• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.329-337
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• 2008

This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

• Structural Engineering and Mechanics
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• v.50 no.5
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• pp.679-695
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• 2014

A design method of second generation wavelet (SGW)-based multivariable finite elements is proposed for static and vibration beam analysis. An important property of SGWs is that they can be custom designed by selecting appropriate lifting coefficients depending on the application. The SGW-based multivariable finite element equations of static and vibration analysis of beam problems with two and three kinds of variables are derived based on the generalized variational principles. Compared to classical finite element method (FEM), the second generation wavelet-based multivariable finite element method (SGW-MFEM) combines the advantages of high approximation performance of the SGW method and independent solution of field functions of the MFEM. A multiscale algorithm for SGW-MFEM is presented to solve structural engineering problems. Numerical examples demonstrate the proposed method is a flexible and accurate method in static and vibration beam analysis.

• Computational Structural Engineering
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• v.7 no.4
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• pp.85-101
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• 1994

A family of variational principles governing the dynamics of laminated plate has been derived using a variationally consistent shear deformable discrete laminated plate theory with particular reference to finite element procedures. The theoretical basis for the derivation is Sandhu's generalized procedure for the variational formulation of linear coupled boundary value problem. As the bilinear mapping to write the operator matrix of the field equations in self-adjoint form, convolution product was employed. Boundary conditions, initial conditions and probable internal discontinuity were explicitly included in the governing functionals. Some interesting extensions and specializations of the general variational principle were presented, which can provide many different finite element formulations for the problem.

• 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 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.