• Smart Structures and Systems
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• v.25 no.5
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• pp.543-557
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• 2020

This paper presents a series of experimental and numerical investigations on a vertical isolation system with quasi-zero stiffness (QZS) property. The isolation system comprises a linear helical spring and disk spring. The disk spring is designed to provide variable stiffness to the system. Orthogonal static tests with different design parameters are conducted to verify the mathematical and mechanical models of the isolation system. The deviations between theoretical and test results influenced by the design parameters are summarized. Then, the dynamic tests for the systems with different under-load degrees are performed, including the fast sweeping tests, harmonic excitation tests, and half-sine impact tests. The displacement transmissibility, vibration reduction rate, and free vibration response are calculated. Based on the test results, the variation of the transmission rule is evaluated and the damping magnitudes and types are identified. In addition, the relevant numerical time history responses are calculated considering the nonlinear behavior of the system. The results indicate that the QZS isolation system has a satisfactory isolation effect, while a higher damping level can potentially promote the isolation performance in the low-frequency range. It is also proved that the numerical calculation method accurately predicts the transmission character of the isolation system.

• Steel and Composite Structures
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• v.36 no.3
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• pp.293-305
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• 2020

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

• Journal for History of Mathematics
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• v.28 no.2
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• pp.65-72
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• 2015

The Joseon dynasty (1392-1910) is basically an agricultural country and therefore, the main source of her national revenue is the farmland tax. Thus the farmland tax system becomes the most important state affair. The 4th king Sejong establishes an office for a new law of the tax in 1443 and adopts the farmland tax system in 1444 which is legalized in Gyeongguk Daejeon (1469), the complete code of law of the dynasty. The law was amended in the 19th king Sukjong era. Jo Tae-gu mentioned the new system in his book Juseo Gwan-gyeon (1718) which is also included in Sok Daejeon (1744). Investigating the mathematical structures of the two systems, we show that the systems involve various aspects of mathematics and that the systems are the most precise applications of mathematics in the Joseon dynasty.

• Journal of the Korean Society for Precision Engineering
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• v.28 no.8
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• pp.966-974
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• 2011

The use of ion beams in the micro/nano scale is greatly increased by technology development. Especially, focused ion beams (FIBs) have a great potential to fabricate the device in sub micro scale. Nevertheless, FIB has several limitations, surface swelling in low ion dose regime, precipitation of incident ions, and the redeposition effect due to the sputtered atoms. In this research, we demonstrate a way which can be used to fabricate mold structures on a silicon substrate using FIBs. For the purpose of the demonstration, two essential subjects are necessary. One is that focused ion beam diameter as well as shape has to be measured and verified. The other one is that the accurate rotational symmetric model of ion-solid interaction has to be mathematically developed. We apply those two, measured beam diameter and mathematical model, to fabricate optical lenses mold on silicon. The characteristics of silicon mold fabrication will be discussed as well as simulation results.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.53-58
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• 2003

Many researchers have rigorously studied the nonlinear behavior of stress-strain relationship of concrete using mathematical curves. Most of model equations for stress-strain relationship, however, have been focused on old age concrete, and were not able to adequately represent the behavior of concrete at an early age. A wide understanding on the behavior of concrete from early age to old age is very important in evaluating the durability and service life of concrete structures. In previous study by authors of this paper, a stress-strain model equation for low- and medium-strength concretes was suggested. In this paper, to extend the application region of compressive stress-strain curve to high-strength concrete, an analytical research was performed. An analytical expression of stress-strain curve with strength and age was developed using regression analyses on the experimental results. For the verification of the proposed model equation, it was compared to the experimental data. The result showed that the proposed model equation was not only compatible with the experimental data quite satisfactorily but also describing well the effect of strength and age on stress-strain curve.

• Wind and Structures
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• v.16 no.3
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• pp.279-300
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• 2013

This paper presents a new analysis framework for predicting the internal buffeting forces in bridge components under skew wind. A linear regressive model between the internal buffeting force and deformation under normal wind is derived based on mathematical statistical theory. Applying this regression model under normal wind and the time history of buffeting displacement under skew wind with different yaw angles in wind tunnel tests, internal buffeting forces in bridge components can be obtained directly, without using the complex theory of buffeting analysis under skew wind. A self-anchored suspension bridge with a main span of 260 m and a steel arch bridge with a main span of 450 m are selected as case studies to illustrate the application of this linear regressive framework. The results show that the regressive model between internal buffeting force and displacement may be of high significance and can also be applied in the skew wind case with proper regressands, and the most unfavorable internal buffeting forces often occur under yaw wind.

• Steel and Composite Structures
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• v.22 no.5
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• pp.1193-1214
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• 2016

In this paper, the 3D stress state and inter-laminar stresses in a rotating thin laminated cylinder shell are studied. The thickness of the cylinder is supposed to be thin and it is made of laminated composite material and can have general layer stacking. The governing equations of the cylindrical shell are obtained by employing the Layerwise theory (LWT). The effect of rotation is considered as rotational body force which is induced due to the rotation of the cylinder about its axis. The Layerwise theory (LWT), is used to discrete the partial differential equations of the problem to ordinary ones, in terms of the displacements of the mathematical layers. By applying the Free boundary conditions the solution of the governing equations is completed and the stress state, the inter-laminar stresses, and the edge effect in the rotating cylindrical shells are investigated in the numerical results. To verify the results, LWT solution is compared with the results of the FEM solution and good agreements are achieved. The inter-laminar normal and shear stresses in rotating cylinder are studied and effects of layer stacking and angular velocity is investigated in the numerical results.

• Earthquakes and Structures
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• v.19 no.5
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• pp.315-329
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• 2020

Through bolt connections in Concrete Filled Steel Tubes (CFSTs) has been proved to be good in terms of seismic performance and constructability. Stiffened extended end plate connection with full through type bolt helps to avoid field weld altogether, and hence to improve the quality of joints. An experimental study was conducted on the hysteretic performance of square interior beam-column connections using flat extended end plates with through bolt. The study focuses on the effect of the bond between the tie rod and the core concrete on the cyclic performance of the joint. The study also quantifies how much the interior joint is getting strengthened due to the confinement effect induced by bi-directional bolting, which is widely used in 3D moment resisting frames. For a better understanding of the mechanism and for the prediction of shear capacity of the panel zone, a mathematical model was generated. The various parameters included in the model are the influence of axial load, amount of prestress induced by bolt tightening, anchorage, and the concrete strut action. The study investigates the strength, stiffness, ductility, and energy dissipation characteristics. The results indicate that the seismic resistance is at par with American Institute of Steel Construction (AISC) seismic recommendations. The bidirectional bolting and bond effect have got remarkable influence on the performance of joints.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.273-284
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• 2012

A ring R is called reversibly Armendariz if $b_ja_i=0$ for all $i$, $j$ whenever $f(x)g(x)=0$ for two polynomials $f(x)=\sum_{i=0}^{m}a_ix^i,\;g(x)=\sum_{j=0}^{n}b_jx^j$ over R. It is proved that a ring R is reversibly Armendariz if and only if its polynomial ring is reversibly Armendariz if and only if its Laurent polynomial ring is reversibly Armendariz. Relations between reversibly Armendariz rings and related ring properties are examined in this note, observing the structures of many examples concerned. Various kinds of reversibly Armendariz rings are provided in the process. Especially it is shown to be possible to construct reversibly Armendariz rings from given any Armendariz rings.

• Journal of KIISE:Software and Applications
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• v.26 no.10
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• pp.1167-1167
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• 1999

Although spatial databases support an efficient spatial management on objects in the real world, they have a characteristic that process only spatial information valid at current time, So in case of change in the spatial domain, it is very hard to support an efficient historical management for time-varying spatial information because they delete an old value and then replace with new value that is valid at current time. To solve these problems, there are rapidly increasing of interest for spatiotemporal databases, which serve historical functions for spatial information as well as spatial management functions for an object. However most of them presented in an abstract time-varying spatial phenomenon, but have not presented a concrete policy in spatiotemporal databases. In this paper, we propose a spatiotemporal data model that supports bitemporal time concepts in three dimensional architecture. In the proposed model, not only data types and their operation for object of spatiotemporal databases have been classified, but also mathematical expressions using formal semantics for them have been given. Then, the data structures and their operations based on relational database model as well as object-oriented database model are presented.