Journal of Theoretical and Applied Mechanics-Bulgaria has been selected for
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DOMINIK KERN 1 , IGNACIO ROMERO2 ,
SERGIO CONDE MARTÍN3 , JUAN CARLOS GARCÍA-ORDEN 3

1 TU Chemnitz, Reichenhainer Straße 70, 09126 Chemnitz, Germany
2 ETSI Industriales, Technical University of Madrid, Madrid, Spain
3 ETSI de Caminos, Canales y Puertos, Technical University of Madrid, Spain
[Received 7 November 2017. Accepted 24 November 2017]


PERFORMANCE ASSESSMENT OF VARIATIONAL
INTEGRATORS FOR THERMOMECHANICAL PROBLEMS


ABSTRACT: 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.

KEY WORDS: Variational integrators, energy-entropy-momentum methods, viscoelasticity, thermomechanical coupling, heat transfer.

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TSVIATKO V. RANGELOV1 , PETIA S. DINEVA2 ,
GEORGE D. MANOLIS 3

1 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
2 Institute of Mechanics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
3 Department of Civil Engineering, Aristotle University, Thessaloniki, GR-54124, Greece
[Received 31 October 2017. Accepted 11 January 2018]



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

ABSTRACT: 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.
KEY WORDS :
In-plane waves, viscoelasticity, fractional derivatives, anisotropy, cracks, nano-scale, surface elasticity, boundary elements, SIF, SCF.


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M. MUTHTAMILSELVAN1 , S. SURESHKUMAR2 ,
1  Department of Mathematics, Bharathiar University, Coimbatore-641046, India
2 Department of Mathematics, Kongu Engineering College, Perundurai, Erode-638052, India
[Received 4 January 2017. Accepted 6 January 2018]




A TILTED LORENTZ FORCE EFFECT ON POROUS MEDIA
FILLED WITH NANOFLUID

ABSTRACT: 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.
KEY WORDS:
Mixed convection; porous cavity; nanofluid; inclined magnetic field.

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R.V.M.S.S. KIRAN KUMAR , S.V.K. VARMA
Department of Mathematics, Sri Venkateswara University, Tirupati-517502, A. P, India
[Received 8 September 2017. Accepted 21 November 2017]



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

ABSTRACT: 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.
KEY WORDS :
Nanofluid flow; Magnetic field; Porous medium; Wall thickness parameter; variable thermal conductivity and molecular diffusivity.

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BALJEET SINGH1, RITU SINDHU2
1 Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh, India
2 Department of Mathematics, Maharishi Dayanand University, Rohtak, India
[Received 16 October 2017. Accepted 10 January 2018]



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

ABSTRACT: 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.
KEY WORDS :
Micropolar, piezoelectric, rayleigh wave, rotation, iteration method.

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