• Transactions of Materials Processing
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• v.16 no.4 s.94
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• pp.276-281
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• 2007

The hardening and the constitutive equation based on the crystal plasticity are introduced for the numerical simulation of hemispherical sheet metal forming. For calculating the deformation and the stress of the crystal, Taylor's model of the crystalline aggregate is employed. The hardening is evaluated by using the Taylor factor, the critical resolved shear stress of the slip system, and the sum of the crystallographic shears. During the hemispherical forming process, the texture of the sheet metal is evolved by the plastic deformation of the crystal. By calculating the Euler angles of the BCC sheet, the texture evolution of the sheet is traced during the forming process. Deformation texture of the BCC sheet is represented by using the pole figure. The comparison of the strain distribution and punch force in the hemispherical forming process between the prediction using crystal plasticity and experiment shows the verification of the crystal plasticity-based formulation and the accuracy of the hardening and constitutive equation obtained from the crystal plasticity.

• Journal of Welding and Joining
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• v.27 no.6
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• pp.49-54
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• 2009

In this study, the numerical analysis model for fatigue life prediction of welded structures are presented. In order to evaluate the structural degradation of welded structures due to fatigue loading, continuum damage mechanics approach is applied. Damage evolution equation of welded structures under arbitrary fatigue loading is constructed as a unified plasticity-damage theory. Moreover, by integration of damage evolution equation regarding to stress amplitude and number of cycles, the simplified fatigue life prediction model is derived. The proposed model is compared with fatigue test results of T-joint welded structures to obtain its validation and usefulness. It is confirmed that the predicted fatigue life of T-joint welded structures are coincided well with the fatigue test results.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.669-688
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• 2021

The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form $$\{{\frac{du}{dt}}+Au=F(t,\;u_t),\;t{\geq}s,\\\;u_s({\theta})={\phi}({\theta}),\;{\forall}{\theta}{\in}(-{{\infty}},\;0],\;s{\in}{\mathbb{R}},$$ where A is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part F may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.923-935
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• 2023

In this paper, we will discuss existence of solution of square-mean pseudo almost automorphic solution for fractional stochastic evolution equations driven by G-Brownian motion which is given as ^c₀D^𝛼_𝜌 Ψ_𝜌 = 𝒜(𝜌)Ψ_𝜌d𝜌 + 𝚽(𝜌, Ψ_𝜌)d𝜌 + ϒ(𝜌, Ψ_𝜌)d ⟨ℵ⟩_𝜌 + χ(𝜌, Ψ_𝜌)dℵ_𝜌, 𝜌 ∈ R. Furthermore, we also prove that solution of the above equation is unique by using Lipschitz conditions and Cauchy-Schwartz inequality. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1003-1013
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• 1996

The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.13-27
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• 2014

The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equations of second order with unbounded principal operators.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.435-459
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• 2004

Identification problems for the system governed by abstract nonlinear damped second order evolution equations are studied. Since unknown parameters are included in the diffusion operator, we can not simply identify them by using the usual optimal control theories. In this paper we present how to solve our identification problems via the method of transposition.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.12
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• pp.2173-2178
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• 2007

Dynamics of plasma sheath was analyzed using simple ion fluid model with poison equation. Incident ion current, energy, potential distribution and space charge density profile were calculated as a function of time. The effects of initial floating sheath on the evolution of biased sheath were compared with ideal matrix sheath. The effects of finite rising time of pulse bias voltage on the ion current and energy was studied. The influence of surface charging on the evolution of sheath was also investigated

• East Asian mathematical journal
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• v.29 no.5
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• pp.481-489
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• 2013

In this paper we deal with approximate controllability for semilinear system in a Hilbert space. In order to obtain the controllability, we assume that the system of the generalized eigenspaces of the principal operator is complete in the state space, which has a simple form and can be applied to many examples. Because of its simple form, some examples of controllability of the systems governed by the semilinear equations will be given.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.359-370
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• 2011

In this work, we obtain new solitary wave solutions for some nonlinear partial differential equations. The Jacobi elliptic function rational expansion method is used to establish new solitary wave solutions for the combined KdV-mKdV and Klein-Gordon equations. The results reveal that Jacobi elliptic function rational expansion method is very effective and powerful tool for solving nonlinear evolution equations arising in mathematical physics.