• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.1-14
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• 2007

Because of complexity, the literature regarding the free vibration analysis of a Timoshenko beam carrying "multiple" spring-mass systems is rare, particular that regarding the "exact" solutions. As to the "exact" solutions by further considering the joint terms of shear deformation and rotary inertia in the differential equation of motion of a Timoshenko beam carrying multiple concentrated attachments, the information concerned is not found yet. This is the reason why this paper aims at studying the natural frequencies and mode shapes of a uniform Timoshenko beam carrying multiple intermediate spring-mass systems using an exact as well as a numerical assembly method. Since the shear deformation and rotary inertia terms are dependent on the slenderness ratio of the beam, the shear coefficient of the cross-section, the total number of attachments and the support conditions of the beam, the individual and/or combined effects of these factors on the result are investigated in details. Numerical results reveal that the effect of the shear deformation and rotary inertia joint terms on the lowest five natural frequencies of the combined vibrating system is somehow complicated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.181-188
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• 1994

Generally, the structural material shows rate dependent behaviors, which require to constitute different strain-stress relations according to strain rates. Conventional rate- independent constitutive equations used in general purpose finite analysis programs are inadequate for dynamic finite strain problems. In this paper, a rate dependent constitutive equation for elastic-plastic material was developed. The plastic stretch rate was modeled based on slip model with dislocation velocity and density so that there is no yielding condition, and no loading conditions. Non-linear hardening rule was also introduced for finite strain. Material constants of present constitutive equation were determined by experimental data of mild steel. The constitutive equation was applied to uniaxile tension. It was appeared that the present constitutive equation well simulates rate dependent behaviors of mild steel.

• Structural Engineering and Mechanics
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• v.53 no.6
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• pp.1167-1182
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• 2015

In this study, the stresses and electric potential redistributions of a cylinder made from functionally graded piezoelectric material (FGPM) are investigated. All the mechanical, thermal and piezoelectric properties are modeled as power-law distribution of volume fraction. Using the coupled electro-thermo-mechanical relations, strain-displacement relations, Maxwell and equilibrium equations are obtained including the time dependent creep strains. Creep strains are time, temperature and stress dependent, the closed form solution cannot be found for this constitutive differential equation. A semi-analytical method in conjunction with the Mendelson method of successive approximation is therefore proposed for this analysis. Similar to the radial stress histories, electric potentials increase with time, because the latter is induced by the former during creep deformation of the cylinder, justifying industrial application of such a material as efficient actuators and sensors.

• Steel and Composite Structures
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• v.45 no.4
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• pp.535-546
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• 2022

The memory response of nonlocal systematical formulation size-dependent coupling of viscoelastic deformation and thermal fields for piezoelectric materials with dual-phase lag heat conduction law is constructed. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern control theory, is applied to the non-dimensional equations. The resulting formulation together with the Laplace transform technique is applied to solve a problem of a semi-infinite piezoelectric rod subjected to a continuous heat flux with constant time rates. The inversion of the Laplace transforms is carried out using a numerical approach. Some comparisons of the impacts of nonlocal parameters and time-delay constants for various forms of kernel functions on thermal spreads and thermo-viscoelastic response are illustrated graphically.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.130-133
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• 2008

The formability of DP steels can be affected by not only initial texture but also deformation texture evolved during plastic deformation. To investigate the evolution of deformation texture during deep drawing, deep drawing process for DP steels was carried out experimentally. A rate sensitive polycrystal model was used to predict texture evolution during deep drawing process. In order to evaluate the strain path during deep drawing, a steady state was assumed in the flange part of deep drawn cup. A rate sensitive polycrystal model successfully predicted the texture development in DP steels during deep drawing process. It was found that the final stable orientations were strongly dependent on the initial location in the blank.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.217-224
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• 2005

A higher order zig-zag shell theory is developed to refine the predictions of the mechanical and thermal behaviors partially coupled. The in-plane displacement fields are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field through the thickness. Smooth parabolic distribution through the thickness is assumed in the out-of-plane displacement in order to consider transverse normal deformation and stress. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses. Thus the proposed theory has only seven primary unknowns and they do not depend upon the number of layers. In the description of geometry and deformation of shell surface, all rigorous exact expressions are used. Through the numerical examples of partially coupled analysis, the accuracy and efficiency of the present theory are demonstrated. The present theory is suitable in the predictions of deformation and stresses of thick composite shell under mechanical and thermal loads combined.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.3
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• pp.47-52
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• 2011

A tracked vehicle is dependent on performance of power pack and suspension systems. Especially, road wheels which are components of suspension system contribute distributing vehicle weight on soil and preventing from misguiding tracks. In this study, the maximum force was calculated that a tracked vehicle is driven on the worst condition. And then, FE analyses were carried out to evaluate strength road wheel under maximum force condition. In standard of quality evaluation for road wheel, FE simulations and experimental works were carried out under thirty degree slant load of normal direction of shaft. And then, A relationship residual deformation for slant load was investigated. The result of this research is applicable to evaluate strength and to make use of basis data.

• Transactions of Materials Processing
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• v.12 no.4
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• pp.408-413
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• 2003

Dies may have to be replaced for a number of reasons, such as changes in dimensions due to die wear or plastic deformation, deterioration of the surface finish, break down of lubrication and cracking or breakage. In this paper, die cooling methods have been suggested to improve die service life considering die wear and plastic deformation in hot forging process. The yield strength of die decreases at higher temperatures and is dependent on hardness. Also, to evaluate die life due to wear, modified Archard's wear model has been proposed by considering the thermal softening of die expressed in terms of the main tempering curve. It was found that the use of die with cooling hole was more effective than that of direct cooling method to increase the die service life for spindle component.

• Geomechanics and Engineering
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• v.19 no.5
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• pp.369-381
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• 2019

The objective of this paper is to study the two dimensional deformation in transversely isotropic thermoelastic medium without energy dissipation due to time harmonic sources using new modified couple stress theory, a continuum theory capable to predict the size effects at micro/nano scale. The couple stress constitutive relationships have been introduced for transversely isotropic thermoelastic medium, in which the curvature tensor is asymmetric and the couple stress moment tensor is symmetric. Fourier transform technique is applied to obtain the solutions of the governing equations. Assuming the deformation to be harmonically time-dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed sources have been considered to show the utility of the solution obtained. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of angular frequency are depicted graphically on the resulted quantities.

• Transactions of Materials Processing
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• v.20 no.7
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• pp.498-503
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• 2011

The strain rate sensitivity index, m, plays an important role in plastic deformation at elevated temperatures. It is affected by strain rate, temperature, and the microstructure of the material. The strain rate sensitivity index has been used as a constant in numerical analysis of plastic forming at a specified strain rate and temperature. However, the value of m varies as deformation proceeds at an elevated temperature and a certain strain rate. Thus, in this present study, the value of m has been characterized as a function of strain by multiple tensile jump tests for AZ31 magnesium alloy sheet, and the variation of m has been discussed in conjunction with the microstructural observations before and after deformation. The experimental results show that the variation of m is dependent on the temperature and strain rate. Grain growth with dynamic recrystallization also affects the variation of m.