Journal of Theoretical and Applied Mechanics

Volume 37, Number 3, 2007

### B. Kazakoff

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,

e-mail

FORCE RESPONSE TRANSMISSIBILITY PREDICTION AND FREQUENCY ANALYSIS OF HIGH DEFLECTION DISP

Abstract: An attempt is performed in this paper to model the dynamic response of vibro isolation mounts utilizing viscoelastic materials using computer code MATLAB and comparison of the results against the experimental test results of the same shock input data. This paper describes an investigation into the use of computer code MATLAB for predicting large (up to 70% strain) dynamic deformations of “benchmark” elements in the form of viscoelastic solid cylinders. The investigation objective was to establish guidelines for MATLAB procedures whereby the computationally efficient models could be used for the early stage of modelling of dynamically scaled models of geometrically scaled vibro-isolation mounts, but compromising the solution accuracy. Dynamic transient responses are measured and compared against the MATLAB predictions.

R. Raghavendra Rao

Department of Mathematics, Eritrea Institute of Technology,

Mai-Nefhi, Eritrea (North east Africa),

e-mail

## K. Raja Sekhar

Department of Mathematics, RVR & J C College of Engineering,

Chowdavaram-522019, India

EFFECTS OF VELOCITY-SLIP IN ROLLING AND NORMAL MOTION

Abstract. A generalized form of Reynolds equation for two symmetrical surfaces is derived considering velocity-slip at the bearing surfaces. This Reynolds equation is applied to study the effects of velocity-slip in the lubrication of roller bearings subjected to combined rolling and normal motion under cavitation boundary conditions. The load capacity, frictional drag increase as the squeezing velocity increases when the surfaces are approaching and they decrease when the surfaces are separating and this decrease is more pronounced due to slip. The effects of these parameters on cavitation point are also discussed.

Key words: Reynolds equation, velocity-slip, viscosity, roller bearings, point of cavitation, load capacity, coefficient of friction.

Sonia Parvanova

University of Architecture, Civil Engineering and Geodesy,

1, Christo Smirnenski Blvd, 1046, Sofia, Bulgaria,

e-mail:

Dual Boundary Elements for Cohesive discrete Cracks by Using “Event-to-Event” Nonlinear Algorithm

Abstract. The present paper is concerned with the 2D numerical implementation of the fictitious crack model in the Dual Boundary Element Method (DBEM) context for crack propagation in plain concrete. The main advantage of the DBEM is that mixed-mode crack problems can be solved successfully with a single region formulation, thus avoiding the ineffective sub-region approach. The Fracture Process Zone (FPZ) is represented in discrete crack manner by Fictitious Crack Model (FCM). With that end in view an adequate modification of the discretized system of dual boundary integral equations is presented in order to capture the behaviour of the points in the undamaged and fracture zones. The nonlinear solution algorithm adopted in the presented software code is worked out without iterations by using an “event-to-event” strategy for the multilinear constitutive law model including the softening branch. The effectiveness of the proposed approach is demonstrated by two numerical simulations and comparisons with experimental results are made.

N. Nikolov

Institute of Mechanics, Bulgarian Academy of Sciences,

# Acad. G. Bonchev Str., Bl. 4, Sofia 1113, Bulgaria,

e-mail

INFLUENCE OF THE ANISOTROPY OF ALUMINUM

BLANK DURING DEEP DRAWING

Abstract. Process of deep drawing of circular aluminum blank having diameter 105 mm and thickness 1.5 mm is discussed. The influence of transversal anisotropy is investigated by change of the anisotropy coefficient in the Hill’s quadratic criterion in limits 0.7-1.3, applied in a numerical simulation. It is established numerically that lower anisotropy leads to waviness on the blank flange, larger increase of the blank height and thickness, and causes plastic strain localization leading to blank failure. Larger anisotropy assures obtaining the qualitative piece. The distribution of strains in blank elements and changes in the blank element sizes are given along the blank radius, which affords an opportunity to predict and investigate the areas of breaking and processes developed in them.

Key words: deep drawing, numerical simulation, transversal anisotropy, plastic strain localization, blank flange waviness.

B. Ould Chikh

Laboratory of LSTE, Department of Mechanics,

Faculty of Science and Engineering, University of Mascara,

BP. 763, Route de Mamounia, Mascara, 29000, Algeria,

# e-mail: chikhb@yahoo.com

J. M. Nianga

Hautes Ecoles d’Ingénieur, 13 Rue de Toul, 59046 Lille cedex, France

Laboratory of Mechanics of Lille, CNRS UMR 8107,

Ecole Polytech’Lille, University of Lille1,

Cité Scientifique, Av. Paul Langevin, 59655 Villeneuve d’Ascq, France

M. Benguediab

Laboratory of Mechanics, University of Sidi bel Abbes 22000, Algeria

CORRELATION BETWEEN THE PARAMETERS C AND m OF PARIS’ LAW AND THE EFFECT OF THEIR VARIABILITY ON THE LIFETIME PREDICTION IN THE CASE OF 12NC6 STEEL

Abstract. The general purpose of this work concerns the effects of the loading parameters on fatigue crack growth in heat treated 12NC6 steel. Four heat treatments were chosen to get the following yield stress values, respectively, 270, 480, 830 and 1070 MPa. Fatigue Crack Propagation (FCP) experiments were performed under room temperature and a Stress Intensity Factor (SIF) range between 17 and 30 MPaÖm. Four values of the load ratio were used 0.05, 0.1, 0.3 and 0.5. The correlation between C and m parameters, obtained in this model, has been examined for this case of steel with different heat treatments. The variability of C and m parameters has been analysed in order to predict the fatigue life engineering structures. The influence of some extrinsic and intrinsic factors on the evolution of these parameters has been also discussed.

Key words: fatigue, lifetime, Paris’ law.