• Coupled systems mechanics
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• v.11 no.6
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• pp.543-556
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• 2022

Delamination of multilayered inhomogeneous beam that exhibits non-linear relaxation behavior is analyzed in the present paper. The layers are inhomogeneous in the thickness direction. The dealamination crack is located symmetrically with respect to the mid-span. The relaxation is treated by applying a non-linear stress-straintime constitutive relation. The material properties which are involved in the constitutive relation are distributed continuously along the thickness direction of the layer. The delamination is analyzed by applying the J-integral approach. A time-dependent solution to the J-integral that accounts for the non-linear relaxation behavior is derived. The delamination is studied also in terms of the time-dependent strain energy release rate. The balance of the energy is analyzed in order to obtain a non-linear time-dependent solution to the strain energy release rate. The fact that the strain energy release rate is identical with the J-integral value proves the correctness of the non-linear solutions derived in the present paper. The variation of the J-integral value with time due to the non-linear relaxation behavior is evaluated by applying the solution derived.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.565-589
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• 2004

The present paper concerns the macroscopic overall description of rheologic properties for steel wire and synthetic fibre cables under variable loading actions according to non-linear creep and/or relaxation theory. The general constitutive equations of non-linear creep and/or relaxation of tension elements - cables under one-step and the variable stress or strain inputs using the product and two types of additive approximations of the kernel functions are presented in the paper. The derived non-linear constitutive equations describe a non-linear rheologic behaviour of the cables for a variable stress or strain history using the kernel functions determined only by one-step - constant creep or relaxation tests. The developed constitutive equations enable to simulate and to predict in a general way non-linear rheologic behaviour of the cables under an arbitrary loading or straining history. The derived constitutive equations can be used for the various tension structural elements with the non-linear rheologic properties under uniaxial variable stressing or straining.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2007.05a
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• pp.209-212
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• 2007

Rubber compounds have high viscoelastic property. One of the viscoelastic behaviors during profile extrusion is the swelling of extrudate. In this study, die swell of rubber compounds at the capillary die have been investigated through an experiment and computer simulation. They have been performed using fluidity tester in experiment and commercial CFD code, Polyflow in computer simulation. Die swell of rubber compounds for relaxation time at several modes under same conditions with the experiment were predicted using non-linear differential viscoelastic model, Phan-Thien-Tanner (PTT) model. The simulation was analyzed compared with the experiment. Viscoelastic behaviors for pressure, velocity and shear rate distribution were analyzed at the capillary die. It is concluded that the PTT model successfully represented the amount of the optimal die swell of rubber compounds for relaxation time at different modes.

• Transactions of Materials Processing
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• v.16 no.4 s.94
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• pp.260-265
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• 2007

Rubber compounds have high viscoelastic property. One of the viscoelastic behaviors during profile extrusion is the swelling of extrudate. In this study, die swells of rubber compounds at the capillary die have been investigated through experiment and computer simulation. Experiments and simulations have been performed using fluidity tester and commercial CFD code, Polyflow respectively. Die swells of rubber compounds in a capillary die were predicted using non-linear differential viscoelastic model, Phan-Thien-Tanner(PTT) model for various relaxation times and relaxation modes. The results of simulation were compared with the experiments. Pressure and velocity distribution, and circulation flows at the comer of capillary die have been investigated through computer simulation. It is concluded that the PTT model successfully represented the amount of the die swell of rubber compounds for various relaxation times at different modes.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.815-818
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• 2002

The elliptic relaxation model(ERM) with the inhomogeneous correction intermediate between near wall with and far from the wall. The source of the ERM usually was appled quasi-homogeneous pressure-strain correlation in homogeneous situations. This formulation was easily applied to the linear model or non-linear pressure-strain model. It is observed that the boundary conditions of the relaxation operator dominate the homogeneous pressure-strain model in the near wall region. While looking at high-Reynolds number flows, it was found necessary to modify the effect of the relaxation operator throughout the log region by accounting for gradients of the flatness variable and turbulent length scales. These effects are kinematic blocking of the wall normal velocity fluctuation and pressure reflections from the surface. This model is wall distances and unit vectors which make the model applicable to flows boundary by a complex geometry. Inhomogeneous correction model is computed inertial and non-inertial channel flow These are compared DNS(Kim et at., Kristofffrsen & Andersson) for channel flow. The present model could be predicted well for rotating flows.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.495-504
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• 2023

This article deals with non-degenerate linear transformations on Euclidean Jordan algebras. First, we study non-degenerate for cone invariant, copositive, Lyapunov-like, and relaxation transformations. Further, we study that the non-degenerate is invariant under principal pivotal transformations and algebraic automorphisms.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.29 no.4
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• pp.169-179
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• 2017

In this study, we applied the wave generation method by relaxation method to the SWASH model, which is a non - hydrostatic numerical model, for stable and accurate wave generation of linear and nonlinear waves. To validate the relaxation wave generation method, we were simulated various wave, including the linear wave and nonliner wave and compared with analytical solution. As a result, the incident wave was successfully generated and propagated in all cases from Stokes waves to cnoidal wave. Also, we were confirmed that the wave height and the waveform were in good agreement with the analytical solution.

• Computational Structural Engineering
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• v.11 no.1
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• pp.179-190
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• 1998

A geometrically nonlinear finite element formulation of spatial cable networks is presented using two cable elements. Firstly, derivation procedures of tangent stiffness and mass matrices for the space truss element and the elastic catenary cable element are summarized. The load incremental method based on Newton-Raphson iteration method and the dynamic relaxation method are presented in order to determine the initial static state of cable nets subjected to self-weights and support motions. Furthermore, static non-linear analysis of cable structures under additional live loads are performed based on the initial configuration. Challenging example problems are presented and discussed in order to demonstrate the feasibility of the present finite element method and investigate static nonlinear behaviors of cable nets.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.757-770
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• 1999

We analyse in this paper the possibility of using preconditioning techniques as for square non-singular systems, also in the case of inconsistent least-squares problems. We find conditions in which the minimal norm solution of the preconditioned least-wquares problem equals that of the original prblem. We also find conditions such that thd Kaczmarz-Extendid algorithm with relaxation parameters (analysed by the author in [4]), cna be adapted to the preconditioned least-squares problem. In the last section of the paper we present numerical experiments, with two variants of preconditioning, applied to an inconsistent linear least-squares model probelm.

• Journal of Korean Physical Therapy Science
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• v.22 no.2
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• pp.37-42
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• 2015

Background : The purpose of this study is to identify how the relaxation music listening during exercise influences body flexibility and stress. Methods : Twenty healthy adults 20s and 30s who lack of body flexibility were recruited and each subjects performed exercise during the relaxation music listening or no listening. Bach, aria of linear G was used as the relaxation music. The experiment was conducted for 4 weeks. In this study, PASW ver 18.0 was utilized to perform non-parametric tests for comparisons. Result : The result with respect to the dependent variables are as follows: When non-parametric tests were conducted to compare body flexibility at the test of the right ear touch behind head by left hand and the stretching hands test between the two groups after exercise, they showed significant differences in statistical terms (p<.05). Conclusion : From the above results of the study it was found that the application of the relaxation music during the exercise is effective, it improved the body flexibility of the right ear touch behind head by left hand and the stretching hands more than the exercise without the relaxation music did. The outcome of the experiment may provide basic data for developing an effective way to increase body flexibility.