Issue 1

JTAM, Sofia, vol. 19 Issue 1 (1988)

Kinematics and Kinetostatics of Spatial Mechanisms. Part II: Kinetostatics of Spatial Mechanisms

P. Genova1, E. Zakhariev2
1High. Inst. Mech. Electr. Eng., Sofia
2Inst. Mech. Biomech., Bulg. Acad. Sci., BI. 8

The paper proposes a generalized approach to force analysis of open and closed polycontour spatial chains. This is a force analysis method that transforms closed spatial chains to open branched chains by means of pair rupture. The link reactions and the link equilibrium condition have been expressed by a function of the pair reactions and a system of linear equations respectively. The system dimension itself turns to be reduced repeatedly as a result.

JTAM, Sofia, vol. 19 Issue 1 pp. 011-020 (1988), [Full Article]

One More Theorem on the Stability Function

R. Krastev
Tsalapitsa, Plovdiv

The stability function is defined in [2]. The paper presents the definition again for reason of convenience. A new theorem is given about the stability in question.

JTAM, Sofia, vol. 19 Issue 1 pp. 021-025 (1988)

A Generalized Scheme for Cutting Right Tooth Cone Gears by the Roundabout Cutter Method

A. Miler

The paper presents the generalized principle scheme for cutting right tooth cone gears by the roundabout cutter method in the general nonconjugate case. The domain of application and the cutting potentialities of the method have been considered.

JTAM, Sofia, vol. 19 Issue 1 pp. 026-029 (1988)

On a Numerical Method in Deformable System Dynamics

S. Simoeonov
High. Inst. Arch. Civ. Eng., 1 Hr. Smirnenski. Sofia

A step two parametric method is proposed to examine dynamic behaviour of linear and nonlinear deformable systems with finite degrees of freedom. The matrix differential equation (1) has been transformed to the form (3) by a discretization at the moment t = t1. It is assumed that the additional equations are of the form (4). The free parameters a, b, c and d can be derived using the process unconditional stability (5), the solution compatibility and the algorithmic dissipation which is proportional to (h/T2). Thus, the formulae (18) have been obtained and the parameter a has been used for dissipation control. What helps the internal resistance modelling is the introduction of the free parameter ζ in (19). An analogy with the viscous resistance appears. It is proved that the algorithm assures the process unconditional stability in case of nonlinear system oscillations (22). The process (32) of finding numerical solutions of the nonlinear equations has been backed with arguments.

JTAM, Sofia, vol. 19 Issue 1 pp. 030-036 (1988)

Inverse and Ill-Posed Problems in Stochastic Geomechanics

V. Dimova, I. Dimov
High. Inst. Geol. Eng., Sofia

A vertical geomaterial plane is considered. The z-axis is opposite to the gravitation force direction, while the x-axis is horizontal. The partial material removing at the level z = 0 perturbs the initial displacement field and all straight lines at the level zi > 0 become curve. Mouldies of motion are obtained. The present paper raises the problem of initial perturbation restoring at the level z = 0 in case of a given effect at the level z = H > 0. The indirect data problem of medium property theoretic determination has been raised too. The problems are reduced to the following ill-posed problems: a) a Cauchie problem for the Fourier equation with an inverse time, b) a Cauchie problem for the Laplace equation, c) a coefficient problem for the Fourier equation.

JTAM, Sofia, vol. 19 Issue 1 pp. 037-045 (1988)

Effective Deformation Characteristics of Spherical Nonhomogeneous Material in the Presence of Peeling

V. Valeva
Inst. Mech. Biomech., Bulg. Acad. Sci., B1. 8

The effective deformation characteristics of a material have been determined using author's solutions. The material itself contains a great number of hard spherical nonhomogenelties with a rare disposition. The presence of peeling is considered in case of a given loading. Some numerical results are produced.

JTAM, Sofia, vol. 19 Issue 1 pp. 046-049 (1988)

Linear Instability of a Viscous Two-Layered Jet

O. Kamenov, S. Radev
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8

The two dimensional model of a viscous two-layered jet and its linear capillary instability have been analyzed. The viscosity stabilization effect on the two-layered jet break-up is shown. This is typical to one-layered jet that flows into infinite medium. The present results have been compared to the nonviscous solution, the one dimensional solution and Weber's approximate viscous solution in case of a thin concentric layer.

JTAM, Sofia, vol. 19 Issue 1 pp. 050-059 (1988)

The Rothe Approximations of Solutions to the Modified System of Equations of Motion of Viscous Compressible Fluid and Their Convergence

F. Jirásek, J. Neustupa

What is examined is the modified system of equations that describes the unsteady motion of a viscous compressible fluid. Rothe-approximation series of weak solutions have been constructed. The weal; solution exists in an arbitrary time interval and that has been proved by means of convergent subseries. The system modification is due to continuity and a regularization operator which is applied to some members of the Novice-Stokes equations. An energetical inequality is derived. It does not depend on the regularization that has been used.

JTAM, Sofia, vol. 19 Issue 1 pp. 060-069 (1988), [Full Article]

Finite-Difference Numerical Analysis of the Thermo-Capillary Two-Dimensional Czochralski Crystal Growth

S. Tabakova
Center of Math., Bulg. Acad. Sci., Plovdiv

A two dimensional mathematical model is constructed to describe a thermocapillary Czochralski crystal growth process. It is shown that the model is over defined. One of the system parameters has been considered to be variable, which assures an unique solution. The crystal radius is chosen to be the additional unknown. The problem itself has been solved in two consecutive stages. The first stage determines the meniscus shape of the smelt free boundary in case of a fixed crystal radius. The modified Stefan problem can be solved in finite differences by means of a point net, which is fixed too. The second stage determines a new crystal radius using the interphase boundary position. Then, we return to the first stage. A radius with a desired accuracy can be obtained repeating the process. The numerical results of Ge monocrystals are analyzed when the wetting smelt-crystal angle and the crucible temperature have been changed.

JTAM, Sofia, vol. 19 Issue 1 pp. 070-080 (1988), [Full Article]

Statistic and Dynamic Stability of an Elliptic Cylindrical Shell under Axial Loading

Nguyen Tien Chiong
High. Inst. Arch Civ. Eng., 1 Hr. Smirnenski, Sofia

The present paper proposes an approach to examine statistic and dynamic stability of an elliptic cylindrical shell under axial loading. The oscillation of the normal shell displacement is assumed proportional to the ellipse radius, i.e. it is inverse proportional to the shell curvature. What is analyzed is the eccentricity influence on the critical force and frequency. The basic shell proper frequency is analyzed too.

JTAM, Sofia, vol. 19 Issue 1 pp. 081-086 (1988)

A Spatial Hybrid Finite Element for Hyperboloid-Paraboloid Shell Investigation

D. Ljutskanov
High. Inst. Arch. Civ. Eng., I Hr. Smirnenski, Sofia

A spatial curve hybrid finite element with thirty two degrees of freedom is developed to examine sloping plan rectangular hyperboloid-paraboloid shells. The element stiffness matrix has been obtained using a suitable function choise. The functions themselves approximate the element domain tensions and the boundary displacements. A numerical comparison has been made with some known solutions.

JTAM, Sofia, vol. 19 Issue 1 pp. 087-091 (1988)

Solving the Optimum Form Problem of a Momentumless Shell by the Boundary Element Method

G. Gospodinov, O. Ianatchkov
High. Inst. Arch. Civ. Eng., 1 Hr. Smirnenski

The boundary element method is applied to solve the optimum form problem of a momentum less shell. The differential equation, which describes the shell stressed state, has been transformed to Poisson differential equation by means of a suitable affine transformation and with respect to the shell surface function. An integral equation obtained applying the corresponding Green's formula and accounting for the boundary value conditions. It contains some unknown functions of the body contour and is solved numerically. The contour is divided into definite boundary elements and the unknown function is approximated. A numerical example is solved. What is traced is the shell form that has been obtained.

JTAM, Sofia, vol. 19 Issue 1 pp. 092-096 (1988)

A Note on the Paper by K. Shulev `A Solution of the Stokes' Problem for a Circular Cylinder'

C. Christov
Inst. Mech. Biomech., Bulg. Acad. Bl. 8

JTAM, Sofia, vol. 19 Issue 1 pp. 097-098 (1988), [Full Article]

Remark on `A Solution of the Stokes' Problem for a Circular Cylinder'

M.M. Konstantinov
Inst. Techn. Cyb. Rob., 1113 Sofia

JTAM, Sofia, vol. 19 Issue 1 pp. 099-099 (1988), [Full Article]