Journal of Theoretical and Applied Mechanics, Sofia, vol. 50 Issue 4 (2020)

Table of contents



MHD ON A CYLINDER IMPLANTED IN A POROUS MEDIA OF MICROPOLAR FLUID

Madasu Krishna Prasad, Tina Bucha
Department of Mathematics, National Institute of Technology, Raipur-492010, Chhattisgarh, India


This article handles MHD flow of micropolar fluid through a rigid cylindrical particle implanted in a porous media. Flow is considered to be uniform at a distance away from the cylinder. A uniform magnetic field is applied perpendicular to the flow direction. Motion in porous media is governed by Brinkman's equation. At the surface of cylinder, we assume no-slip of velocity components and no-spin of microrotational component. Exact solution for the problem is reported. Influence of Hartmann number, permeability and micropolarity parameters on the coefficient of drag and tangential velocity are discussed numerically. In deduction, various results of flow past impenetrable cylinder are obtained which are in good agreement with earlier published works.

JTAM, Sofia, vol. 50 Issue 4 pp. 307-320 (2020), [Full Article]




INFLUENCE OF COLUMNS OF SUPPORTED CONE ROOFS ON NATURAL FREQUENCIES OF STORED LIQUID

Lyubomir Zdravkov
University of Architecture, Civil Engineering and Geodesy, 1 Hr. Smirnenski blvd., 1046, Sofia, Bulgaria


Fluid, stored in tank, does not have behaviour of a solid during seismic impact. Hypothetically, the liquid response could be divided into two components – passive and active. Each of them has own natural frequencies. The standards have a various approach to determine the natural frequency of the active component. A common in all of them is that only liquid level-body radius ratio is taken into account. The possible presence of elements inside the tanks is not taken into account. A considerable number of tanks have cone roofs, supported by internal columns, which contact with the liquid. The question is, could we be able to follow the procedures described in the standards, for reservoirs with columns in the liquid?

JTAM, Sofia, vol. 50 Issue 4 pp. 321-329 (2020), [Full Article]




ANALYSIS OF MOTION OF SUBSTANCE IN CHANNEL OF NETWORK IN PRESENCE OF PUMPING

Nikolay K. Vitanov1, Rumen Borisov1, Tsvetelina Ivanova1, Zlatinka I. Dimitrova2
1Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev. Str., Bl. 4, 1113 Sofia, Bulgaria
2G. Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria


We study motion of substance in a channel of network in presence of possibility for inflow of substance to nodes of the channel. Stationary state of motion of substance can exist in this case and we discuss conditions for existence of such state. We obtain probability distribution connected to distribution of substance in nodes of channel.

JTAM, Sofia, vol. 50 Issue 4 pp. 330-337 (2020), [Full Article]




CHARACTERIZATION OF POROUS MEDIA BY A SIZE SENSITIVE HOMOGENIZATION APPROACH

Ludmila Parashkevova
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev. Str., Bl. 4, 1113 Sofia, Bulgaria


The present study concerns the mechanical properties assessment of porous media with a moderate porosity of a closed-cells type. On the base of the generalized mixture rule coupled with a size-sensitive variant of Mori-Tanaka theory the new explicit formulae are obtained. The elastic characteristics and the initial yield stress of a porous composite are calculated by two models, accounting for pore sizes. In both model variants the matrix is considered as a micropolar centrosymmetric medium. The size effect predicted depends on the ratio between the mean pore size/ the matrix intrinsic length. It is stronger if the pores are very small, but always remains limited.

JTAM, Sofia, vol. 50 Issue 4 pp. 338-353 (2020), [Full Article]




NEW RESULTS FOR THE MASS-INERTIAL PARAMETERS OF THE HUMAN BODY BASED ON 3D MATHEMATICAL MODELLING

Gergana Nikolova, Daniel Dantchev, Mihail Tsveov
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev. Str., Bl. 4, 1113 Sofia, Bulgaria


Geometric modelling is one of the methods for determination of the mass-inertial parameters of the different segments of the body, as well as of the body as a whole. The current article presents new 20-segment 3D mathematical model of the human body, generated in a computer environment, allowing the mass-inertial parameters of all body segments to be calculated. Some data obtained from it for all segments of the body are reported. We also present a brief review of some of our results related to (i) a new type of mathematical modelling of the thigh of the human body; (ii) investigation of mass – inertial characteristics in basic body position as selected by NASA. Next, we outline some further improvements and future developments of the models under consideration. Let us note that the proposed models are oriented towards applications in medicine (orthopaedics and traumatology), rehabilitation robotics, computer simulations, sports and areas such as ergonomics, forensics and more.

JTAM, Sofia, vol. 50 Issue 4 pp. 354-369 (2020), [Full Article]




BEM-DERIVED IMPEDANCE FUNCTIONS FOR 2D INHOMOGENEOUS SOIL MEDIA: AN ENGINEERING PRACTICE CASE STUDY

Georgios A. Chatzistefanou, George D. Manolis
Laboratory for Experimental Mechanics, Department of Civil Engineering, Aristotle University, GR-54124 Thessaloniki, Greece


A methodology is presented here for the determination of complex-valued dynamic impedance functions for arbitrarily shaped embedded strip foundations, by using the displacement-based boundary element method (BEM). More specifically, the formulation incorporates a frequency-dependent fundamental solution obtained in closed form for continuous soil inhomogeneity under plane strain conditions and for viscoelastic material behavior. The recovery of the impedance functions in engineering practice is illustrated via a case study of an instrumented and well-documented public building, whereby the BEM-derived stiffness and damping coefficients are compared to widely used impedance function formulations found in the literature. Finally, the challenges and shortcomings associated with the derivation and use of impedance functions for studying soil-structure interaction (SSI) problems are discussed, where it is pointed out that an effective approach seems to be a re-casting of the BEM formulation as a macro-element to be used in conjunction with a finite element method (FEM) representation of the structure in question.

JTAM, Sofia, vol. 50 Issue 4 pp. 370-388 (2020), [Full Article]




COMPARISON OF THE METHODS OF DETERMINING SIF AND ERR AND THEIR APPLICATION TO RECYCLED MATERIALS

Ana Yanakieva, Gergana Nikolova
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev. Str., Bl. 4, 1113 Sofia, Bulgaria


The paper presents summation of the results of a number of our studies treating the mechanical behaviour of cracked structural elements and especially the methods of determining the Stress Intensity Factor (SIF) and the Energy Release Rate (ERR). Two possible methods are outlined – an analytical one (using the energy approach of fracture mechanics) and a computational one (using ANSYS). Comparison of the results found using the two methods is made. A parametric analysis with respect to initial crack and external loading is also performed. The basic idea of the study is to analyse structural elements fabricated from recycled material using respective data published in literature.

JTAM, Sofia, vol. 50 Issue 4 pp. 389-396 (2020), [Full Article]