• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.875-882
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• 2004

Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let $\Delta$$_{p}$,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec($\Delta$$_{p}$,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.ant.

• Bulletin of the Korean Chemical Society
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• v.33 no.12
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• pp.3939-3940
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• 2012

• Magazine of the Korean Society of Agricultural Engineers
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• v.28 no.4
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• pp.49-56
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• 1986

This study was carried out to investigate mechanical characteristics of the uniformly loaded skew-plate at 4 kinds of boundary condition : i) all edges are clamped (BC-1) , ii) all edges are simply supported (BC- 2), iii) two opposite edges are clamped and the other two edges are free (BC-3), and iv )two opposite edges are simply supported and the other two edges are free (BC-4). Various skew angles, 0$^{\circ}$, 10$^{\circ}$, 15$^{\circ}$, 30$^{\circ}$, 40: 45: and 60, of the plate were tested for the above boundary conditions. Resutts obtained from the study are summarized as follows ; 1.The lateral displacement at the center of a skew- plate was decreased as the skewangle increased at all of the boundary conditions. The decrements of the conditions of BC-3 and BC-4 were considerable. And, difference of the displacement between the boundary conditions was decreased as the skew-angle was increased. 2. X-moments (to the Y-axis) at the center of a skew- plate and the minimum principal moments were shown as a similar pattern of change with respect to the skew-angle variation between BC-i and BC-2 and between BC-3 and BC-4, and the pattern of change at the conditions of BC-3 and BC-4 were shown higher rates than those for the conditions of BC-i and BC-2 3.Y-moments (to the X- axis) at the center of a skew-plate and the maximum principal moment were decreased as the skew-angle increased in a similar pattern at all of the boundary conditions. 4.X-moments at the obtuse angle side of a skew-plate were shown as a parabolic pattern of change (frist increased after then decreased) as the skew-angle increased, and a skew-angle resulting the maximum absolute moment was depended on the boundary conditions. 5.Y-moments at the obtuse angle side of a skew-plate were affected by the skewangle much more at the boundary condtions of BC-2 and BC-4 than at the conditions of BC-i and BC-3. 6.Maximum principal moments at the obtuse angle side of a skew-plate at the skew angle of 40$^{\circ}$- 45$^{\circ}$ were resulted almost the same value at all of the boundary conditions .

• Structural Engineering and Mechanics
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• v.54 no.1
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• pp.55-67
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• 2015

Taking the mid-span/center-point of the structure as the reference point of capturing the maximum dynamic response is very customary in the available literature of the moving load problems. In this article, the absolute maximum dynamic response of an Euler-Bernoulli beam subjected to a moving mass is widely investigated for various boundary conditions of the base beam. The response of the beam is obtained by utilizing a robust numerical method so-called OPSEM (Orthonormal Polynomial Series Expansion Method). It is underlined that the absolute maximum dynamic response of the beam does not necessarily take place at the mid-span of the beam and thus the conventional analysis needs modifications. Therefore, a comprehensive parametric survey of the base beam absolute maximum dynamic response is represented in which the contribution of the velocity and weight of the moving inertial objects are scrutinized and compared to the conventional version (maximum at mid-span).

• Journal of Distribution Science
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• v.19 no.12
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• pp.15-22
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• 2021

Purpose: There is still lack of guidance for merchants toward price discount presentations (absolute/relative), especially for consumers in different purchase contexts. Based on the general evaluability theory, this study investigates consumers' preferences for the presentation of discounts in various contexts through experiments. Research design, data and methodology: The relationship between discount presentation and consumers' preference is investigated in Study 1 using a two-factor between-subject design of 2 (purchase type: material vs. experiential) ×2 (discount type: absolute vs. relative). The Moderating effect of thinking mode has been examined in Study 2 via a multi-factor intergroup design of 2 (purchase type: material vs. experiential) ×2 (discount type: absolute vs. relative) ×2 (cognitive load: high vs. low). One-way ANOVA and planned contrast have been performed for analysis. Results: Experiment 1 reveals that consumers prefer absolute discounts rather than relative discounts when in material purchases. However, when in experiential purchases, they are willing to choose relative discounts. Experiment 2 verifies the boundary conditions of matching effect and illustrates the generation of matching effect is determined by thinking mode. Conclusions: Our study enriches the theories of purchase type and thinking mode. Simultaneously, the results provide practical guidance for merchants to formulate the discount presentation and distribution pricing strategies.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.1
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• pp.152-159
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• 2005

The dynamic properties between catenary and pantograph of high-speed train are very important factors to affect the stable electric power supply. So as to design the reliable current collection system, a multibody simulation model is needed. In this paper, the dynamic analysis method for a pantograph-catenary cable system of high-speed train is presented. The very deformable motion of a catenary cable is demonstrated using nonlinear continuous beam theory, which is based on an absolute nodal coordinate formulation, and the pantograph is modeled as a rigid multibody. The proposed method might be very efficient, because this method can present the nonlinear properties of a flexible catenary cable and set a various boundary conditions.

• Journal of Energy Engineering
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• v.13 no.3
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• pp.181-190
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• 2004

Computational models for analyzing the in-reactor behavior of metallic fuel pins under transient conditions in liquid-metal reactors are developed and implemented in the TRAMAC (TRAnsient thermo-Mechanical Analysis Code) for a metal fuel rod under transient operation conditions. Not only the basic models for a fuel rod performance but also some sub-models used for transient condition are installed in TRAMAC. Among the models, a fission gas release model, which takes the multi-bubble size distribution into account to characterize the lenticular bubble shape and the saturation condition on the grain boundary and the cladding deformation model have been developed based mainly on the existing models in the MAC-SIS code. Finally, cladding strains are calculated from the amount of thermal creep, irradiation creep, and irradiation swelling. The cladding strain model in TRAMAC predicts well the absolute magnitudes and gen-eral trends of their predictions compared with those of experimental data. TRAMAC results for the FH-1,2,6 pins are more conservative than experimental data and relatively reasonable than those of FPIN2 code. From the calculation results of TRAMAC, it is apparent that the code is capable of predicting fission gas release, and cladding deformation for LMR metal fuel finder transient operation conditions. The results show that in general, the predictions of TRAMAC agree well with the available irradiation data.

• Structural Engineering and Mechanics
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• v.9 no.5
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• pp.449-467
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• 2000

The natural frequencies and the corresponding mode shapes of a non-uniform beam carrying multiple point masses are determined by using the analytical-and-numerical-combined method. To confirm the reliability of the last approach, all the presented results are compared with those obtained from the existing literature or the conventional finite element method and close agreement is achieved. For a "uniform" beam, the natural frequencies and mode shapes of the "clamped-hinged" beam are exactly equal to those of the "hinged-clamped" beam so that one eigenvalue equation is available for two boundary conditions, but this is not true for a "non-uniform" beam. To improve this drawback, a simple transformation function ${\varphi}({\xi})=(e+{\xi}{\alpha})^2$ is presented. Where ${\xi}=x/L$ is the ratio of the axial coordinate x to the beam length L, ${\alpha}$ is a taper constant for the non-uniform beam, e=1.0 for "positive" taper and e=1.0+$|{\alpha}|$ for "negative" taper (where $|{\alpha}|$ is the absolute value of ${\alpha}$). Based on the last function, the eigenvalue equation for a non-uniform beam with "positive" taper (with increasingly varying stiffness) is also available for that with "negative" taper (with decreasingly varying stiffness) so that half of the effort may be saved. For the purpose of comparison, the eigenvalue equations for a positively-tapered beam with five types of boundary conditions are derived. Besides, a general expression for the "normal" mode shapes of the non-uniform beam is also presented.

• Structural Engineering and Mechanics
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• v.37 no.5
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• pp.475-487
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• 2011

In a flexible multi-body dynamic system the typical topological optimization method for structures cannot be directly applied, as the stiffness varies with position. In this paper, the topological optimization of the flexible multi-body dynamic system is converted into structural optimization using the equivalent static load method. First, the actual boundary conditions of the control system and the approximate stiffness curve of the mechanism are obtained from a flexible multi-body dynamical simulation. Second, the finite element models are built using the absolute nodal coordination for different positions according to the stiffness curve. For efficiency, the static reanalysis method is utilized to solve these finite element equilibrium equations. Specifically, the finite element equilibrium equations of key points in the stiffness curve are fully solved as the initial solution, and the following equilibrium equations are solved using a reanalysis method with an error controlled epsilon algorithm. In order to identify the efficiency of the elements, a non-dimensional measurement is introduced. Finally, an improved evolutional structural optimization (ESO) method is used to solve the optimization problem. The presented method is applied to the optimal design of a die bonder. The numerical results show that the presented method is practical and efficient when optimizing the design of the mechanism.

• Earthquakes and Structures
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• v.16 no.3
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• pp.359-368
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• 2019

This paper focuses on the study of dynamic analysis of thick plates resting on Winkler foundation. The governing equation is derived from Mindlin's theory. This study is a parametric analysis of the reflections of the thickness / span ratio, the aspect ratio and the boundary conditions on the earthquake excitations are studied. In the analysis, finite element method is used for spatial integration and the Newmark-${\beta}$ method is used for the time integration. While using finite element method, a new element is used. This element is 17-noded and it's formulation is derived from using higher order displacement shape functions. C++ program is used for the analyses. Graphs are presented to help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that the 17-noded finite element is used in the earthquake analysis of thick plates. It is shown that the changes in the aspect ratio are more effective than the changes in the aspect ratio. The center displacements of the reinforced concrete thick clamped plates for b/a=1, and t/a=0.2, and for b/a=2, and t/a=0.2, reached their absolute maximum values of 0.00244 mm at 3.48 s, and of 0.00444 mm at 3.48 s, respectively.