• Structural Engineering and Mechanics
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• v.69 no.2
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• pp.205-219
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• 2019

This paper analyzes nonlinear free vibration of the circular nano-tubes made of functionally graded materials in the framework of nonlocal strain gradient theory in conjunction with a refined higher order shear deformation beam model. The effective material properties of the tube related to the change of temperature are assumed to vary along the radius of tube based on the power law. The refined beam model is introduced which not only contains transverse shear deformation but also satisfies the stress boundary conditions where shear stress cancels each other out on the inner and outer surfaces. Moreover, it can degenerate the Euler beam model, the Timoshenko beam model and the Reddy beam model. By incorporating this model with Hamilton's principle, the nonlinear vibration equations are established. The equations, including a material length scale parameter as well as a nonlocal parameter, can describe the size-dependent in linear and nonlinear vibration of FGM nanotubes. Analytical solution is obtained by using a two-steps perturbation method. Several comparisons are performed to validate the present analysis. Eventually, the effects of various physical parameters on nonlinear and linear natural frequencies of FGM nanotubes are analyzed, such as inner radius, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume indexes, different beam models.

• Advances in nano research
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• v.14 no.5
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• pp.475-493
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• 2023

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.10
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• pp.36-43
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• 2006

• Tribology and Lubricants
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• v.32 no.1
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• pp.1-8
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• 2016

This paper focuses on the thermal deformation induced preload change in the tilting pad journal bearing, using a three-dimensional (3D) thermo-hydro-dynamic (THD) approach. Preload is considered as a critical factor in designing the tilting pad journal bearing. The initial preload measured under nil external load and nil thermal gradient is influenced by two factors, namely, the thermal deformation and elastic deformation. Thermal deformation is due to a temperature distribution in the bearing pads, whereas the elastic deformation is due to fluid forces acting on the pads. This study focuses on the changes induced in preload and film clearance due to thermal deformation. The generalized Reynolds equation is used to evaluate the force of the fluid and the 3D energy equation is used to calculate the temperature of the lubricant. The abovementioned equations are combined by establishing a relationship between viscosity and temperature. The heat transfer within the bearing pads, the lubricant, and the spinning journal is calculated using the heat flux boundary condition. The 3D Finite Element Method (FEM) is used in modeling the (1) heat conduction in the spinning journal and bearing pads, (2) thermal gradient induced thermal distortion of the spinning journal and pads, and (3) viscous shearing, and heat conduction and convection in a thin film. This evaluation method has an increased fidelity, and it can prove to be a cost-effective tool that can be used by designers to predict the dynamic behavior of a bearing.

• Journal of Korea Multimedia Society
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• v.17 no.10
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• pp.1229-1238
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• 2014

Various 2D Shape deformation techniques has been presented recently. Concerning intuitive control of deformation, gradient domain 2D deformation techniques have an advantage over FFD(Free-form deformation) approaches, since they can deform objects with less control points. However, semantic shape properties such as thickness or length are difficult to handle in these approaches due to they treat the whole shape as a simple flat shape without structural meaning. In this paper, we propose a 2D shape deformation algorithm that deforms shapes using thin, deformable skeletal structure called freeform deformation axis (FDA). This concept separates the target shape and the deformable structure and thus enables user to manipulate shapes more intuitively.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.693-701
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• 2018

This paper develops a nonlocal strain gradient plate model for vibration analysis of graphene sheets under thermal environments. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on elastic substrate are derived via Hamilton's principle. Differential quadrature method (DQM) is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as temperature rise, nonlocal parameter, length scale parameter, elastic foundation and aspect ratio on vibration characteristics a graphene sheets are studied. It is seen that vibration frequencies and critical buckling temperatures become larger and smaller with increase of strain gradient and nonlocal parameter, respectively.

• Transactions of Materials Processing
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• v.32 no.2
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• pp.74-80
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• 2023

A deformation behavior of commercially pure titanium (CP-Ti) is highly dependent on material and processing parameters, such as deformation temperature, deformation direction, and strain rate. This study aims to predict the multivariable and nonlinear tensile behavior of CP-Ti using machine learning based on three algorithms: artificial neural network (ANN), light gradient boosting machine (LGBM), and long short-term memory (LSTM). The predictivity for tensile behaviors at the cryogenic temperature was lower than those in the room temperature due to the larger data scattering in the train dataset used in the machine learning. Although LGBM showed the lowest value of root mean squared error, it was not the best strategy owing to the overfitting and step-function morphology different from the actual data. LSTM performed the best as it effectively learned the continuous characteristics of a flow curve as well as it spent the reduced time for machine learning, even without sufficient database and hyperparameter tuning.

• Transactions of Materials Processing
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• v.15 no.8 s.89
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• pp.544-549
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• 2006

In this work, we have employed the strain gradient plasticity theory to investigate the effect of material size on the deformation behavior in metal forming process. Flow stress is expressed in terms of strain, strain gradient (spatial derivative of strain) and intrinsic material length. The least square method coupled with strain gradient plasticity was used to calculate the components of strain gradient at each element of material. For demonstrating the size effect, the proposed approach has been applied to plane compression process and micro rolling process. Results show when the characteristic length of the material comes to the intrinsic material length, the effect of strain gradient is noteworthy. For the microcompression, the additional work hardening at higher strain gradient regions results in uniform distribution of strain. In the case of micro-rolling, the strain gradient is remarkable at the exit section where the actual reduction of the rolling finishes and subsequently strong work hardening take places at the section. This results in a considerable increase in rolling force. Rolling force with the strain gradient plasticity considered in analysis increases by 20% compared to that with conventional plasticity theory.

• Steel and Composite Structures
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• v.47 no.6
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• pp.795-811
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• 2023

When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.

• Geomechanics and Engineering
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• v.11 no.4
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• pp.571-585
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• 2016

The crest of the Pubugou central core rockfill dam (CCRD) cracked in the first and second impounding periods. To evaluate the safety of the Pubugou CCRD, an inversion analysis of the constitutive model parameters for rockfill materials is performed based on the in situ deformation monitoring data. The aim of this work is to truly reflect the deformation state of the Pubugou CCRD and determine the causes of the dam crest cracks. A novel real-coded genetic algorithm based upon the differences in gene fragments (DGFX) is proposed. It is used in combination with the radial based function neural network (RBFNN) to perform the parameters back analysis. The simulated settlements show good agreements with the monitoring data, illustrating that the back analysis is reasonable and accurate. Furthermore, the deformation gradient of the dam crest has been analysed. The dam crest has a great possibility of cracking due to the uncoordinated deformation, which agrees well with the field investigation. The deformation gradient decreases to the value lower than the critical one and reaches a stable state after the second full reservoir.