAMS AT LARGE VIBRATION AMPLITUDES, PART II: MULTIMODE APPROACH TO THE STEADY STATE FORCED PERIODIC RESPONSE

Journal of Sound and Vibration, 2002

... 23. G. VENKATESWARA RAO, K. KANAKA RAJU and IS RAJU, Finite element formulation for large amp... more ... 23. G. VENKATESWARA RAO, K. KANAKA RAJU and IS RAJU, Finite element formulation for large amplitude free vibration of beams and ... L. AZRAR, C. COCHELIN, N. DAMIL and M. POTIER-FERRY, As asymptotic-numerical method for nonlinear vibrations of elastic structures. ...

Research paper thumbnail of NON-LINEAR FORCED VIBRATIONS OF PLATES BY AN ASYMPTOTIC–NUMERICAL METHOD

Journal of Sound and Vibration, 2002

... 3 L. AZRAR, R. BENAMAR and M. POTIER-FERRY, An Asymptotic–Numerical Method for large amplitud... more ... 3 L. AZRAR, R. BENAMAR and M. POTIER-FERRY, An Asymptotic–Numerical Method for large amplitude free vibrations of thin elastic plates. Journal of Sound and Vibration, 220 (1999), pp. 695–727. ... 12 CY CHIA, Non-linear Analysis of Plates, Mc-Graw Hill, New York (1980). ...

Research paper thumbnail of AN ASYMPTOTIC-NUMERICAL METHOD FOR LARGE-AMPLITUDE FREE VIBRATIONS OF THIN ELASTIC PLATES

Journal of Sound and Vibration, 1999

An Asymptotic-Numerical Method has been developed for large amplitude free vibrations of thin ela... more An Asymptotic-Numerical Method has been developed for large amplitude free vibrations of thin elastic plates. It is based on the perturbation method and the finite element method. This method eliminates the major difficulties of the classical perturbation methods, namely the complexity of the right hand sides and the limitation of the validity of the solution obtained. The applicability of this method to non-linear vibrations of plates is clearly presented. Based on the Von Karman theory and the harmonic balance method, a cubic non-linear operational formulation has been obtained. By using the mixed stress-displacement Hellinger-Reissner principle, a quadratic formulation is given. The displacement and frequency are expanded into power series with respect to a control parameter. The non-linear governing equation is then transformed into a sequence of linear problems having the same stiffness matrix, which can be solved by a classical FEM. Needing one matrix inversion, a large number of terms of the series can be easily computed with a small computation time. The non-linear mode and frequency are then obtained up to the radius of convergence. Taking the starting point in the zone of validity, the method is reapplied in order to determine a further part of the non-linear solution. Iteration of this method leads to a powerful incremental method. In order to increase the validity of the perturbed solution, another technique, called Pade´approximants, is shrewdly incorporated. The solutions obtained by these two concepts coincide perfectly in a very large part of the backbone curve. Comprehensive numerical tests for non-linear free vibrations of circular, square, rectangular and annular plates with various boundary conditions are reported and discussed.

Research paper thumbnail of Damping and Forced Vibration Analyses of Viscoelastic Shells

International Journal for Computational Methods in Engineering Science and Mechanics, 2010

... The present work is a generalized extension of the one developed for straight viscoelastic be... more ... The present work is a generalized extension of the one developed for straight viscoelastic beams and plates when the viscoelastic core is modelled by a constant and a simplified Maxwell model [11. Abdoun, A., Azrar, L., Daya, EM and Potier-Ferry, M. 2009. ... Krishnan et al. ...

Research paper thumbnail of An asymptotic-numerical method to compute the postbuckling behaviour of elastic plates and shells

International Journal for Numerical Methods in Engineering, 1993

In this paper, we apply an asymptotic-numerical method for computing the postbuckling behaviour o... more In this paper, we apply an asymptotic-numerical method for computing the postbuckling behaviour of plate and shell structures. The bifurcating branch is sought in the form of polynomial expansions, and it is determined by solving numerically (FEM) several linear problems with a single stiffness matrix. A large number of terms of the series can easily be computed by using recurrent formulas. In comparison with a more classical step-by-step procedure, the method is rapid and automatic. However, the polynomial expansions have a radius of convergence which limits the validity of the solution to a neighbourhood of the bifurcation point. in the present form, the method should be viewed as a cheap and automatic way of completing a linear buckling analysis. It is illustrated in two examples: a square plate under in-plane compression and a cylindrical shell under pressure.

Research paper thumbnail of Forced harmonic response of viscoelastic structures by an asymptotic numerical method

Computers & Structures, 2009

ABSTRACT

Research paper thumbnail of Dynamics Instability Analysis of Multi-Walled Carbon Nanotubes Conveying Fluid

ABSTRACT The dynamic instability analysis of conveying fluid multi-walled carbon nanotubes (MWCNT... more ABSTRACT The dynamic instability analysis of conveying fluid multi-walled carbon nanotubes (MWCNT) is analyzed. Based on the nonlocal elasticity theory, Donnells shell model, potential flow theory and the van der Waal interaction between walls, the governing equations are formulated. The small scale parameter and the internal fluid interaction effects on the dynamic behaviors of the MWCNT-fluid system as well as the instabilities induced by the fluid velocity are investigated. The critical velocity and the frequency-amplitude relationships are obtained with respect to physical and material parameters.

Research paper thumbnail of Lateral post-buckling analysis of thin-walled open section beams

Thin-Walled Structures, 2002

Thin-walled beams with open sections are studied using a nonlinear model. This model is developed... more Thin-walled beams with open sections are studied using a nonlinear model. This model is developed in the context of large displacements and small deformations, by accounting for bending-bending and bending-torsion couplings. The warping and shortening effects are considered in the torsion equilibrium equation. The governing coupled equilibrium equations obtained from Galerkin's method are solved by a Newton-Raphson iterative process. It is established that the buckling loads are highly dependent on the pre-buckling deformations of the beam. The bifurcated branches are unstable and strongly influenced by shortening effects. Some comparisons are presented with the solutions commonly used in linear stability, like in the standard European steel code (Eurocode 3). The regular solutions appear to be very conservative, especially for I sections with large flanges. 

Research paper thumbnail of An amplitude equation for the non-linear vibration of viscoelastically damped sandwich beams

Journal of Sound and Vibration, 2004

... The goal of this paper is to establish the simplest consistent theory for the non-linear vibr... more ... The goal of this paper is to establish the simplest consistent theory for the non-linear vibration analysis of a viscoelastic sandwich beam. The non-linearity arises from axial stretching of theelastic face layers and the damping from the shear deformation of the viscoelastic core ...

Research paper thumbnail of A SEMI-ANALYTICAL APPROACH TO THE NON-LINEAR DYNAMIC RESPONSE PROBLEM OF BEAMS AT LARGE VIBRATION AMPLITUDES, PART II: MULTIMODE APPROACH TO THE STEADY STATE FORCED PERIODIC RESPONSE

Journal of Sound and Vibration, 2002

... 23. G. VENKATESWARA RAO, K. KANAKA RAJU and IS RAJU, Finite element formulation for large amp... more ... 23. G. VENKATESWARA RAO, K. KANAKA RAJU and IS RAJU, Finite element formulation for large amplitude free vibration of beams and ... L. AZRAR, C. COCHELIN, N. DAMIL and M. POTIER-FERRY, As asymptotic-numerical method for nonlinear vibrations of elastic structures. ...

Research paper thumbnail of NON-LINEAR FORCED VIBRATIONS OF PLATES BY AN ASYMPTOTIC–NUMERICAL METHOD

Journal of Sound and Vibration, 2002

... 3 L. AZRAR, R. BENAMAR and M. POTIER-FERRY, An Asymptotic–Numerical Method for large amplitud... more ... 3 L. AZRAR, R. BENAMAR and M. POTIER-FERRY, An Asymptotic–Numerical Method for large amplitude free vibrations of thin elastic plates. Journal of Sound and Vibration, 220 (1999), pp. 695–727. ... 12 CY CHIA, Non-linear Analysis of Plates, Mc-Graw Hill, New York (1980). ...

Research paper thumbnail of AN ASYMPTOTIC-NUMERICAL METHOD FOR LARGE-AMPLITUDE FREE VIBRATIONS OF THIN ELASTIC PLATES

Journal of Sound and Vibration, 1999

An Asymptotic-Numerical Method has been developed for large amplitude free vibrations of thin ela... more An Asymptotic-Numerical Method has been developed for large amplitude free vibrations of thin elastic plates. It is based on the perturbation method and the finite element method. This method eliminates the major difficulties of the classical perturbation methods, namely the complexity of the right hand sides and the limitation of the validity of the solution obtained. The applicability of this method to non-linear vibrations of plates is clearly presented. Based on the Von Karman theory and the harmonic balance method, a cubic non-linear operational formulation has been obtained. By using the mixed stress-displacement Hellinger-Reissner principle, a quadratic formulation is given. The displacement and frequency are expanded into power series with respect to a control parameter. The non-linear governing equation is then transformed into a sequence of linear problems having the same stiffness matrix, which can be solved by a classical FEM. Needing one matrix inversion, a large number of terms of the series can be easily computed with a small computation time. The non-linear mode and frequency are then obtained up to the radius of convergence. Taking the starting point in the zone of validity, the method is reapplied in order to determine a further part of the non-linear solution. Iteration of this method leads to a powerful incremental method. In order to increase the validity of the perturbed solution, another technique, called Pade´approximants, is shrewdly incorporated. The solutions obtained by these two concepts coincide perfectly in a very large part of the backbone curve. Comprehensive numerical tests for non-linear free vibrations of circular, square, rectangular and annular plates with various boundary conditions are reported and discussed.

Research paper thumbnail of Damping and Forced Vibration Analyses of Viscoelastic Shells

International Journal for Computational Methods in Engineering Science and Mechanics, 2010

... The present work is a generalized extension of the one developed for straight viscoelastic be... more ... The present work is a generalized extension of the one developed for straight viscoelastic beams and plates when the viscoelastic core is modelled by a constant and a simplified Maxwell model [11. Abdoun, A., Azrar, L., Daya, EM and Potier-Ferry, M. 2009. ... Krishnan et al. ...

Research paper thumbnail of An asymptotic-numerical method to compute the postbuckling behaviour of elastic plates and shells

International Journal for Numerical Methods in Engineering, 1993

In this paper, we apply an asymptotic-numerical method for computing the postbuckling behaviour o... more In this paper, we apply an asymptotic-numerical method for computing the postbuckling behaviour of plate and shell structures. The bifurcating branch is sought in the form of polynomial expansions, and it is determined by solving numerically (FEM) several linear problems with a single stiffness matrix. A large number of terms of the series can easily be computed by using recurrent formulas. In comparison with a more classical step-by-step procedure, the method is rapid and automatic. However, the polynomial expansions have a radius of convergence which limits the validity of the solution to a neighbourhood of the bifurcation point. in the present form, the method should be viewed as a cheap and automatic way of completing a linear buckling analysis. It is illustrated in two examples: a square plate under in-plane compression and a cylindrical shell under pressure.

Research paper thumbnail of Forced harmonic response of viscoelastic structures by an asymptotic numerical method

Computers & Structures, 2009

ABSTRACT

Research paper thumbnail of Dynamics Instability Analysis of Multi-Walled Carbon Nanotubes Conveying Fluid

ABSTRACT The dynamic instability analysis of conveying fluid multi-walled carbon nanotubes (MWCNT... more ABSTRACT The dynamic instability analysis of conveying fluid multi-walled carbon nanotubes (MWCNT) is analyzed. Based on the nonlocal elasticity theory, Donnells shell model, potential flow theory and the van der Waal interaction between walls, the governing equations are formulated. The small scale parameter and the internal fluid interaction effects on the dynamic behaviors of the MWCNT-fluid system as well as the instabilities induced by the fluid velocity are investigated. The critical velocity and the frequency-amplitude relationships are obtained with respect to physical and material parameters.