Journal of Theoretical and Applied Mechanics

Volume 32, Number 1, 2002

Contents

D. Chakarov

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: mit@imbm.bas.bg

STUDY OF THE STIFFNESS OF HYBRID MANIPULATORS WITH FORCE REDUNDANCY

ABSTRACT. The paper presents a study of hybrid manipulators that comprise a serial anthropomorphic kinematic chain and redundant number of parallel driving chains, fixed to the serial one. The paper studies and specifies the stiffness resulting from the antagonistic interaction between the redundant driving forces. The author designs a kinematic model of a hybrid manipulator with redundancy and a model of the end effector antagonistic stiffness. Conditions of specifying an arbitrary stiffness are analyzed and computer experiments are performed. The end effector stiffness is estimated by following the change of the orientation of the axes of the compliance ellipse. The results are presented graphically. Possibilities of generating an arbitrary stiffness are outlined.

KEY WORDS: serial-parallel manipulator, redundant actuation, kinematics model, antagonistic stiffness, compliance ellipse.

S. D. Iliev

Institute of Mechanics, Bulgarian Academy of Sciences,

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

NUMERICAL INVESTIGATION OF THE STATIC LIQUID DROPS ON HORIZONTAL HETEROGENEOUS SOLID SURFACE.

Abstract. The effect of heterogeneity of a solid surface on its wettability by a liquid droplet has been studied numerically. Our study considers the case when the solid surface consists of set of patches, and the contact angle in each patch has a random quantity. To calculate the equilibrium droplet shape and contact line we employ the minimizing method [1]. Set of equilibrium drop shapes on horizontal plane is obtained.

Key words: solid-liquid systems, liquid drops, contact line.

I. T. Dimitrova

University of Rousse “A. Kanchev”,8, Studentska Str., 7017 Rousse, Bulgaria,e-mail: ita@ami.ru.acad.bg

CONSERVATION LAWS AND SYMMETRIC FORMS OF THE SHALLOW WATER MODEL EQUATIONS

Abstract. The full set of first-order conservation laws for the shallow water model is derived by a direct method, without using group analysis and variational principle. Also, the symmetric forms of the shallow water model equations are discussed and an entropy function is introduced.

Key words: shallow water model, conservation laws, symmetrization, entropy function.

S. H. Stefanov

University of Forestry Engineering,

10, Kliment Ohridski Blvd 10, 1756 Sofia, Bulgaria

FATIGUE LIFE PREDICTION WITHOUT CYCLE COUNTING (BY MEANS OF THE INTEGRAL METHOD)

Abstract. The main idea of the infinitesimal calculus is well known: introducing differentials and integrating them universally under arbitrary integration conditions. Nevertheless, this approach was not explored for fatigue life prediction before our investigations. An integral method has been developed under general plane stressing - multiaxial, non-proportional, cyclic or non-cyclic, arbitrary, deterministic or random. The method does not need any reduction of multiaxiality nor any cycle counting because damage differentials on loading differentials are integrated directly. Life prediction without cycle counting is surprising because, after Wöhler, Palmgren and Miner, a stress-time function is always divided into cycles, they are counted, and relative damages per cycles are summed. Although the integral method is directed to the less researched general plane stressing, it should be verified with the established (rain flow etc.) cycle-counting-Miner-rule approach. For this purpose, a reduced version of the integral method has been developed, analyzed and verified.

Key words: fatigue life prediction, fatigue damage accumulation, cycle counting.

Marie-France Robbe,

CEA Saclay, SEMT, 91191 Gif sur Yvette cedex, France,

e-mail: mfrobbe@cea.fr

Michel Lepareux,

CEA Saclay, SEMT, 91191 Gif sur Yvette cedex, France,

e-mail: mlepareux@cea.fr

Evaluation of the mechanical consequences of a steam explosion in a nuclear reactor

Abstract. Steam explosions are considered as potential severe accidents for Pressurised Water Reactors in case of core melting. By falling down into the water remaining in the reactor lower plenum, the molten core transfers fastly its energy to water, which vaporizes. The violent vaporization may damage the reactor vessel and endanger plant safety. This paper presents a synthesis of the computations we carried out to estimate the consequences of an in-vessel steam explosion on the vessel lower head.

The mechanical consequences of the explosion were studied with the general fast dynamics EUROPLEXUS code, estimating roughly and globally the thermodynamic data. The computations aimed at once at predicting the lower head response and at weighting up the sensibility to the parameters used to model steam explosion.

Key words: explosion, numerical simulation, dynamic, fluid-structure interaction.

Sava Grozdev

Institute of Mechanics, Bulgarian Academy of Sciencves,

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

e-mail: savagroz@math.bas.bg

Mathematical Modelling of educational process

Abstract. It is proposed a quasi-dynamical model of training talented high school students and preparation for International Olympiads and competitions. The model accounts for the appearance of critical points in the training process and the influence of the velocity index of learning on individual mathematical behaviour. A sufficient condition for the preparation effectiveness is derived.

Key words: Mathematical Education, Synergetics, index of learning, velocity, dynamics, differential equation.