• Interaction and multiscale mechanics
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• v.2 no.4
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• pp.375-396
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• 2009

In the present work, the elasto-viscoplastic behavior, interactions between grains, and the texture evolution in polycrystalline materials subjected to finite deformations are modeled using a multiscale analysis procedure within a finite element framework. Computational homogenization is used to relate the grain (meso) scale to the macroscale. Specifically, a polycrystal is modeled by a material representative volume element (RVE) consisting of an aggregate of grains, and a periodic distribution of such unit cells is considered to describe material behavior locally on the macroscale. The elastic behavior is defined by a hyperelastic potential, and the viscoplastic response is modeled by a simple power law complemented by a work hardening equation. The finite element framework is based on a Lagrangian formulation, where a kinematic split of the deformation gradient into volume preserving and volumetric parts together with a three-field form of the Hu-Washizu variational principle is adopted to create a stable finite element method. Examples involving simple deformations of an aluminum alloy are modeled to predict inhomogeneous fields on the grain scale, and the macroscopic effective stress-strain curve and texture evolution are compared to those obtained using both upper and lower bound models.

• Advances in nano research
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• v.9 no.4
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• pp.251-261
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• 2020

In this article, vibration attributes of single walled carbon nanotubes based on Galerkin's method have been investigated. The influence of power law index subjected to different end supports has been overtly examined. Application of the Hamilton's variational principal leads to the formation of partial differential equations. The effects of different physical and material parameters on the fundamental frequencies are investigated for armchair and zigzag carbon nanotubes with clamped-clamped, simply supported and clamped-free boundary conditions. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of Single-Walled Carbon Nanotubes (SWCNTs) are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. MATLAB software package has been utilized for extracting tube frequency spectra. The obtained results are confirmed by comparing with available literature.

• Journal of Ocean Engineering and Technology
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• v.19 no.6 s.67
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• pp.16-21
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• 2005

In the design of super tankers or LNG carriers, which transport a large amount of liquid in the cargo tanks, the structural d11mage due to liquid sloshing is an important problem. The impact pressure from sloshing is most violent when the liquid motion of a partially filled tank is in resonance with the motion of a ship. In this study, the sloshing natural periods of a baffled tank, often installed to reduce liquid motion, is analyzed. A variational method is adopted to estimate the sloshing natural periods for a prismatic cargo tank with baffles of arbitrary filling depth of liquid; the results are compared with Lloyd's Register regulations on sloshing periods. In this study, using an effective liquid-fill-depth concept, sloshing periods for a baffled tank can be expressed by the same form as rectangular prismatic tanks without baffles. In contrast to Lloyd's Register regulations, which can be applicable only to cargo tanks with constant baffle size and distribution, the present results can be applicable to cases of variable baffle size and distribution.

• Smart Structures and Systems
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• v.13 no.4
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• pp.501-515
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• 2014

This paper presents a linear computational homogenization framework to evaluate the effective (or generalized) electromechanical coupling coefficient (EMCC) of adaptive structures with piezoelectric structural fiber (PSF) composite elements. The PSF consists of a silicon carbide (SiC) or carbon core fiber as reinforcement to a fragile piezo-ceramic shell. For the micro-scale analysis, a micromechanics model based on the variational asymptotic method for unit cell homogenization (VAMUCH) is used to evaluate the overall electromechanical properties of the PSF composites. At the macro-scale, a finite element (FE) analysis with the commercial FE code ABAQUS is performed to evaluate the effective EMCC for structures with the PSF composite patches. The EMCC is postprocessed from free-vibrations analysis under short-circuit (SC) and open-circuit (OC) electrodes of the patches. This linear two-scale computational framework may be useful for the optimal design of active structure multi-functional composites which can be used for multi-functional applications such as structural health monitoring, power harvest, vibration sensing and control, damping, and shape control through anisotropic actuation.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.7
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• pp.510-517
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• 2015

The free vibration and stability analysis of a spinning composite shaft modelled as a thin-walled closed beam is performed for several design parameters, such as ply angle, aspect ratio, and spin speed. The governing equations of spinning shafts based on the Timoshenko beam theory are derived via Hamilton's variational principle. Coriolis acceleration and anisotropy of constituent materials are incorporated in the derivation. The equations of motion are then transformed to the standard form of an eigenvalue problem for free vibration and stability analysis. Analytical results both for uniform circular cylindrical shaft and rectangular cross-section shaft are obtained by using extended Galerkin method, and the results are compared with those from FEM ANSYS analysis for a verification.

• Nuclear Engineering and Technology
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• v.43 no.5
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• pp.447-458
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• 2011

This paper proposes an approximated contact force model to identify the nonlinear behavior of a fuel rod with gap supports; also, the numerical prediction of interfacial forces in the mechanical contact of fuel rods with gap supports is studied. The Newmark integration method requires the current status of the contact force, but the contact force is not given a priori. Taylor's expansion can be used to predict the unknown contact force; therefore, it should be guaranteed that the first derivative of the contact force is continuous. This work proposes a continuous and differentiable contact force model with the ability to estimate the current state of the contact force. An approximated convex and differentiable potential function for the contact force is described, and a variational formulation is also provided. A numerical example that considers the particularly stiff supports has been studied, and a fuel rod with hardening supports was also examined for a realistic simulation. An approximated proper solution can be obtained using the results, and abrupt changes from the contacting state to non-contacting state, or vice versa, can be relieved. It can also be seen that not only the external force but also the developed contact force affects the response.

• Korean Journal of Computational Design and Engineering
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• v.12 no.4
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• pp.255-262
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• 2007

In the finite element analysis of forming process, objects are described with a finite number of elements and nodes and the approximated solutions can be obtained by the variational principle. One of the shortcomings of a finite element analysis is that the structure of mesh has become inefficient and unusable because discretization error increases as deformation proceeds due to severe distortion of elements. If the state of current mesh satisfies a certain remeshing criterion, analysis is stopped instantly and resumed with a reconstructed mesh. In the study, a new remeshing algorithm using tetrahedral elements has been developed, which is adapted to the desired mesh density. In order to reduce the discretization error, desired mesh sizes in each lesion of the workpiece are calculated using the Zinkiewicz and Zhu's a-posteriori error estimation scheme. The pre-constructed mesh is constructed based on the modified point insertion technique which is adapted to the density function. The object domain is divided into uniformly-sized sub-domains and the numbers of nodes in each sub-domain are redistributed, respectively. After finishing the redistribution process of nodes, a tetrahedral mesh is reconstructed with the redistributed nodes, which is adapted to the density map and resulting in good mesh quality. A goodness and adaptability of the constructed mesh is verified with a testing measure. The proposed remeshing technique is applied to the finite element analyses of forging processes.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.727-739
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• 2002

Based on a generalized variational principle for magneto-thermo-elasticity, a theoretical model is proposed to describe the coupled magneto-thermo-elastic interaction in soft ferromagnetic plates. Using the linearized theory of magneto-elasticity and perturbation technique, we analyze the magneto-elastic and magneto-thermo-elastic instability of simply supported ferromagnetic plates subjected to thermal and magnetic fields. A nonlinear finite element procedure is developed next to simulate the magneto-thermo-elastic behavior of a finite-size ferromagnetic plates. The effects of thermal and magnetic fields on the magneto-thermo-elastic bending and buckling is investigated in some detail.

• Journal of Magnetics
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• v.21 no.1
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• pp.6-11
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• 2016

The magnetic anisotropy energy (MAE) and the saturation magnetization $B_s$ of (110) $Fe_nCo_n$ heterostructures with n = 1, 2, and 3 are investigated in first-principles within the density functional theory by using the precise full-potential linearized augmented plane wave (FLAPW) method. We compare the results employing two different exchange correlation potentials, that is, the local density approximation (LDA) and the generalized gradient approximation (GGA), and include the spin-orbit coupling interaction of the valence states in the second variational way. The MAE is found to be enhanced significantly compared to those of bulk Fe and Co and the magnetic easy axis is in-plane in agreement with experiment. Also the MAE exhibits the in-plane angle dependence with a two-fold anisotropy showing that the $[1{\overline{I}}0]$ direction is the most favored spin direction. We found that as the periodicity increases, (i) the saturation magnetization $B_s$ decreases due to the reduced magnetic moment of Fe far from the interface, (ii) the strength of in-plane preference of spin direction increases yielding enhancement of MAE, and (iii) the volume anisotropy coefficient decreases because the volume increase outdo the MAE enhancement.

• Journal of Ocean Engineering and Technology
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• v.21 no.1 s.74
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• pp.75-80
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• 2007

Measuring the ground speed and the rotation speeds of tracks is an easy and realistic method to detect the track slips. It is very advantageous if the slips can be measured and applied to real time control of the vehicle. With a proper speed, the tractive force of a tracked vehicle may be calculated from the vehicle dynamics. For the control of tracked vehicle, the relationship between the slip and the tractive force is necessary. In this paper, a series of drawbar-pull tests, in which slips of two tracks are measured under the variational draw-bar weight, is executed to directly obtain the slip-tractive force relationship. For the purpose of the test, a tractive vehicle model was manufactured, and an artificial soil was simulated by using a bentonite-water mixture.