• Smart Structures and Systems
• /
• v.5 no.5
• /
• pp.531-546
• /
• 2009

In the present analysis, the spline finite strip with higher-order shear deformation is formulated for the static analysis of piezoelectric composite plates. The proposed method incorporates Reddy's third-order shear deformation theory, Touratier's "Sine" model, Afaq's exponential model, Cho's higher-order zigzag laminate theory, as well as the classic plate theory and the first-order plate theory. Thus, the analysis can be conducted based on any of the above-mentioned theories. The selection of a specific method is done by simply changing a few terms in a 2 by 2 square matrix and the results, obtained according to different plate theories, can be compared to each other. Numerical examples are presented for piezoelectric composite plates subjected to mechanical loading. The results based on different shear deformation theories are compared with the three-dimensional solutions. The behaviours of piezoelectric composite plates with different length-to-thickness ratios, fibre orientations, and boundary conditions are also investigated in these examples.

• Structural Engineering and Mechanics
• /
• v.89 no.2
• /
• pp.199-211
• /
• 2024

The loading capacity of engineering structures/components reduces after the initiation and propagation of crack eventually leads to the final failure. Hence, it becomes essential to deal with the crack and its effects at the design and simulation stages itself, by detecting the prone area of the fracture. The phase-field (PF) method has been accepted widely in simulating fracture problems in complex geometries. However, most of the PF methods are formulated with second order continuity theoryinvolving C⁰ continuity. In the present study, PF method based on fourth-order (i.e., higher order) theory, maintaining C¹ continuity has been proposed for ductile fracture simulation. The formulation includes fourth-order derivative terms of phase field variable, varying between 0 and 1. Applications of fourth-order PF theory to ductile fracture simulation resulted in novelty in this area. The proposed formulation is numerically solved using a two-dimensional finite element (FE) framework in 3-layered manner system. The solutions thus obtained from the proposed fourth order theory for different benchmark problems portray the improvement in the accuracy of the numerical results and are well matched with experimental results available in the literature. These results are also compared with second-order PF theory and a comparison study demonstrated the robustness of the proposed model in capturing ductile behaviour close to experimental observations.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.12 no.4
• /
• pp.239-247
• /
• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

• Bulletin of the Korean Chemical Society
• /
• v.35 no.6
• /
• pp.1697-1702
• /
• 2014

A novel complex [$Zn(phen)(o-AB)_2$] [phen: 1,10-phenanthroline o-AB: o-aminobenzoic acid] was synthesized and characterized by elemental analysis and X-ray diffraction single-crystal analysis. The crystal crystallizes in monoclinic, space group P2(1)/c with $a=7.6397(6){\AA}$, $b=16.8761(18){\AA}$, $c=17.7713(19){\AA}$, ${\alpha}=90^{\circ}$, ${\beta}=98.9570(10)^{\circ}$, ${\gamma}=90^{\circ}$, $V=2.2633(4)nm^3$, Z = 4, F(000) = 1064, S = 1.058, $Dc=1.520g{\cdot}cm^{-3}$, $R_1=0.0412$, $wR_2=0.0948$, ${\mu}=1.128mm^{-1}$. The Zn(II) is six coordinated by two nitrogen and four oxygen atoms from the 1,10-phenanthroline and o-aminobenzoic acid to furnish a distorted octahedron geometry. The complex exhibits intense fluorescence at room temperature. Theoretical studies of the title complex were carried out by density functional theory (DFT) B3LYP method. CCDC: 898291.

• Honam Mathematical Journal
• /
• v.41 no.2
• /
• pp.421-433
• /
• 2019

Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra $H^{sl_n}(c)$ of type $sl_n$, which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra $H^{gl_n}(c)$ of type $gl_n$. We also introduce the raising and lowering element of $H^{sl_n}(c)$ which are useful in the representation theory of the algebra $H^{sl_n}(c)$, and provide simple results related to these elements.

• Journal of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.265-291
• /
• 2012

In this paper, we consider the regularity theory and the existence of smooth solution of a degenerate fully nonlinear equation describing the evolution of the rolling stones with nonconvex sides: $\{M(h)=h_t-F(t,z,z^{\alpha}h_{zz})\;in\;\{0<z{\leq}1\}{\times}[0,T] \\ h_t(z,t)=H(h_z(z,t),h)\;{on}\;\{z=0\}$. We establish the Schauder theory for $C^{2,{\alpha}}$-regularity of h.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.4 no.3
• /
• pp.236-242
• /
• 2009

When two-link flexible arm is rotated about an joint axis, transverse vibration may occur. In this paper, vibration dynamics of flexible robot arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Using the fact that matrix $\dot{D}$-2C is skew symmetric, new controllers which have a simplified structure with less computational burden is proposed. Lyapunov stability theory is applied to achieve a stable deterministic nonlinear controller for the regulation of joint angle.

• Bulletin of the Korean Chemical Society
• /
• v.34 no.10
• /
• pp.2889-2894
• /
• 2013

A new complex [$Ni(phen)(C_9H_8Br_2NO_3)_2{\cdot}2CH_3OH{\cdot}2H_2O$] [phen: 1,10-phenanthroline $C_9H_8Br_2NO_3$: 3,5-dibromo-L-tyrosine] was synthesized and characterized by IR, elemental analysis and single crystal X-ray diffraction. X-ray crystallography shows that Ni(II) ion is six-coordinated. The Ni(II) ion coordinates with four nitrogen atoms and two oxygen atoms from three ligands, forming a mononuclear Ni(II) complex. The crystal crystallizes in the Orthorhombic system, space group $P2_12_12$ with a = 12.9546 ${\AA}$, b = 14.9822 ${\AA}$, c = 9.9705 ${\AA}$, V = 1935.2 ${\AA}$, Z = 1, F(000) = 1008, S = 0.969, ${\rho}_{calcd}=1.742g{\cdot}cm^{-3}$, ${\mu}=4.688mm^{-1}$, $R_1$ = 0.0529 and $wR_2$ = 0.0738 for 3424 observed reflections (I > $2{\sigma}(I)$). Theoretical study of the title complex was carried out by density functional theory (DFT) method and the B3LYP method employing the $6-3l+G^*$ basis set. The energy gap between HOMO and LUMO indicates that this complex is prone to interact with DNA. CCDC: 908041.

• Bulletin of the Korean Chemical Society
• /
• v.33 no.3
• /
• pp.1029-1036
• /
• 2012

Push-pull-type copolymers - low-band-gap copolymers of electron-rich fused-ring units (such as cyclopentadithiophene; CPDT) and electron-deficient units (such as benzothiadiazole; BT) - are promising donor materials for organic solar cells. Following a design principles proposed in our previous study, we investigate the electronic structure of a series of new CPDTBT derivatives with various electron-withdrawing groups using the time-dependent density functional theory and predict their power conversion efficiency from a newlydeveloped protocol using the Scharber diagram. Significantly improved efficiencies are expected for derivatives with carbonyl [C=O], carbonothioyl [C=S], dicyano [$C(CN)_2$] and dicyanomethylene [C=$C(CN)_2$] groups, but these polymers with no long alkyl side chain attached to them are likely to be insoluble in most organic solvents and inapplicable to low-cost solution processes. We thus devise several approaches to attach alkyl side chains to these polymers while keeping their high efficiencies.

• Bulletin of the Korean Chemical Society
• /
• v.26 no.1
• /
• pp.63-71
• /
• 2005

Equilibrium geometries, electronic structures, and energies of borocarbon clusters (binary compounds of carbon and boron), an unexplored class of molecules with highly unusual characteristics and potential for further development, have been investigated by means of B3LYP/6-311+G$^*$ density functional theory computations. A large number of B$_7$C${_1}^{1-}$, B$_6C_2$, and B$_5C_{3}\,^{1+}$ clusters with planar and non-planar monocyclic and polycyclic rings, as well as cage structures, have been systematically studied. Unexpectedly, planar forms are predicted not only to be the most stable structures, but also, in many cases, to have unprecedented planar heptacoordinate boron (p-heptaB) and planar heptacoordinate carbon (p-heptaC) arrangements. All these pheptaB and p-heptaC have 6π electrons and are aromatic according to the nucleus independent chemical shift (NICS). This novel bonding pattern is analyzed in terms of natural bond orbital (NBO) analysis. For virtually all possible B$_7$C${_1}^{1-}$, B$_6C_2$, and B$_5C_{3}\,^{1+}$ combinations, the p-heptaB arrangements are the more stable than other type structures.