Computational Methods in Engineering

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One of the great enemies of rubber compounds is heat. Heat will cause chemical and physical degradation of vulcanized rubber as well as a considerable loss in its strength. A major source of heat generation in a tire is due to internal friction resulting from the viscoelastic deformation of the tire as it rolls along the road. Another source of heat generation in a tire is due to its contact friction with the road. Prediction of the temperature rise at different parts of the tire will help to detect the behavior of the tire as regards its strength and its failure. In the present work, initially the data required for the thermal analysis of the tire are determined which include: the thermal conductivity of rubber compounds, the tire rolling resistance and its heat build-up rate. The thermomechanical analysis of a typical tire then follows based on the thermodynamics of an irriversible process. The mechanical dissipatives, i.e. the hystersis losses are assummed to be the major source of heat in the mathematical formulation. A finite element code is developed for two-dimensional heat transfer analysis of the tire. The results obtained show that the highest temperature rise will occur on the carcass-tread interface in a tire specially at heavy loading and under high speed conditions. Keywords: Heat Generation, Rubber, Contact Friction, Design, Finite Element, Viscoelastic Deformation

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This paper presents a new super-element with twelve degrees of freedom for latticed columns. This elements is developed such that it behaves, with an acceptable approximation, in the same manner as a reference model does. The reference model is constructed by using many Solid elements. The cross section area, moments of inertia, shear coefficient and torsoinal rigidity of the developed new element are derived. Since the reference model has a large number of degrees of freedom (especially for nonlinear cases), computation of the equivalent essential parameters of the proposed element is very time consuming, so, a model using only beam elements is also presented. For the super element, a general purpose program is developed that is capable of performing linear and nonlinear analysis of 3D-frames with latticed columns. In order to derive the essential parameters of the proposed super-element, many latticed columns are analyzed while shear deformations are taken into consideration. Using these essential equivalent parameters approximate relations are proposed for the compution of parameters of any latticed column based on geometric characteristics. Finally, to show the accuracy of the proposed element, several examples are presented. Keywords: Finite elements, Super-element, Latticed column, Shear deformations, 3D-frames

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This paper presents the results of a recent study about the following aspects relevant to tunneling in soft grounds:e) The domain of deformations due to tunneling in soft ground can be specified within a boundary of a parabolic shape. This boundary is defined by a parabolic formula as a function of a central angle which depends on the soil type i.e., either cohesive or cohesionless. This parabolic shape can also be verified by a finite element computation.f) A finite element program has been applied to investingate the deformation characteristics around and above circular tunnels and to find the settlement ratio as a function of known variables such as, depth ratio, modulus of elasticity, and the thickness of soil layer beneath the tunnel. The finite element computations were carried out by assuming a given distribution of displacements around the tunnel perimeter, for which reason the method may be called “compulsory displacements”. It was found that although all the variables mentioned affect both the settlement ratio and the type of soil deformations, changing the values of modulus of elasticity affects only on the amount of deformation components, but not the settlement ratio.g) The results of finite element computations for the settlement ratio have been compared to other analytical curves and empirical data from some available case studies from which excellent agreements were found. also the contours of Equal deformation components from the finite element program and from the simple formulae proposed by the author were found to be quite similar and in acceptable agreement.h) Because the results obtained from the proposed formulae for the distribution of settlement at the ground surface are in excellent agreement with the relationships recently proposed by Loganathan & Poulos and the empirical data available, it is concluded that the simple analysis proposed here and the finite element computations based on the elasticity assumption can both be used to predict the deformation pattern around excavations in soft ground.

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In this paper, an elastic constitutive model based on the Eulerian corotational rate of the logarithmic strain tensor is proposed. Using this model, the large deformation of a closed cycle containing tension, shear, compression and inverse shear is analyzed. Since the deformation path includes a closed cycle and the material is considered as an isotropic elastic material, the normal and shear components of the stress at the end of the cycle must vanish. Using conventional constitutive models, the non-zero solution for the stress components is obtained. Using the proposed constitutive model, the normal and shear components of stress at the end of the cycle are obtained to be exactly equal to zero.

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Among the titanium alloys, Ti-6Al-4V is the most widely used. In the present work, the uniaxial hot compressive behavior of Ti-6Al-4V has been investigated under constant strain rates. A series of dilatometery experiments were carried out to determine the transformation temperatures at different cooling rates. Specimens were homogenized at 1050 °C for 10 minutes followed by fast cooling to different straining temperatures from 1050 to 850°C. The cooling rate was chosen fast enough to prevent high temperature transformation during cooling. A series of isothermal compression tests were conducted at different temperatures of 850, 900, 950, 1000, 1050°C at constant true strain rates of 0.1, 0.01 and 0.001 s-1, respectively. Samples were uniaxialy compressed to a true strain of 0.55 followed by water quenching to room temperature. The apparent activation energy for compression in two phase regions was calculated at 840 KJmol-1. The partial globularization of a-phase was observed in the specimens deformed at low strain rates and at temperatures near the transformation zone followed by annealing.

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In this study, two CCCT diagrams are drawn to be compared with a CCT diagram. The CCCT diagrams represent continuous cooling transformations in stress assisted state. The increased Md and Bd temperatures of CCCT diagrams were also compared with those of the CCT diagrams and the cause was investigated from both thermodynamic and metallurgical viewpoints. Thermodynamic examinations revealed that stress causes the mechanical driving force to increase but the total free energy of transformation to decrease hence, Md and Bd will rise. Metallurgical investigations showed that if deformation temperatures are selected in a manner to increase the structural strength of the original austenite grains prior to deformation, the shear force required for martensite and bainite transformations will arduously obtain hence, Md and Bd will fall. However, if recrystallization or full recovery occurs during or after deformation, interior grain structure softens and the shear force required for martensite and bainite transformations will readily obtain hence, Md and Bd will rise. It was also found that the nose in CCCT curves are shifted to the left as compared to that of CCT curves. This indicates that deformation of steel enhances bainite formation more readily than that of the martensite phase.

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The cross-stream migration of a deformable drop in two-dimensional Poiseuille flow at finite Reynolds numbers is studied numerically. In the limit of a small Reynolds number (<1), the motion of the drop depends strongly on the ratio of the viscosity of the drop fluid to the viscosity of the suspending fluid. For a viscosity ratio 0.125, the drop moves toward the centre of the channe while for the ratio 1.0, it moves away from the centre until halted by wall repulsion. The rate of migration increases with the deformability of the drop. At higher Reynolds numbers (5-50), the drop either moves to an equilibrium lateral position about halfway between the centerline and the wall according to the so-called Segre-Silberberg effect or undergoes oscillatory motions. The steady-state position depends only weakly on the various physical parameters of the flow but the length of the transient oscillations increases as Reynolds number is raised, the density of the drop is increased, or the viscosity of the drop is decreased. Once the Reynolds number is high enough, the oscillations appear to persist forever and no steady state is observed. The numerical results are in good agreement with experimental observations, especially for drops that reach steady-state lateral position.

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A semi-analytical finite strip method was developed for the buckling analysis of laminated composite plates based on zigzag and third order shear deformation theories. The displacement functions of the plates were evaluated using a continuous harmonic function series in the longitudinal direction that satisfied the simply supported boundary conditions and a piecewise interpolation polynomial in the transverse direction. By considering the displacement-strain relations and strain-stress relations, the standard and geometric matrices were evaluated using the virtual work principle. The numerical results related to the buckling of single-layer and multi-layer plates were presented based on two different plate theories. The effects of different  boundary conditions, length to thickness ratio, fiber orientation and modulus of elasticity were also investigated through numerical examples.

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The stored deformation energy in the dislocation structures in a polycrystalline metal can provide a sufficient  driving force to move grain boundaries during annealing. In this paper, a thermodynamically-consistent three-dimensional, finite-strain and dislocation density-based crystal viscoplasticity constitutive theory has been developed to describe the distribution of stored energy and dislocation density in a polycrystalline metal. The developed constitutive equations have been numerically implemented into the Abaqus finite element package via writing a user material subroutine. The simulations have been performed using both the simple Taylor model and the full micromechanical finite element model. The theory and its numerical implementation are then verified using the available data in literature regarding the physical experiments of the single crystal aluminum. As an application of the developed constitutive model, the relationship between the stored energy and the strain induced grain boundary migration in aluminum polycrystals has been investigated by the Taylor model and also, the full finite element model. The obtained numerical results indicated that the Taylor model could not precisely simulate the distribution of the stored deformation energy within the polycrystalline microstructure; consequently, the strain induced grain boundary migration.  This is due to the fact that the strain induced grain boundary migration in a plastically deformed polycrystalline microstructure is principally dependent on the spatial distribution of the stored deformation energy rather than the overall stored energy value.

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Plates made of laminated composite materials with variable stiffness can have wide applications in various branches of engineering due to such advantages as high strength /stiffness to weight ratio. In these composites, curved fibers are used to reinforce each lamina instead of the straight fibers. In this paper, the application of finite strip method for the buckling analysis of moderately thick composite plates with variable stiffness is investigated. For buckling analysis, a semi-analytical finite strip method based on the first-order shear deformation theory is employed. In this method, all displacements are presumed by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. The minimum potential energy method has been used to develop the stability formulations. This analysis examines the effect of using curved fibers instead of straight fibers on the laminate composites. The critical loads obtained from this analysis are compared with those of other researchers and the efficiency and accuracy of the developed finite strip method are confirmed. Comparison of the analysis results of these plates shows that changing the slope of the fibers can lead to a significant change in the buckling response. Also, increasing the number of the terms of shape functions in the longitudinal direction has a significant effect on the convergence to the desired results.

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In this paper, nonlinear bending analysis of functionally graded rectangular and sectorial micro/nano plates is investigated using the modified couple stress theory. For this purpose, a higher-order shear deformation theory and von Kármán geometrically nonlinear theory are employed. The equilibrium equations and the boundary conditions for rectangular and annular sector plates are derived from the principle of minimum total potential energy and solved using the Semi-Analytical Polynomial Method (SAPM). One of the advantages of the implemented shear deformation theory is removing the defects of higher order shear deformation theory, and obtaining the response of the first and the third-order shear deformation theories at the same time. Afterwards, beside investigating the benefits of this theory compared with other ones, the results are verified with those by other researches. At the end, the effects of length scale parameter, boundary conditions, power law index, and geometrical dimensions are investigated

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In order to simulate multiphase flow in the presence of dielectric current using the Lattice Boltzmann Method (LBM), three distribution functions are used, two of which for using the He-Chen-Zhang phase field model and one for solving the potential field. Initially, the ability of the code to apply surface tension was tested using the Laplace law and the drop release test. The results show that the present numerical program is capable of modeling well the regulated surface tension force. Then, the Rayleigh–Taylor instability simulation is used to evaluate the code's ability in applying volume forces. The results by the developed numerical program are in good agreement with the numerical results in the references. In this study, for the first time, the effect of electric field on a droplet immersed in another fluid and the presence of droplet in a porous medium is investigated by LBM. For this purpose, first the droplet motion due to the potential difference in the porous and non-porous media is investigated. After modeling the droplet motion due to the potential difference, two electric fields areapplied to the droplet to reverse the droplet deformation. Through various tests, it is shown that at a given potential difference, the droplet breaks down after much deformation and is divided into smaller droplets. The decomposition of droplets in a pre-mixed emulsion is a common technique in the production of monodisperse droplets. The presence of monodisperse droplets in an emulsion improves the physical properties of polymer science experts.