• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.255-263
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• 2023

In general, the rigidity problem of braced rectangular frameworks is determined by the connectivity of the bipartite graph induced by given rectangular framework. In this paper, we study how to solve the rigidity problem of the braced rectangular framework using the Laplacian matrix of the matrix induced by a braced rectangular framework.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.161-173
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• 2022

In this paper, we present a fixed point theorem for Meir-Keeler contraction in the framework of Rectangular M_b-metric Space. Our main result improves some existing results in literature. An example is also adopted to exhibit the utility of our main result.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.753-774
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• 2023

The fundamental aim of the proposed work is to introduce the concept of soft rectangular b-metric spaces, which involves generalizing the notions of rectangular metric spaces and b-metric spaces. Furthermore, an investigation into specific characteristics and topological aspects of the underlying generalization of metric spaces is conducted. Moreover, the research establishes fixed point theorems for mappings that satisfy essential criteria within soft rectangular b-metric spaces. These theorems offer a broader perspective on established results in fixed point theory. Additionally, several congruous examples are presented to enhance the understanding of the introduced spatial framework.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.1
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• pp.141-146
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• 1995

In this study the plastic buckling analysis of a simply supported plate under biaxial compression/tension loading is carried out considering the plastic compressibility. Plastic buckling of a biaxially loaded rectangular plate is governed by two kinds of mechanism, the tension strengthening and plastic weakening under which the optimal combination of tension and compression is obtained for the buckling strength. To consider the plastic compressibility, the Drucker-Prayer plastic potential is employed. General eigenvalue equations are derived for a rectangular plate within the framework of small strain plasticity and isotropic hardening.

• Journal of architectural history
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• v.26 no.2
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• pp.31-42
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• 2017

This study investigates how the spatial recognition structure is emerging through the case of rectangular plan combined with a combination of Dang-Sil(堂室) and Gong(工) shape roof, and identifies a type of architecture in the early Joseon Dynasty that has never been revealed. The conclusion of this study is as follows. First, the Dang and the Sil are connected to each other, but the architectural elements such as pillars, frame, and windows are distinguished and appear as separate buildings. Second, the distinction between Dang and Sil is evident by the difference in the number of ridges and the shape of the roof. In addition, the roof and roof framework of the independent rooms and the rooms were common in the right angled architecture where the direction and the expandability of each structure were maintained. Third, the construction of the Dang-Sil combined structure, in which two or more structure frameworks were combined with the rectangular combined flat roof structure, gradually changed into a single structure with a single ridge. Fourth, this change means that people of the early Joseon Dynasty recognized the Dang and Sil as separate architecture, but the strict sense of spatial separation has disappeared over time.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.711-722
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• 2020

An optimization framework using genetic algorithms has been developed towards an automated parametric optimization of the Octabuoy semi-submersible design. Compared with deep draft production units, the design of the shallow draught Octabuoy semi-submersible provides a floating system with improved motion characteristics, being less susceptible to vortex induced motions in loop currents. The relatively large water plane area results in a decreased natural heave period, which locates the floater in the wave period range with more wave energy. Considering this, the hull design of Octabuoy semi-submersible has been optimized to improve the floater's motion performance. The optimization has been conducted with optimized parameters of the pontoon's rectangular cross section area, the cone shaped section's height and diameter. Through numerical evaluations of both the 1st-order and 2nd-order hydrodynamics, the optimization through genetic algorithms has been proven to provide improved hydrodynamic performance, in terms of heave and pitch motions. This work presents a meaningful framework as a reference in the process of floating system's design.

• Wind and Structures
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• v.11 no.2
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• pp.153-178
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• 2008

Based on the empirical formulas for power spectra of generalized modal forces and local fluctuating wind forces in across-wind and torsional directions, the wind-induced lateral-torsional coupled response analysis of a representative rectangular tall building was conducted by setting various parameters such as eccentricities in centers of mass and/or rigidity and considering different torsional to lateral stiffness ratios. The eccentricity effects on the lateral-torsional coupled responses of the tall building were studied comprehensively by structural dynamic analysis. Extensive computational results indicated that the torsional responses at the geometric center of the building may be significantly affected by the eccentricities in the centers of mass and/or rigidity. Covariance responses were found to be in the same order of magnitude as the along-wind or across-wind responses in many eccentricity cases, suggesting that the lateral-torsional coupled effects on the overall wind-induced responses can not be neglected for such situations. The calculated results also demonstrated that the torsional motion contributed significantly to the total responses of rectangular tall buildings with mass and/or rigidity eccentricities. It was shown through this study that the framework presented in this paper provides a useful tool to evaluate the wind-induced lateral-torsional coupled responses of rectangular buildings, which will enable structural engineers in the preliminary design stages to assess the serviceability of tall buildings, potential structural vibration problems and the need for a detailed wind tunnel test.

• Geomechanics and Engineering
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• v.13 no.3
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• pp.505-515
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• 2017

Based on the collapse characteristics of a shallow rectangular cavity, a three-dimensional failure mechanism which can be used to study the collapsing region of the rock mass above a shallow cavity roof is constructed. Considering the effects of surcharge pressure and surface bolt on the collapsing block, the external rate of works produced by surcharge pressure and surface bolt are included in the energy dissipation calculation. Using variational approach, an analytic expression of surface equation for the collapsing block, which can be used to study the collapsing region of the rock mass above a shallow cavity roof, is derived in the framework of upper bound theorem. Based on the analytic expression of surface equation, the shape of the collapsing block for shallow cavity is drawn. Moreover, the changing law of the collapsing region for different parameters indicates that the collapsing region of rock mass decreases with the increase of the density of surface bolt. This conclusion can provide reference for practicing geotechnical engineers to achieve an optimal design of supporting structure for a shallow cavity.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.1 no.1
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• pp.81-86
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• 1989

Herein the surge-heave-pitch motion of a ship has been analyzed within the framework of linear potential theory. The ship is assumed slender weakly moored along the centerline of a rectangular harbor with constant depth and straight coastline. The method of matched asymptotic expansion is us-ed to obtain the leading-order solution. The ship and harbor responses to incident long waves can be re-presented in terms of Green's function, which is the solution of the Helmholtz equation satisfying necessary boundary conditions. Numerical results clearly indicate the importance of the surge motion.

• Wind and Structures
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• v.34 no.1
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• pp.15-27
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• 2022

This work comes within the framework of the "Benchmark on the Aerodynamics of a Rectangular Cylinder" that investigates a rectangular cylinder of length-to-depth ratio equal to 5. The present study reports and discusses velocity fields acquired using planar Particle Image Velocitmetry for several angles of attack and Reynolds numbers. In particular, for a cylinder depth-based Reynolds number of 2 × 10⁴ and zero incidence angle, the flow features along the lateral (parallel to the freestream) upper and lower surfaces of the cylinder are reported. Using first and second order statistics of the velocity field, the main flow features are discussed, especially the size and location of the time-averaged flow structures and the distribution of the Reynolds stresses. The variation of the flow features with the incidence is also studied considering angles of attack up to 6°. It is shown that the time-averaged flow is fully detached for incidence higher than 2°. For an angle of attack of 0°, the effects of the Reynolds number varying between 5 × 10³ and 2 × 10⁴ are investigated looking at flow statistics. It is shown that the time-averaged location of the reattachment point and the shape and position of the time-averaged main vortex are mostly constant with the Reynolds number. However, the size of the inner region located below the time-averaged shear layer and just downstream the leading edge corner appears to be strongly dependent on the Reynolds number.