• East Asian mathematical journal
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• v.37 no.4
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• pp.355-379
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• 2021

In this article, we investigated plane figures introduced in elementary school mathematics in the perspective of traditional classification, and also analyzed plane figures focused on the invariance of plane figures out of traditional classification. In the view of traditional classification, how to treat trapezoids was a key argument. In the current mathematics curriculum of the elementary school mathematics, the concept of sliding, flipping, and turning are introduced as part of development activities of spatial sense, but it is rare to apply them directly to figures. For example, how are squares and rectangles different in terms of symmetry? One of the main purposes of geometry learning is the classification of figures. Thus, the activity of classifying plane figures from a symmetrical point of view has sufficiently educational significance from Klein's point of view.

• Steel and Composite Structures
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• v.2 no.4
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• pp.237-246
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• 2002

In this paper, the solution of a semi-infinite plane with one circular hole is presented. This solution is induced by repeatedly superposing the solution of an infinite plane with one circular hole and that of a semi-infinite plane without holes to cancel out the stresses arising on both boundaries. This procedure is carried out until the stresses arising on both boundaries converge. This method does not require complicated calculation procedures as does the method using stress functions defined in a bipolar coordinate system. Some numerical results are shown by graphical representations.

• Steel and Composite Structures
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• v.21 no.5
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• pp.963-980
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• 2016

The jib system with middle strut is widely used to achieve the large arm length in the large scale tower crane and the deployability in the mobile construction crane. In this paper, an analytical solution for the out-of-plane buckling of the jib system with middle strut is proposed. To obtain the analytical expression of the buckling characteristic equation, the method of differential equation was adopted by establishing the bending and torsional differential equation of the jib system under the instability critical state. Compared with the numerical solutions of the finite element software ANSYS, the analytical results in this work agree well with them. Therefore, the correctness of the results in this work can be confirmed. Then the influences of the lateral stiffness of the cable fixed joint, the dip angle of the strut, the inertia moment of the strut, and the horizontal position of the cable fixed joint on the out-of-plane buckling behavior of the jib system were investigated.

• Structural Engineering and Mechanics
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• v.81 no.3
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• pp.379-394
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• 2022

Shallow footings usually belonged to the category of thick plate structures. For accurate analysis of thick plates, the contribution of out-of-plane components of the stress tensor should be considered in the formulation. Most of the available shallow footing models are based on the classical plate theories, which usually neglect the effects of the out-of-plane stresses. In this study, a mixed-field plate finite element model (FEM) is developed for the analysis of shallow footings rested on soil foundations. In addition to displacement field variables, the out-of-plane components of the stress tensor are also assumed as a priori unknown variables. For modeling the interaction effect of the soil under and outside of the shallow footings, the modified Vlasov theory is used. The tensionless nature of the supporting soil foundation is taken into account by adopting an incremental, iterative procedure. The equality requirement of displacements at the interface between the shallow footing and soil is fulfilled using the penalty approach. For validation of the present mixed FEM, the obtained results are compared with the results of 3D FEM and previous results published in the literature. The comparisons show the present mixed FEM is an efficient and accurate tool for solving the problems of shallow footings rested on subsoil.

• Steel and Composite Structures
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• v.42 no.1
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• pp.49-57
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• 2022

This paper presents a study on the behavior of a bolted T-stub to square tube connection using Thread-fixed One-side Bolts (TOBs) through tests and numerical simulations. It outlines a research work of four connections with focus on the failure modes and strengths of the connection under tensile load. It was observed that the thread anchor failure caused by shear failure of hole threads controlled the final failure of the connection in the tests. Meanwhile, the out-of-plane deformation of tube wall resulted in the contact separation between hole threads and bolt threads, which in turn reduced the shear strength of hole threads. Finite element models (FEMs) allowing for the configuration details of the TOBs fixed connection are then developed and compared with the test results. Subsequently, the failure mechanism of hole threads and stress distribution of each component are analyzed based on FEM results. It was concluded that the ultimate strength of connection was not only concerned with the shear strength of hole threads, but also was influenced by the plastic out-of-plane deformation of tube wall. These studies lay a foundation for the establishment of suitable design methods of this type of connection.

• Wind and Structures
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• v.19 no.5
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• pp.481-503
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• 2014

A new theoretical model on rain-wind induced vibration (RWIV) of a continuous stay cable is developed in this paper. Different from the existing theoretical analyses in which the cable was modeled as a segmental rigid element, the proposed scheme focuses on the in-plane and out-of-plane responses of a continuous stay cable, which is identical with the prototype cable on cable-stayed bridge. In order to simplify the complexities, the motion law of the rivulet on the cable surface is assumed as a sinusoidal way according to some results obtained from wind tunnel tests. Quasi-steady theory is utilized to determine the aerodynamic forces on the cable. Equations of motion of the cable are derived in a Cartesian Coordinate System and solved by using finite difference method to obtain the in-plane and out-of-plane responses of the cable. The results show that limited cable amplitudes are achieved within a limited range of wind velocity, which is a unique characteristic of RWIV of stay cable. It appears that the in-plane cable amplitude is much larger than the out-of-plane cable amplitude. Rivulet frequency, rivulet distribution along cable axis, and mean wind velocity profile, all have significant effects on the RWIV responses of the prototype stay cable. The effects of damping ratio on RWIVs of stay cables are carefully investigated, which suggests that damping ratio of 1% is needed to well mitigate RWIVs of prototype stay cables.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.7
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• pp.1119-1124
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• 2001

Nonlinear Vibration of a flexible circular ring is studied in this paper. Based upon the von Karman strain theory, the nonlinear governing equations are derived, in which the in-plane bending and extension displacements as well as the out-of-plane bending displacement are fully coupled. After discretizing the governing equations by the Galerkin approximation method, we obtain the linearlized equation by using the pertubation method. The results from the linearlized equations show that the in-plane displacement has effects on the natural frequencies of the out-of-plane displacement.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.4
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• pp.361-371
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• 1983

The turbulent structures of the free plane jet and two dimensional impinging jet are investigated experimentally. In order to get the two dimensional jet, the contour of the cubic equation suggested by Morel is used for a contracting nozzle. A linearized constant-temperature hot-wire anemometer is used for measurement. Mean velocities and turbulent intensities are measured along the centerline of the jet. Jet halp width spatial double velocity correlation coefficients and integral length scales are obtained. It is established that the free plane jet is truly self-preserving about 40 slot widths downstream of the nozzle. The experiments for the impinging jet are carried out at four different impingement wall locations within the self-preserving region of the free plane jet, and comparing the results with that of free plane jet, the mean velocity is changed in the region of 0.25H and turbulent intensities are affected in the region of 0.2H from the wall, respectively, where H means the distance between the nozzle exit and the wall.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.226-230
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• 2001

Electronic Speckle Pattern Interferometry (ESPI) has been recently developed and widely used because it has advantage to be able to measure surface deformations of engineering components and materials in industrial areas with non-contact. The spekle patterns to be formed with interference phenomena of scattering phenomena measure the out-of-plane deformations, together with the use of digital image equipment to process the informations included in the speckle patterns and the display consequent interferogram on a computer monitor. In this study, the experimental results of a canti-levered plate using ESPI were compared with those obtained from the simple beam theory. The ESPI results of the canti-levered plate analyzed by 4-step phase shifting method are close to the theoretical expectation. Also, out-0of-plane displacements of a spot welded canti-levered plate were measured by ESPI with 4-step phase shifting technique. The phase map of the spot welded canti-levered plate is quite different from that of the canti-levered plate without spot welding.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.843-855
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• 2020

X-plane submarines show better maneuverability as they have much longer span of control plane than that of cross plane submarines. In this study, captive model tests were conducted to evaluate the maneuverability of an X-plane submarine using Computational Fluid Dynamics (CFD) and a mathematical maneuvering model. For CFD analysis, SNUFOAM, CFD software specialized in naval hydrodynamics based on the open-source toolkit, OpenFOAM, was applied. A generic submarine Joubert BB2 was selected as a test model, which was modified by Maritime Research Institute Netherlands (MARIN). Captive model tests including propeller open water, resistance, self-propulsion, static drift, horizontal planar motion mechanism and vertical planar motion mechanism tests were carried out to obtain maneuvering coefficients of the submarine. Maneuvering simulations for turning circle tests were performed using the maneuvering coefficients obtained from the captive model tests. The simulated trajectory showed good agreement with that of free running model tests. From the results, it was proved that CFD simulations can be applicable to obtain reliable maneuvering coefficients for X-plane submarines.