• Structural Engineering and Mechanics
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• v.11 no.1
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• pp.105-122
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• 2001

A new three-dimensional 13-node hexahedral element with rotational degrees of freedom, which is designated as MR-H13 element, is presented. The proposed element is established by adding five nodes to one of the six faces of basic 8-node hexahedral element. The new element can be effectively used in the connection between the refined mesh and the coarser mesh. The derivation of the current element in this paper is based on the variational principles in which the rotation and skew-symmetric stress are introduced as independent variables. Numerical examples show that the performance of the new element is satisfactory.

• Geomechanics and Engineering
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• v.32 no.6
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• pp.553-566
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• 2023

A circular tank foundation resting on the ground and subjected to axisymmetric horizontal and vertical loads and moments is analyzed using the variational principles of mechanics. The circular foundation is assumed to behave as a Kirchhoff plate with in-plane and transverse displacements. The soil beneath the foundation is assumed to be a multi-layered continuum in which the horizontal and vertical displacements are expressed as products of separable functions. The differential equations of plate and soil displacements are obtained by minimizing the total potential energy of the plate-soil system and are solved using the finite element and finite difference methods following an iterative algorithm. Comparisons with the results of equivalent two-dimensional finite element analysis and other researchers establish the accuracy of the method.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.405-432
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• 2022

Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the first principles using the Extended Hamilton's Principle, accounting for non-conservative forces. The variational formulation of the equations is stated in terms of the subdifferentials of the bending and axial potential energies. The equations are given in their abstract (weak), as well as in classical forms.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.17 no.7
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• pp.691-696
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• 2004

The electronic state and chemical bonding of $\beta$-MnO$_2$ with transition metal dopants were theoretically investigated by DV-X$_{\alpha}$ (the discrete variational X$_{\alpha}$) method, which is a sort of the first principles molecular orbital method using the Hartree-Fock-Slater approximation. The calculations were performed with a $_Mn_{14}$ MO$_{56}$ )$^{-52}$ (M = transition metals) cluster model. The electron energy level, the density of states (DOS), the overlap population, the charge density distribution, and the net charges, were calculated. The energy level diagram of MnO$_2$ shows the different band structure and electron occupancy between the up spin states and down spin states. The dopant levels decrease between the conduction band and the valence band with the increase of the atomic number of dopants. The covalency of chemical bonding was shown to increase and ionicity decreased in increasing the atomic number of dopants. Calculated results were discussed on the basis of the interaction between transition metal 3d and oxygen 2p orbital. In conclusion it is expected that when the transition metals are added to MnO$_2$ the band gap decreases and the electronic conductivity increases with the increase of the atomic number of dopants. the atomic number of dopants.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.12
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• pp.822-829
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• 2015

A transfer matrix method has been developed to determine the more accurate natural frequencies for the bending vibration of Bernoulli-Euler beam with linearly reduced width and a concentrated tip mass. The proposed method can be computed an infinite number of the natural frequencies using a single element. Using the differential equation, shear force, and bending moment in which can be deduced by the diverse variational principles, a transfer matrix is formulated. The roots of the differential equation are computed by the Frobenius method. The effect of the concentrated mass for the natural frequencies of width-tapered beams is examined through a parametric study, and to show the accuracy of the proposed method, the computed results compared with those obtained from commercial finite element analysis program(ANSYS).

• Composites Research
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• v.17 no.5
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• pp.78-84
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• 2004

In this paper, a study of thermal response of two types of functionally graded materials (FCM) plates composed of $\textrm{Al}_2\textrm{O}_3$ and Ti-6Al-4V is presented. The material properties of the functionally graded plates are assumed to vary continuously through the thickness of the plate according to a power law distribution of the volume fraction of the constituents. It is supposed that the top and bottom surfaces of the plate are heated and kept as constant thermal boundary conditions. The fundamental equations for rectangular plates of FGM are obtained using Hamilton's variational principles. The solution is obtained in terms of Navier Solution. The influence of volume fraction and temperature is studied on the static deflection and natural frequency of FCM plate.

• Structural Engineering and Mechanics
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• v.38 no.3
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• pp.261-281
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• 2011

A new method of formulation of a class of elements that are immune to mesh distortion effects is proposed here. The simple three-noded bar element with an offset of the internal node from the element center is employed here to demonstrate the method and the principles on which it is founded upon. Using the function space approach, the modified formulation is shown here to be superior to the conventional isoparametric version of the element since it satisfies the completeness requirement as the metric formulation, and yet it is in agreement with the best-fit paradigm in both the metric and the parametric domains. Furthermore, the element error is limited to only those that are permissible by the classical projection theorem of strains and stresses. Unlike its conventional counterpart, the modified element is thus not prone to any errors from mesh distortion. The element formulation is symmetric and thus satisfies the requirement of the conservative nature of problems associated with all self-adjoint differential operators. The present paper indicates that a proper mapping set for distortion immune elements constitutes geometric and displacement interpolations through parametric and metric shape functions respectively, with the metric components in the displacement/strain replaced by the equivalent geometric interpolation in parametric co-ordinates.

• Wind and Structures
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• v.38 no.1
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• pp.75-91
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• 2024

Reliable wind signal reconstruction can be beneficial to the operational safety of long-span bridges. Non-Gaussian characteristics of wind signals make the reconstruction process challenging. In this paper, non-Gaussian wind signals are converted into a combined prediction of two kinds of features, actual wind speeds and wind angles of attack. First, two decomposition techniques, empirical mode decomposition (EMD) and variational mode decomposition (VMD), are introduced to decompose wind signals into intrinsic mode functions (IMFs) to reduce the randomness of wind signals. Their principles and applicability are also discussed. Then, four artificial intelligence (AI) algorithms are utilized for wind signal reconstruction by combining the particle swarm optimization (PSO) algorithm with back propagation neural network (BPNN), support vector regression (SVR), long short-term memory (LSTM) and bidirectional long short-term memory (Bi-LSTM), respectively. Measured wind signals from a bridge site in a deep-cutting gorge are taken as experimental subjects. The results showed that the reconstruction error of high-frequency components of EMD is too large. On the contrary, VMD fully extracts the multiscale rules of the signal, reduces the component complexity. The combination of VMD-PSO-Bi-LSTM is demonstrated to be the most effective among all hybrid models.

• Journal of Surface Science and Engineering
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• v.42 no.1
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• pp.8-12
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• 2009

Electronic structures and chemical bonding of Li-intercalated $LiTiS_2$ and $LiTiO_2$ were investigated by using discrete variational $X{\alpha}$ method as a first-principles molecular-orbital method. ${\alpha}-NaFeO_2$ structure is the equilibrium structure for $LiCoO_2$, which is widely used as a commercial cathode material for lithium secondary battery. The study especially focused on the charge state of Li ions and the magnitude of covalency around Li ions. The average voltage of lithium intercalation was calculated using pseudopotential method and the average intercalation voltage of $LiTiO_2$ was higher than that of $LiTiS_2$. It can be explained by the differences in Mulliken charge of lithium and the bond overlap population between the intercalated Li ions and anions in $LiTiO_2$ as well as $LiTiS_2$. The Mulliken charge, which means the ionicity of Li atom, was approximately 0.12 in $LiTiS_2$ and the bond overlap population (BOP) indicating the covalency between Ti and S was about 0.339. One the other hands, the Mulliken charge of lithium was about 0.79, which means that Li is fully ionized. The BOP, the covalency between Ti and O, was 0.181 in $LiTiO_2$. Because of high ionicity of Li and the weak covalency between Ti and the nearest anion, $LiTiO_2$ has a higher intercalation voltage than that of $LiTiS_2$.

• Journal of the Korean Magnetics Society
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• v.26 no.2
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• pp.39-44
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• 2016

Determination of the structural, electronic, and magnetic properties of the magnetically doped bismuth-telluride alloys are drawing lots of interest in the fields of the thermoelectric application as well as the research on magnetic interaction and topological insulator. In this study, we performed the first-principles electronic structure calculations within the density functional theory for the Gd doped bismuth-tellurides in order to study its magnetic properties and magnetic phase stability. All-electron FLAPW (full-potential linearized augmented plane-wave) method is employed and the exchange correlation potentials of electrons are treated within the generalized gradient approximation. In order to describe the localized f-electrons of Gd properly, the Hubbard +U term and the spin-orbit coupling of the valence electrons are included in the second variational way. The results show that while the Gd bulk prefers a ferromagnetic phase, the total energy differences between the ferromagnetic and the antiferromagnetic phases of the Gd doped bismuth-telluride alloys are about ~1meV/Gd, indicating that the stable magnetic phase may be changed sensitively depending on the structural change such as defects or strains.