• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.820-833
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• 1995

An analysis is performed to examine the equilibrium state and the stability of modeled Reynolds stress equations for homogeneous turbulent shear flows. The system of the governing equations consists of four coupled ordinary differential equations. The equilibrium states are found by the steady state solution of the governing equations. In order to investigate the stability of the system about its state in equilibrium, and eigenvalue problem is constructed. As a result, constraints for the coeffieients in the model equations are obtained by the stability condition of the equilibrium state as well as by their physically realizable bounds. It is observed that the models with pressure-strain rate correlation that are linear in the anisotropy tensor are stable and produce reasonable equilibrium tensor do not behave properly. Stability considerations about three most commonly used models are given in detail in the final section.

• Geomechanics and Engineering
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• v.8 no.6
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• pp.783-799
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• 2015

In this study, effect of horizontal in situ stress on failure mechanism around underground openings excavated in isotropic, elastic rock zones is investigated. For estimating the plastic zone occurrence, an induced stress influence area approach (Bray Equations) was modified to define critical stress ratio according to the Mohr-Coulomb failure criterion. Results obtained from modified calculations were compared with results of some other analytical solutions for plastic zone thickness estimation and the numerical modelling (finite difference method software, FLAC2D) study. Plastic zone and its geometry around tunnels were analyzed for different in situ stress conditions. The modified equations gave similar results with those obtained from the other approaches. However, safer results were calculated using the modified equations for high in situ stress conditions and excessive ratio of horizontal to vertical in situ stresses. As the outcome of this study, the modified equations are suggested to use for estimating the plastic zone occurrence and its thickness around the tunnels with circular cross-section.

• Korea-Australia Rheology Journal
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• v.14 no.1
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• pp.33-45
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• 2002

Recent results obtained for the port-pom model and the constitutive equations with time-strain separability are examined. The time-strain separability in viscoelastic systems Is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation at long times. The violation of separability in the short-time response just after a step strain is also well understood (Archer, 1999). In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency in the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard-type unstable or dissipative unstable. The conclusion drawn in this study is shown to be applicable to the Doi-Edwards model (with independent alignment approximation). Hence, the Hadamardtype instability of the Doi-Edwards model results from the time-strain separability in its formulation, and its remedy may lie in the transition mechanism from Rouse to reptational relaxation supposed by Doi and Edwards. Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the port-pom equations have been derived in the integral/differential form and also in the simplifled differential type by McLeish and carson on the basis of the reptation dynamics with simplifled branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable, and the integral model seems stable, as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given. However cautious attention has to be paid when one employs the simplified version of the constitutive equations without arm withdrawal, since neglecting the arm withdrawal immediately yields Hadamard instability. In the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong discontinuity at the moment of change of chain dynamics mechanisms.

• Wind and Structures
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• v.32 no.1
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• pp.31-46
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• 2021

The current research deals with, stability/instability and cylindrical composite nano-scaled shell's resonance frequency filled by graphene nanoplatelets (GPLs) under various thermal conditions (linear and nonlinear thermal loadings). The piece-wise GPL-reinforced composites' material properties change through the orientation of cylindrical nano-sized shell's thickness as the temperature changes. Moreover, in order to model all layers' efficient material properties, nanomechanical model of Halpin-Tsai has been applied. A functionally modified couple stress model (FMCS) has been employed to simulate GPLRC nano-sized shell's size dependency. It is firstly investigated that reaching the relative frequency's percentage to 30% would lead to thermal buckling. The current study's originality is in considering the multifarious influences of GPLRC and thermal loading along with FMCS on GPLRC nano-scaled shell's resonance frequencies, relative frequency, dynamic deflection, and thermal buckling. Furthermore, Hamilton's principle is applied to achieve boundary conditions (BCs) and governing motion equations, while the mentioned equations are solved using an analytical approach. The outcomes reveal that a range of distributions in temperature and other mechanical and configurational characteristics have an essential contribution in GPLRC cylindrical nano-scaled shell's relative frequency change, resonance frequency, stability/instability, and dynamic deflection. The current study's outcomes are practical assumptions for materials science designing, nano-mechanical, and micromechanical systems such as micro-sized sensors and actuators.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.179-193
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• 1996

This paper is concerned with the penalized stationary incompressible Navier-Stokes system with the inhomogeneous Dirichlet boundary condition on the part of the boundary. By taking a generalized velocity space on which the homogeneous essential boundary condition is imposed and corresponding trace space on the boundary, we pose the system to the weak form which the stress force is involved. We show the existence and convergence of the penalized system in the regular branch by extending the div-stability condition.

• Structural Engineering and Mechanics
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• v.39 no.5
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• pp.643-659
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• 2011

The design of box girders requires the determinations the buckling stress of the flange and the webs. Existing design equations available in codes of practice ignore the interactions between the box girder components. The paper illustrates the influence of the geometric interaction on the buckling stress of box girders. Generalized equations are first derived in terms of the web the flange geometric properties. Industrial examples are then presented showing the variation of the flange buckling stress for various stiffening configurations. The influence of the flange/web proportions on the buckling stress of box girder components is also highlighted. It is shown that buckling strength of the flange is largely affected by the restraints imposed by the webs or attached diaphragms. Graphs are presented showing various limiting states of box girders. These graphs are useful to use in practice in order to achieve economical and efficient design of box girders and rationally predict local buckling stress.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.1041-1061
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• 2015

The influence of hygrothermal effects on the vibration frequency and buckling load of a shear deformable composite plate with arbitrary initial stresses was investigated. The governing equations of the effects of humid, thermal and initial stresses are established using the variational method. The material properties of the composite plate are affected by both temperature and moisture. The initial stress is taken to be a combination of uniaxial load and pure bending in a hygrothermal environment. The influence of various parameters, such as the fiber volume fraction, temperature, moisture concentration, length/thickness ratios, initial stresses and bending stress ratio on the vibration and stability of the response of a laminated plate are studied in detail. The behavior of vibration and stability are sensitive to temperature, moisture concentration, fiber volume fraction and initial stresses.

• Journal of Mechanical Science and Technology
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• v.20 no.12
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• pp.2178-2188
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• 2006

The stress collapse in the formation of shear bands in elasto-thermo-viscoplatic materials is systematically studied within the framework of one-dimensional formulation via analytical and numerical methods. The elastic energy released in a domain is found to play an important role in the collapse behavior of shear localization. A non-dimensional parameter named the stability indicator is introduced to characterize the collapse behavior, with approximate forms of the incremental governing equations. The stability indicator offers useful information regarding the degree of severity of an abrupt change of deformations during the stress collapse. Numerical experiments are carried out to verify the stability indicator by varying material properties.

• Journal of the Korea institute for structural maintenance and inspection
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• v.10 no.6
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• pp.163-176
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• 2006

The paper proposes rating equations for main components such as girders, towers and cables in cable-stayed bridges. Load rating equations for girders and towers are proposed using stress and stability equations and load rating equation for cables is presented. A moving load analysis is performed and distribution types of live loads are determined for the cases of a maximum axial tensile force, a maximum axial compressive force, a maximum positive and a negative moment for each component. The Dolsan Grand bridge is used to verify a validity of proposed equations, The conventional rating equation overestimates rating factors of girders and towers in the Dolsan Grand bridge, whereas proposed rating equations properly reflect the axial-flexural interaction behavior of girders and towers in cable-stayed bridges.

• Steel and Composite Structures
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• v.17 no.1
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• pp.105-121
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• 2014

A fundamental limitation of steel structures is the decrease in their load-bearing capacity at high temperatures in fire situations such that structural members may require some additional treatment for fire resistance. In this regard, this paper evaluates the structural stability of fire-resistant steel, introduced in the late 1999s, through tensile coupon tests and proposes some experimental equations for the yield stress, the elastic modulus, and specific heat. The surface temperature, deflection, and maximum stress of fire-resistant steel H-section columns were calculated using their own mechanical and thermal properties. According to a comparison of mechanical properties between fire-resistant steel and Eurocode 3, the former outperformed the latter, and based on a comparison of structural performance between fire-resistant steel and ordinary structural steel of equivalent mechanical properties at room temperature, the former had greater structural stability than the latter through $900^{\circ}C$.