• Structural Engineering and Mechanics
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• v.21 no.1
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• pp.19-33
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• 2005

An improved shear deformable thin-walled curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled free vibration and elastic analysis. For this, the displacement field considering the shear deformation effects is presented by introducing displacement parameters defined at the centroid and shear center axes. Next the elastic strain and kinetic energies considering the shear effects due to the shear forces and the restrained warping torsion are rigorously derived. Then the equilibrium equations are consistently derived for curved beams with non-symmetric thin-walled sections. It should be noticed that this formulation can be easily reduced to the warping-free beam theory by simply putting the sectional properties associated with warping to zero for curved beams with L- or T-shaped sections. Finally in order to illustrate the validity and the accuracy of this study, finite element solutions using the isoparametric curved beam elements are presented and compared with those in available references and ABAQUS's shell elements.

• Structural Engineering and Mechanics
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• v.75 no.2
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• pp.133-144
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• 2020

This investigation is to study the effect of gravitational field and diffusion on a microstretch thermoelastic medium heating by a non-Gaussian laser beam. The problem was studied in the context of the dual-phase-lag model. The normal mode analysis is used to solve the problem to obtain the exact expressions for the non-dimensional displacement components, the micro-rotation, the stresses, and the temperature distribution. The effect of time parameter, heat flux parameter and gravity response of three theories of thermoelasticity i.e. dual-phase-lag model (DPL), Lord and Shulman theory (L-S) and coupled theory (CT) on these quantities have been depicted graphically for a particular model.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.133-150
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• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• Structural Engineering and Mechanics
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• v.44 no.3
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• pp.267-288
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• 2012

Free vibration analysis of arbitrary quadrilateral thick plates with internal columns and elastic edge supports is presented by using the powerful pb-2 Ritz method and Reddy's third order shear deformation plate theory. The computing domain of arbitrary quadrilateral planform is mapped onto a standard square form by coordinate transformation. The versatile pb-2 Ritz functions defined by the product of a two-dimensional polynomial and a basic function are taken to be the admissible functions. Substituting these displacement functions into the energy functional and minimizing the total energy by differentiation, leads to a typical eigenvalue problem, which is solved by a standard eigenvalue solver. Stiffness and mass matrices are numerically integrated over the plate by using Gaussian quadrature. The accuracy and efficiency of the proposed method are demonstrated through several numerical examples by comparison and convergency studies. A lot of numerical results for reasonable natural frequency parameters of quadrilateral plates with different combinations of elastic boundary conditions and column supports at any locations are presented, which can be used as a benchmark for future studies in this area.

• Advances in nano research
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• v.7 no.2
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• pp.77-88
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• 2019

This paper infer the transient vibration of piezoelectric sandwich nanobeams, In present work, the flexoelectric effect on the mechanical properties of vibration piezoelectric sandwich nanobeam with different boundary conditions is investigated. According to the Nonlocal elasticity theory in nanostructures, the flexoelectricity is believed to be authentic for such size-dependent properties. The governing equations are derived by Hamilton's principle and boundary condition solved by Galerkin-based solution. This research develops a nonlocal flexoelectric sandwich nanobeam supported by Winkler-Pasternak foundation. The results of this work indicate that natural frequencies of a sandwich nanobeam increase by increasing the Winkler and Pasternak elastic constant. Also, increasing the nonlocal parameter at a constant length decreases the natural frequencies. By increasing the length to thickness ratio (L/h) of nanobeam, the nonlocal frequencies reduce.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.5 no.2
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• pp.141-149
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• 2004

The aim of this study was to test the validity of the hypothesis that the karyotypes of four species of Lepilemuridae were formed spontaneously from their ancestral hybrid karyotype. Hypothetical ancestral haploid Karyotype of Lepilemuridae is composed of 18 autosomes and X chromosomes. Lepilemur mustelinus karyotype has four tandem fused chromosomes and one Robertsonian translocated chromosome pairs. Lepilemur septentrionalis septentrionalis karyotype has only two pairs of translocated chromosomes. We reconstruct and suggest ancestral karyotype of LMU(ancLMU) and LSS(ancLSS), from which all four studied species were derived. Hybrids of ancLMU and ancLSS were formed and produce differently fused equilibrated gametes via circular form arrangement during gametogenesis. Five unit of trivalent homologous chromosome pairs were engaged in a circular form to give new gamete corresponding to the karyotype of L. dorsalis, orientation of one unit of trivalent was inversed in the circle to gave new gamete corresponding to the karyotype of L. leucopus. Seven homologous chromosome pairs were engaged in circular form to give haploid karyotype of Lepilemur ruficaudatus. Only one homologous chromosome pair is dissociated and the other chromosome pairs rearranged in the circle to form haploid karyotype of Lepilemur edwardsi. The new gametes could be produced from these circular forms. When the new gamete fertilized with the same type of gamete, The new homozygote is produced as existing L. dorsalis, L. leucopus, L. edwardsi and L. ruficaudatus. These results support the theory that new species could be formed in hybrid population through activated chromosome fusion, chromosome rearrangement in circular from at zygotene stage and production of equilibrated gametes to form homozygote new species.

• Steel and Composite Structures
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• v.51 no.2
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• pp.185-202
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• 2024

In this research paper, and for the first time, wave propagations in sigmoidal imperfect functionally graded material plates are investigated using a simplified quasi-three-dimensionally higher shear deformation theory (Quasi-3D HSDTs). By employing an indeterminate integral for the transverse displacement in the shear components, the number of unknowns and governing equations in the current theory is reduced, thereby simplifying its application. Consequently, the present theories exhibit five fewer unknown variables compared to other Quasi-3D theories documented in the literature, eliminating the need for any correction coefficients as seen in the first shear deformation theory. The material properties of the functionally graded plates smoothly vary across the cross-section according to a sigmoid power law. The plates are considered imperfect, indicating a pore distribution throughout their thickness. The distribution of porosities is categorized into two types: even or uneven, with linear (L)-Type, exponential (E)-Type, logarithmic (Log)-Type, and Sinus (S)-Type distributions. The current quasi-3D shear deformation theories are applied to formulate governing equations for determining wave frequencies, and phase velocities are derived using Hamilton's principle. Dispersion relations are assumed as an analytical solution, and they are applied to obtain wave frequencies and phase velocities. A comprehensive parametric study is conducted to elucidate the influences of wavenumber, volume fraction, thickness ratio, and types of porosity distributions on wave propagation and phase velocities of the S-FGM plate. The findings of this investigation hold potential utility for studying and designing techniques for ultrasonic inspection and structural health monitoring.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.10a
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• pp.39-44
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• 1992

This paper is concerned with formulations of the hierarchical $C^{o}$-plate element on the basis of Reissner-Mindlin plate theory. On reason for the development of the aforementioned element is that it is still difficult to construct elements based on h-version concepts which are accurate and stable against the shear locking effects. An adaptive mesh refinement and selective p-distribution of the polynomial degree using hp-version of the finite element method we proposed to verify the superior convergence and algorithmic efficiency with the help of the clamped L-shaped plate problems.s.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.355-387
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• 2009

Functoriality conjecture is one of the central and influential subjects of the present day mathematics. Functoriality is the profound lifting problem formulated by Robert Langlands in the late 1960s in order to establish nonabelian class field theory. In this expository article, I describe the Langlands-Shahidi method, the local and global Langlands conjectures and the converse theorems which are powerful tools for the establishment of functoriality of some important cases, and survey the interesting results related to functoriality conjecture.

• Journal of The Korean Astronomical Society
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• v.18 no.2
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• pp.41-69
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• 1985

For the well observed 16 globular clusters with known metal abundance (Z), the helium abundances (Y) and ages are determined by various methods, and the relations between Y, Z and age are examined. The luminosity $L_{RR}$ of RR Lyrae stars is known to be dependent of evolutionary models and pulsation theory in the sense that the pulsation theory and horizontal branch (HB) models yield the anticorrelation between $L_{RR}$ and Z whereas main sequence (MS) and red giant branch (RGB) models yield the direct correlation between them. Similarly the anticorrelation between Y and Z is obtained from the HB models and pulsation theory whereas the direct correlation between them is obtained when the RGB model is applied. The current evolutionary models yield the anticorrelation between Z and age of clusters whenever the direct correlation between Y and Z holds. However when the anticorrelation between Y and Z is applied for age determination, the similar age of clusters is obtained as shown by Sandage (1982b). The ages, which are determined by the fitting of C-M diagrams to isochrones in the ($M_v$, B-V)-plane, suggest the two different chemical enrichment processes, which could be accounted for by the disk-halo model for the chemical evolution of the Galaxy (Lee and Ann 1981). Also it is known that the R-method is very useful for Y-determination and the derived Y's show the increasing rate of $\frac{{\Delta}Y}{{\Delta}Z}{\simeq}0.5$ which is comparable to the observed value of $\frac{{\Delta}Y}{{\Delta}Z}{\simeq}0.3$ from HII regions and planetary nebulae by Peimbert and Torres-Peimbert (1976). In this case, the age-metallicity relation of globular clusters could be explained by the disk-halo model.