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Volume 7, Number 5, October 2018

A hierarchical multi-scale modeling strategy devoted to the study of a Bitumen-Bound Gravel (BBG) is presented in this paper. More precisely, the paper investigates the temperature-dependent linear viscoelastic of the material when submitted to low deformations levels and moderate number of cycles. In such a hierarchical approach, 3D digital Representative Elementary Volumes are built and the outcomes at a scale (here, the sub-mesoscale) are used as input data at the next higher scale (here, the mesoscale). The viscoelastic behavior of the bituminous phases at each scale is taken into account by means of a generalized Maxwell model: the bulk part of the behavior is separated from the deviatoric one and bulk and shear moduli are expanded into Prony series. Furthermore, the viscoelastic phases are considered to be thermorheologically simple: time and temperature are not independent. This behavior is reproduced by the Williams-Landel-Ferry law. By means of the FE simulations of stress relaxation tests, the parameters of the various features of this temperature-dependent viscoelastic behavior are identified.

Key Words
hierarchical multi-scale modeling; road aggregates; bitumen; viscoelasticy; Prony series; thermorheological simplicity; WLF law; standardized elastic moduli; standardized volume moduli

Libasse Sow:
1) Laboratoire de Genie Civil et Genie Mecanique (LGCGM), INSA de Rennes, France
2) Ecole Superieure Polytechnique, Universite Cheikh Anta Diop de Dakar, Senegal
Fabrice Bernard and Siham Kamali-Bernard: Laboratoire de Genie Civil et Genie Mecanique (LGCGM), INSA de Rennes, France
Cheikh Mouhamed Fadel Kebe: Ecole Superieure Polytechnique, Universite Cheikh Anta Diop de Dakar, Senegal

The paper deals with the study of the dynamics of the oscillating moving ring load acting in the interior of the hollow circular cylinder surrounded by an elastic medium. The axisymmetric loading case is considered and the study is made by employing the exact equations and relations of linear elastodynamics. The focus is on the influence of the oscillation of the moving load and the problem parameters such as the cylinder\'s thickness/radius ratio on the critical velocities. At the same time, the dependence between the interface stresses and load moving velocity under various frequencies of this load, as well as the frequency response of the mentioned stresses under various load velocity are investigated. In particular, it is established that oscillation of the moving load can cause the values of the critical velocity to decrease significantly and at the same time the oscillation of the moving load can lead to parametric resonance. It is also established that the critical velocity decreases with decreasing of the cylinder\'s thickness/radius ratio.

Key Words
critical velocity; oscillating moving load; frequency response; parametric resonance; stress distribution

Surkay D. Akbarov:
1) Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering,
Yildiz Campus, 34349, Besiktas, Istanbul-Turkey
2) Institute of Mathematics and Mechanics of National Academy of Science of Azerbaijan, 37041, Baku, Azerbaijan
Mahir A. Mehdiyev:
1) Institute of Mathematics and Mechanics of National Academy of Science of Azerbaijan, 37041, Baku, Azerbaijan
2) Azerbaijan State Economic University, Department of Mathematics, Baku, Azerbaijan

The moment-resistant steel frames are frequently used as a load-bearing structure of buildings. Global response of a moment-resistant frame structure strongly depends on connections behavior, which can significantly influence the response and load-bearing capacity of a steel frame structure. The analysis of a steel frame with included joints behavior is the main focus of this work. In particular, we analyze the behavior of two connection types through experimental tests, and we propose numerical beam model capable of representing connection behavior. The six experimental tests, under monotonic and cyclic loading, are performed for two different types of structural connections: end plate connection with an extended plate and end plate connection. The proposed damage-plasticity model of Reissner beam is able to capture both hardening and softening response under monotonic and cyclic loading. This model has 18 constitutive parameters, whose identification requires an elaborate procedure, which we illustrate in this work. We also present appropriate loading program and arrangement of measuring equipment, which is crucial for successful identification of constitutive parameters. Finally, throughout several practical examples, we illustrate that the steel structure connections are very important for correct prediction of the global steel frame structure response.

Key Words
steel frame structures; connection behavior; end plate connection; parameters identification

Ismar Imamovic:
1) Laboratoire Roberval, Universite de Technologie de Compiegne / Sorbonne Universites, France
2) Faculty of Civil Engineering, University Sarajevo, Sarajevo, Bosnia and Herzegovina
Adnan Ibrahimbegovic: Laboratoire Roberval, Universite de Technologie de Compiegne / Sorbonne Universites, France
Esad Mesic: Faculty of Civil Engineering, University Sarajevo, Sarajevo, Bosnia and Herzegovina

This paper discusses the issues associated with modeling frictional contact between solid bodies undergoing large deformations. The most common model for friction on contact interfaces in solid mechanics is the Coulomb friction model, in which two distinct responses are possible: stick and slip. Handling the transition between these two phases computationally has been a source of algorithmic instability, lack of convergence and non-unique solutions, particularly in the presence of large deformations. Most computational models for frictional contact have used penalty or updated Lagrangian approaches to enforce frictional contact conditions. These two approaches, however, present some computational challenges due to conditioning issues in penalty-type implementations and the iterative nature of the updated Lagrangian formulation, which, particularly in large simulations, may lead to relatively slow convergence. Alternatively, a plasticity-inspired implementation of frictional contact has been shown to handle the stick-slip conditions in a local, algorithmically efficient manner that substantially reduces computational cost and successfully avoids the issues of instability and lack of convergence often reported with other methods (Laursen and Simo 1993). The formulation of this approach, however, has been limited to the small deformations realm, a fact that severely limited its application to contact problems where large deformations are expected. In this paper, we present an algorithmically consistent formulation of this method that preserves its key advantages, while extending its application to the realm of large-deformation contact problems. We show that the method produces results similar to the augmented Lagrangian formulation at a reduced computational cost.

Key Words
frictional contact; Coulomb model; large deformations

Layla. K. Amaireh: Applied Science University, Amman, Jordan
Ghadir Haikal: Lyles School of Civil Engineering, Purdue University, West Lafayette, Indiana, USA

We theoretically consider a possible influence of periodic oceanic tides on non-periodic changes in the dynamics of the Earth and Moon over a long time scale. A particular emphasis will be placed on the contribution from rotating tidal waves, which rotate along the inner edge of an oceanic basin surrounded by topographic boundary. We formulate the angular momentum and the mechanical energy of the rotating tidal wave in terms of celestial parameters with regard to the Earth and Moon. The obtained formula are used to discuss how the energy dissipation in the rotating tidal wave should be relevant to the secular variation in the Earth\'s spin rotation and the Earth-Moon distance. We also discuss the applicability of the formula to general oceanic binary planets subject to tidal coupling.

Key Words
ocean tide; tidal energy dissipation; Kelvin wave; celestial mechanics; lunar orbit

Natsuki Uchida and Hiroyuki Shima: Department of Environmental Sciences, University of Yamanashi, 4-4-37, Takeda, Kofu, Yamanashi 400-8510, Japan

Laser beam welding is more advantageous compared to conventional methods. Titanium/Aluminium dissimilar alloy thin sheet metals are difficult to weld due to large difference in melting point. The performance of the weldment depends upon interlayer formation and distribution of intermetallics. During welding, aluminium gets lost at the temperature below the melting point of titanium. Therefore, it is needed to improve a new metal joining techniques between these two alloys. The present work is carried for welding TI6AL4V and AA2024 alloy by using Nd:YAG Pulsed laser welding unit. The performance of the butt welded interlayer structures are discussed in detail using hardness test and SEM. Test results reveal that interlayer fracture is caused near aluminium side due to low strength at the weld joint.

Key Words
titanium; aluminium; laser welding; interlayer characteristics

Kalaiselvan K.: KMCT College of Engineering, Calicut, Kerala, India
Elango A.: Department of Mechanical Engineering, A C College of Engg and Tech, Karaikudi, Tamilnadu, India
Nagarajan N.M.: Department of Mechanical Engineering, National Institute of Technology, Calicut, Kerala, India
Mathiazhagan N.: Department of Mech. Engg, Meenakshi Ramaswamy Engineering College, Ariyalur, Tamilnadu, India
Vignesh Kannan: Sappi Consultant, IBM India Pvt Ltd, Hyderabad, India

Dynamic problems arising from the Euler-Bernoulli beam model with inhomogeneous elastic properties are considered. The method of Green\'s function and perturbation theory are employed to find the deflection in the beam correct to the first-order. Eigenvalue problems appearing from transverse vibrations of inhomogeneous beams in linear and nonlinear cases are also discussed.

Key Words
vibration; inhomogeneous; Euler-Bernoulli beam

Ebrahim S. Bakalah, F.D. Zaman and Khairul Saleh: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

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