Issue 3
JTAM, Sofia, vol. 42 Issue 3 (2012)

On Traveling Waves in Lattices: The Case of Riccati Lattices

Zlatinka I. Dimitrova
“G. Nadjakov” Institute of Solid State Physics, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chausse 72, 1784, Sofia, Bulgaria


The method of simplest equation is applied for analysis of a class of lattices described by differential-difference equations that admit traveling-wave solutions constructed on the basis of the solution of the Riccati equation. We denote such lattices as Riccati lattices. We search for Riccati lattices within two classes of lattices: generalized Lotka–Volterra lattices and generalized Holling lattices. We show that from the class of generalized Lotka–Volterra lattices only the Wadati lattice belongs to the class of Riccati lattices. Opposite to this many lattices from the Holling class are Riccati lattices. We construct exact traveling wave solutions on the basis of the solution of Riccati equation for three members of the class of generalized Holling lattices.

JTAM, Sofia, vol. 42 Issue 3 pp. 03-22 (2012), [Full Article]

Fracture in Composites – An Overview (Part II)

V. I. Rizov
Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1, Chr. Smyrnensky Blvd, 1046 Sofia, Bulgaria

An overview of the literature for the last twenty years on the fracture mechanics of unidirectional fibre reinforced polymer composites is presented. Pure mode (I, II, and III) as well as mixed mode longitudinal cracks (i.e., cracks that propagate along the fibres) are considered mainly. It is shown that the strain energy released rate is the most widely used parameter for fracture toughness characterization. Various solutions for determination of the strain energy release rate in composites using linear-elastic fracture mechanics are presented. Studies on fracture in composite sandwich structures are reviewed, too. Some analyses of damages and their influence on fracture behaviour also are considered. Topical problems of composite fracture mechanics are formulated.

JTAM, Sofia, vol. 42 Issue 3 pp. 23-32 (2012), [Full Article]

Reflection of Plane Waves in a Rotating Transversly Isotropic Magneto-Thermoelastic Solid Half-Space

Baljeet Singh1, Anand Kumar Yadav2
1Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh, India
2Department of Mathematics, Shishu Niketan Model Senior Secondary School, Chandigarh, India

The governing equations of a rotating transversely isotropic magnetothermoelastic medium are solved to obtain the velocity equation, which indicates the existence of three quasi plane waves. Reflection of these plane waves from a stress-free thermally insulated surface is studied to obtain the reflection coefficients of various reflected waves. The effects of anisotropy, rotation, thermal and magnetic fields are shown graphically on these coefficients.

JTAM, Sofia, vol. 42 Issue 3 pp. 33-60 (2012), [Full Article]

Mechanical Behaviour of Conventional Materials at Experimental Conditions of Deep Drawing Technological Process

N. Nikolov, D. Pashkouleva, V. Kavardzhikov
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria

The paper deals with experimental investigations on the mechanical behaviour of body-centred-cubic (BCC) and face-centred-cubic (FCC)-conventionally structured sheet metalic-metalic materials under stress-strain conditions of a deep drawing process determined by a coefficient close to the limiting one for Steel 08 and punch diameter of 50 mm. The mechanical characteristics of the investigated materials are identified by one-dimensional tension tests. The materials’ responses, as results of identical loading conditions, are described by the change of blank sizes and characteristics of the forming processes. The chosen deformation path ensures obtaining a qualitative steel piece and leads to failures of aluminium and brass blanks. The reported results could be useful for investigations and predictions of the mechanical responses of such type metallic structures applying microscopic instrumented observations and numerical simulations.

JTAM, Sofia, vol. 42 Issue 3 pp. 61-74 (2012), [Full Article]

Elastic Wavefield Evaluation in Discontinuous Poroelastic Media by BEM: SH-Waves

Petia S. Dineva1, Frank Wuttke2, George D. Manolis3
1Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria
2Chair of Geomechanical Modeling, Bauhaus University 99421 Weimar, Germany
3Department of Civil Engineering, Aristotle University, 54124 Thessaloniki, Greece

This work examines the anti-plane strain elastodynamic problem for poroelastic geological media containing discontinuities in the form of cavities and cracks. More specifically, we solve for: (i) a mode III crack; (ii) a circular cylindrical cavity, both embedded in an infinite poroelastic plane; and (iii) a mode III crack in a finite-sized poroelastic block. The source of excitation in all cases are time-harmonic, horizontally polarized shear (SH) waves. These three cases depict a situation whereby propagating elastic waves are diffracted and scattered by the presence of discontinuities in poroelastic soil, and this necessitates the computation of stress concentration factors (SCF) and stress intensity factors (SIF). Thus, the sensitivity of the aforementioned factors to variations in the material parameters of the surrounding poroelastic continuum must be investigated. Bardet’s model is introduced by assuming saturated soils as the computationally efficient viscoelastic isomorphism to Biot’s equations of dynamic poroelasticity, and stress fields are then evaluated for an equivalent one-phase viscoelastic medium. The computational tool employed is an efficient boundary element method (BEM) defined in terms of the non-hypersingular, traction-based formulation. Finally, the results obtained herein demonstrate a marked dependence of the SIF and the SCF on the mechanical properties of the poroelastic continuum, while the advantages of the proposed method as compared to alternative analytical and/or numerical approaches are also discussed.

JTAM, Sofia, vol. 42 Issue 3 pp. 75-100 (2012), [Full Article]