Issue 2
JTAM, Sofia, vol. 48 Issue 2 (2018)

PERFORMANCE ASSESSMENT OF VARIATIONAL INTEGRATORS FOR THERMOMECHANICAL PROBLEMS

Dominik Kern1, Ignacio Romero2, Sergio Conde Martín3, Juan Carlos García-Orden3
1TU Chemnitz, Reichenhainer Straße 70, 09126 Chemnitz, Germany
2ETSI Industriales, Technical University of Madrid, Madrid, Spain
3ETSI de Caminos, Canales y Puertos, Technical University of Madrid, Spain


Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms is still an active topic. Conservative formulations, such as the thermo-elastic case without heat conduction, fit well into a variational framework and have been solved with variational integrators, whereas the inclusions of viscosity and heat conduction are still under investigation. To encompass viscous forces and the classical heat transfer (Fourier’s law), an extension of Hamilton’s principle is required. In this contribution we derive vari-ational integrators for thermo-viscoelastic systems with classical heat transfer. Their results are compared for two discrete model problems vs. energy-entropy-momentum methods.

JTAM, Sofia, vol. 48 Issue 2 pp. 03-23 (2018), [Full Article]

DYNAMIC RESPONSE OF A CRACKED VISCOELASTIC ANISOTROPIC PLANE USING BOUNDARY ELEMENTS AND FRACTIONAL DERIVATIVES

Tsviatko V. Rangelov1, Petia S. Dineva2, George D. Manolis3
1Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
2Institute of Mechanics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
3Department of Civil Engineering, Aristotle University, Thessaloniki, GR-54124, Greece

The aim of this study is to develop an efficient numerical technique using the non-hypersingular, traction boundary integral equation method (BIEM) for solving wave propagation problems in an anisotropic, viscoelastic plane with cracks. The methodology can be extended from the macro-scale with certain modifications to the nano-scale. Furthermore, the proposed approach can be applied to any type of anisotropic material insofar as the BIEM formulation is based on the fundamental solution of the governing wave equation derived for the case of general anisotropy. The following examples are solved: (i) a straight crack in a viscoelastic orthotropic plane, and (ii) a blunt nano-crack inside a material of the same type. The mathematical modelling effort starts from linear fracture mechanics, and adds the fractional derivative concept for viscoelastic wave propagation, plus the surface elasticity model of M. E. Gurtin and A. I. Murdoch, which leads to nonclassical boundary conditions at the nano-scale. Conditions of plane strain are assumed to hold. Following verification of the numerical scheme through comparison studies, further numerical simulations serve to investigate the dependence of the stress intensity factor (SIF) and of the stress concentration factor (SCF) that develop in a cracked inhomogeneous plane on (i) the degree of anisotropy, (ii) the presence of viscoelasticity, (iii) the size effect with the associated surface elasticity phenomena, and (iv) finally the type of the dynamic disturbance propagating through the bulk material.

JTAM, Sofia, vol. 48 Issue 2 pp. 24-49 (2018), [Full Article]

A TILTED LORENTZ FORCE EFFECT ON POROUS MEDIA FILLED WITH NANOFLUID

M. Muthtamilselvan1, S. Sureshkumar2
1Department of Mathematics, Bharathiar University, Coimbatore-641046, India
2Department of Mathematics, Kongu Engineering College, Perundurai, Erode-638052, India

This paper is intended to investigate the effects of an inclined magnetic field on the mixed convection flow in a lid-driven porous enclosure filled with nanofluid. Both the left and right vertical walls of the cavity are thermally insulated while the bottom and top horizontal walls are maintained at constant but different temperatures. The governing equations are solved numerically by using finite volume method on a uniformly staggered grid system. The computational results are obtained for various combinations of Richardson number, Darcy number, Hartmann number, inclination angle of magnetic field, and solid volume fraction. It is found that the presence of magnetic field deteriorates the fluid flow, which leads to a significant reduction in the overall heat transfer rate. The inclination angle of magnetic field plays a major role in controlling the magnetic field strength and the overall heat transfer rate is enhanced with the increase of inclination angle of magnetic field. Adding the nanoparticles in the base fluid significantly increases the overall heat transfer rate in the porous medium whether the magnetic field is considered or not.

JTAM, Sofia, vol. 48 Issue 2 pp. 50-71 (2018), [Full Article]

MHD BOUNDARY LAYER FLOW OF NANOFLUID THROUGH A POROUS MEDIUM OVER A STRETCHING SHEET WITH VARIABLE WALL THICKNESS: USING CATTANEO–CHRISTOV HEAT FLUX MODEL

R.V.M.S.S. Kiran Kumar, S.V.K. Varma
Department of Mathematics, Sri Venkateswara University, Tirupati-517502, A. P, India

The hydromagnetic nanofluid flow over a stretching sheet in a porous medium with variable wall thickness in the presence of Brownian motion and thermophoresis is investigated. The heat transfer characteristics with variable conductivity are explored by using Cattaneo-Christov heat flux model. The governing non-linear ordinary differential equations are solved by using boundary value problem default solver in MATLAB bvp4c package. The impact of various important flow parameters on velocity, temperature and nanoparticle concentration as well as the friction factor coefficient and the rate of heat and mass transfer coefficients are presented and discussed through graphs and tables. It is found that the fluid velocity is accelerated with an increase in wall thickness parameter for n > 1, while the reverse trend is observed for n < 1.

JTAM, Sofia, vol. 48 Issue 2 pp. 72-92 (2018), [Full Article]

ROTATIONAL EFFECTS ON PROPAGATION OF RAYLEIGH WAVE IN A MICROPOLAR PIEZOELECTRIC MEDIUM

Baljeet Singh1, Ritu Sindhu2
1Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh, India
2Department of Mathematics, Maharishi Dayanand University, Rohtak, India

In this paper, the governing equations of a linear, homogeneous and transversely isotropic rotating micropolar piezoelectric medium are solved for surface wave solutions. The appropriate solutions satisfying the radiation conditions are obtained in a half-space. These solutions are applied to suitable boundary conditions at the free surface of the half- space. A frequency equation for Rayleigh wave is obtained for both charge free and electrically shorted cases. Using iteration method, the non-dimensional wave speed of Rayleigh wave is computed for relevant material constants modelling the medium. The effects of rotation, piezoelectricity, frequency and material parameters are observed graphically on the propagation speed.

JTAM, Sofia, vol. 48 Issue 2 pp. 93-105 (2018), [Full Article]