• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.866-875
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• 1994

The problem of a rigid rod sliding on a rough horizontal surface in the plane is analyzed, which is commonly cited as an example of the inconsistency of rigid body frictional mechanics. The inconsistency is demonstrated by analyzing the normal reaction force at the contact point with the surface, and the concept of tangential collision is derived to resolve the inconsistency. Using the Poisson's hypothesis for the coefficient of restitution and Coulomb's law for the friction, the general methodology for solving the tangential collision is presented. The problem of the inconsistency generated in the sliding rod is completely resolved, building the concept of the tangential collision and adopting the theory of frictional impact. The result presented in this paper will obviate a generic obstacle to the development of simulation packages for planar rigid body mechanical systems with temporary contacts, and planning efficient motion strategies for robot manipulators.

• Journal of Mechanical Science and Technology
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• v.17 no.9
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• pp.1316-1323
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• 2003

This paper presents a structural analysis on the rigid and deformed motion of the leaflet induced by the blood flow required in the design of a bileaflet mechanical heart valve (MHV) prosthesis. In the study on the design and the mechanical characteristics of a bileaflet mechanical heart valve, the fluid mechanics analysis on the blood flow passing through leaflets, the kinetodynamics analysis on the rigid body motion of the leaflet induced by the pulsatile blood flow, and the structural mechanics analysis on the deformed motion of the leaflet are required sequentially and simultaneously. Fluid forces computed in the previous hemodynamics analysis on the blood flow are used in the kinetodynamics analysis on the rigid body motion of the leaflet. Thereafter, the structural mechanics analysis on the deformed motion of the leaflet follows to predict the structural strength variation of the leaflet as the leaflet thickness changes. Analysis results show that structural deformations and stresses increase as the fluid pressure increases and the leaflet thickness decreases. Analysis results also show that the leaflet becomes structurally weaker and weaker as the leaflet thickness becomes smaller than 0.6 mm.

• Structural Engineering and Mechanics
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• v.82 no.4
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• pp.503-515
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• 2022

The multi-rigid-body matrix method (MRBMM) is a generalized modeling method for obtaining the displacements, forces, and dynamic characteristics of a compliant mechanism without performing inner-force analysis. The method discretizes a compliant mechanism of any type into flexure hinges and rigid bodies by implementing a multi-body mass-spring model using coordinate transformations in a matrix form. However, in this method, the deformations of bodies that are assumed to be rigid are inherently omitted. Consequently, it may yield erroneous results in certain mechanisms. In this paper, we present a multi-compliant-body matrix-method (MCBMM) that considers a rigid body as a compliant element, while retaining the generalized framework of the MRBMM. In the MCBMM, a rigid body in the MRBMM is segmented into a certain number of body nodes and flexure hinges. The proposed method was verified using two examples: the first (an XY positioning stage) demonstrated that the MCBMM outperforms the MRBMM in estimating the static deformation and dynamic mode. In the second example (a bridge-type displacement amplification mechanism), the MCBMM estimated the displacement amplification ratio more accurately than several previously proposed modeling methods.

• Computers and Concrete
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• v.21 no.2
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• pp.219-229
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• 2018

In this paper, a modified rigid body spring model (RBSM) is proposed and used to analyze the damage and failure process of reinforced concrete (RC) structures. In the proposed model, the concrete is represented by an assembly of rigid blocks connected with a uniform distribution of normal and tangential springs to simulate the macroscopic mechanical behavior of concrete. Steel bars are evenly dispersed into rigid blocks as a kind of homogeneous axial material, and an additional uniform distribution of axial and dowel springs is defined to consider the axial stiffness and dowel action of steel bars. Perfect bond between the concrete and steel bars is assumed, and tension stiffening effect of steel bars is modeled by adjusting the constitutive relationship for the tensile reinforcement. Adjacent blocks are allowed to separate at the contact interface, which makes it convenient and easy to simulate the cracking process of concrete. The failure of the springs is determined by the Mohr-Coulomb type criterion with the tension and compression caps. The effectiveness of the proposed method is confirmed by elastic analyses of a cantilever beam under different loading conditions and failure analyses of a RC beam under two-point loading.

• Structural Engineering and Mechanics
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• v.35 no.1
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• pp.53-65
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• 2010

The rigid body inertia properties of a structure including the mass, the center of gravity location, the mass moments and principal axes of inertia are required for structural dynamic analysis, modeling of mechanical systems, design of mechanisms and optimization. The analytical approaches such as solid or finite element modeling can not be used efficiently for estimating the rigid body inertia properties of complex structures. Several experimental approaches have been developed to determine the rigid body inertia properties of a structure via Frequency Response Functions (FRFs). In the present work two experimental methods are used to estimate the rigid body inertia properties of a frame. The first approach consists of using the amount of mass as input to estimate the other inertia properties of frame. In the second approach, the property of orthogonality of modes is used to derive the inertia properties of a frame. The accuracy of the estimated parameters is evaluated through the comparison of the experimental results with those of the theoretical Solid Work model of frame. Moreover, a thorough discussion about the effect of accuracy of measured FRFs on the estimation of inertia properties is presented.

• Structural Engineering and Mechanics
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• v.2 no.3
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• pp.257-267
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• 1994

Motions of an unsymmetric rigid body on a rigid floor subjected to earthquake excitations with special attention to coefficient of friction are investigated. Motions of a body in a plane are classified (Ishiyama 1980) into six types, i.e. (1) rest, (2) slide, (3) rotation, (4) slide rotation, (5) translation jump, (6) rotation jump. Based upon the theoretical and experimental research work special attention is paid to the sliding of a body. The equations of motions and the behavior of coefficient of friction in the time of floor excitation are studied. One of the features of this investigation is the introduction and estimation of the "time dependent" coefficient of friction. It has been established that the constant kinetic coefficient of friction $${\mu}(kin){\sim_\sim}0.8{\mu}(stat)$$ does not give the appropriate results. The method for the estimation of the friction coefficient variation during the time is given.

• Journal of the Society of Naval Architects of Korea
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• v.44 no.2 s.152
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• pp.166-173
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• 2007

Collision analysis problems between ship to ship can be generally classified into the external mechanics(outer dynamics) and internal mechanics(inner dynamics). The former can be also dealt with the concept of fluid-structure interaction and the use of rigid body dynamic program, depending on the ways handling the hydrodynamic pressure due to surrounding water. In this study, full scale ship collision simulation was carried out, such as a DWT 75,000 ton striking ship collided at right angle to the middle of a DWT 150,000 struck ship with 10 knots velocity, coupling MCOL, a rigid body mechanics program for modeling the dynamics of ships, to hydrocode LS-DYNA. It could be confirmed that more suitable damage estimation would be performed in the case of the collision simulations with consideration of surrounding water through the comparison with the collision simulation results of fixed struck ships without it. Through this study, the opportunity could be obtained to establish a more effective ship collision simulation technique between ship to ship.

• Structural Engineering and Mechanics
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• v.18 no.3
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• pp.343-362
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• 2004

Rocking response of rigid bodies with rectangular footprint, freely standing on horizontal rigid plane is studied analytically. Bodies are subjected to simulated single component of horizontal earthquakes. The effect of baseline correction, applied to simulated excitations, on the rocking response is first examined. The sensitiveness of rocking motion to the details of earthquakes and geometric properties of rigid bodies is investigated. Due to the demonstrated sensitivity of rocking response to these factors, prediction of rocking stability must be made in the framework of probability theory. Therefore, using a large number of simulated earthquakes, the effects of duration and shape of intensity function of simulated earthquakes on overturning probability of rigid bodies are studied. In the case when a rigid body is placed on any floor of a building, the corresponding probability is compared to that of a body placed on the ground. For this purpose, several shear frames are employed. Finally, the viability of the energy balance equation, which was introduced by Housner in 1963 and widely used by nuclear power industry to estimate the rocking stability of bodies, is evaluated. It is found that the equation is robust. Examples are also given to show how this equation can be used.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.293-310
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• 2006

In seismic prone areas it is possible to meet very different objects (equipment components, on shelf artefacts, simple architectural elements) that can be modelled as a rigid body rocking on a rigid foundation. The interest in their behaviour can have different reasons: seismological, in order to estimate the ground motion intensity, or more strictly mechanical, in order to limit the response severity and to avoid overturning. The behaviour of many rigid bodies subjected to twenty wide ranging acceleration recordings is studied here. The response of the blocks is described using kinematic and energy parameters. A condition under which a so called scale effect is tangible is highlighted. The capacity of the signals to produce overturning is compared to different ground motion parameters, and a good correlation with the Peak Ground Velocity is unveiled.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.7
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• pp.91-97
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• 1998

The analysis model is the infinite body consisted of power law creep material containing a rigid inclusion with line crack shape subjected to the arbitrarily directional stress on an infinite boundary. The crack analysis is performed using the complex pseudo-stress function. The strain rate intensity factor is determined in the closed form as new fracture mechanics parmeter which represents the magnitudes of stress and strain rate near the tip in power law creep material.