• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.813-823
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• 2021

In this work, we present the classical formulation for the antiplane problem of a eletro-viscoelastic materialswith total sliprate dependent friction and write the corresponding variational formulation. In the second step, we prove that the solution converges to the solution of the corresponding electro-elastic problem as the viscosity converges to zero.

• Structural Engineering and Mechanics
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• 제7권2호
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• pp.147-157
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• 1999

An analytical methodology for solving antiplane problem of anisotropic materials is proposed and discussed in detail in this study. The material considered in this study possesses a symmetry plane at z=0. The relationship between the problems of anisotropic materials and the corresponding isotropic problems are established by Ma (1996) on the basis of the general solutions for the shear stresses and displacement in both the polar and Cartesian coordinate systems. This implies that any solution of an anisotropic problem can be obtained by solving a corresponding isotropic problem. In this study some examples and numerical results are presented as an explanation of how the complicated anisotropic problem could be solved by the associated simpler isotropic problem.

• Structural Engineering and Mechanics
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• 제64권6권
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• pp.695-701
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• 2017

This paper investigates some general properties in the degenerate scale problem of antiplane elasticity or Laplace equation. For a given configuration, the degenerate scale problem is solved by using conformal mapping technique, or by using the null field BIE (boundary integral equation) numerically. After solving the problem, we can define and evaluate the degenerate area which is defined by the area enclosed by the contour in the degenerate configuration. It is found that the degenerate area is an important parameter in the problem. After using the conformal mapping, the degenerate area can be easily evaluated. The degenerate area for many configurations, from triangle, quadrilles and N-gon configuration are evaluated numerically. Most properties studied can only be found by numerical computation. The investigated properties provide a deeper understanding for the degenerate scale problem.

• 대한기계학회논문집A
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• 제39권9호
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• pp.859-869
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• 2015

횡등방성 압전재료에 기하학적 비대칭인 쐐기균열문제를 해석하였다. 기계적 집중면외하중과 전기적 집중 면내하중이 쐐기표면 점에 작용하고 있고, 반면에 균열면 한점에는 기계적 집중하중만 작용한다. 균열면은 침투형 얇은 슬릿으로 가정하여, 전기변위의 수직성분 및 전위가 균열면을 가로질러 연속으로 두었다. Mellin 변환을 사용하여 문제를 수식화하고, Wiener-Hopf 식을 유도하였다. 이 식을 풀므로써 폐형으로 주어지는 해를 얻었다. 임의 균열길이나 경사각, 쐐기각에 대해서도 적용이 가능한 응력 및 전기변위 강도계수를 구하였다. 장의 강도계수들은 전기적 하중에는 무관하고, 전기변위강도계수는 응력강도계수만의 함수로 표현되었다. 전기장 강도계수는 영으로 계산되었다. 또한 에너지방출률을 얻었다. 이 해는 중첩에 의하여 임의로 분포하는 전기기계하중문제에 대한 해를 제공하는 기본해로 사용될 수 있다.

• 대한기계학회논문집A
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• 제39권6호
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• pp.589-596
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• 2015

횡등방성 압전재료에 대한 모서리경사균열 문제를 해석하였다. 두 기계적 집중 면외하중과 전기적 집중 면내하중이 표면과 균열면에 각각 작용하고, 균열면은 절연균열면이다. 일반화된 변위벡터를 도입하고 Mellin 변환을 사용하여 문제를 수식화하고, 이로부터 Wiener-Hopf 식을 유도하였다. 이식을 풀므로써 폐형으로 주어지는 해를 얻었다. 임의의 균열길이나 경사각에 대해서도 적용이 되는 응력 및 전기변위 강도계수와 에너지 방출율을 구하였다. 이 해는 중첩에 의하여 임의로 분포하는 전기기계하중 문제에 대한 해를 제공하는 기본해로 사용될 수 있다.

• Journal of Mechanical Science and Technology
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• 제18권8호
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• pp.1375-1387
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• 2004

A solution is given for the elastodynamic problem of a crack perpendicular to the graded interfacial zone in bonded materials under the action of anti plane shear impact. The interfacial zone is modeled as a nonhomogeneous interlayer with the power-law variations of its shear modulus and mass density between the two dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the transient problem to the solution of a Cauchy-type singular integral equation in the Laplace transform domain. Via the numerical inversion of the Laplace transforms, the values of the dynamic stress intensity factors are obtained as a function of time. As a result, the influences of material and geometric parameters of the bonded media on the overshoot characteristics of the dynamic stress intensities are discussed. A comparison is also made with the corresponding elastostatic solutions, addressing the inertia effect on the dynamic load transfer to the crack tips for various combinations of the physical properties.

• 대한기계학회논문집A
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• 제32권1호
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• pp.43-53
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• 2008

Surface edge crack in transversely isotropic piezoelectric material is analyzed. The concentrated antiplane mechanical and inplane electrical loadings are applied to an arbitrary point of the surface, where the impermeable crack boundary condition is imposed. Using Mellin transform the problem is formulated, from which Wiener-Hopf equations are derived. By solving the equations the solution is obtained in a closed form. Mechanical and electric intensity factors and energy release rate are obtained and discussed. This problem could be used as a Green's function to generate the solutions of other problems with the same geometry but of different loading conditions.

• 대한기계학회논문집A
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• 제36권6호
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• pp.665-672
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• 2012

면외 기계적 하중 및 면내 전기적 하중하의 횡등방성 이종 압전재료에 대한 계면균열문제를 해석하였다. 복소함수를 도입하여 문제를 수식화 하고, 이로부터 Hilbert 문제를 구성하였다. Hilbert 문제를 풀므로써, 일반해를 얻었다. 일반해를 사용하여, 반무한 균열 혹은 한 개 유한균열 및 두 개 유한균열에 대한 폐형 해를 각각 구하였다. 이때 하중은 한 개의 집중 기계하중 및 전기적하중이 균열면에 작용한다. 이 문제는 기하조건만 동일하면, 임의의 하중에 대해서도 해를 얻을 수 있는 Green 함수로서 사용될 수 있다.

• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.59-69
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• 2001

The paper deals with the interaction between three Griffith cracks propagating under antiplane shear stress at the interface of two dissimilar infinite elastic half-spaces. The Fourier transform technique is used to reduce the elastodynamic problem to the solution of a set of integral equations which has been solved by using the finite Hilbert transform technique and Cooke’s result. The analytical expressions for the stress intensity factors at the crack tips are obtained. Numerical values of the interaction efect have been computed for and results show that interaction effects are either shielding or amplification depending on the location of each crack with respect to other and crack tip spacing. AMS Mathematics Subject Classification : 73M25.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.487-510
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• 2023

We propose a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation. The behavior of the material is described with a linearly electro-viscoelastic constitutive law with long term memory. The mechanical process is dynamic and the electrical conductivity coefficient depends on the total slip rate, the friction is modeled with Tresca's law which the friction bound depends on the total slip rate with taking into account the electrical conductivity of the foundation both. The main results of this paper concern the existence and uniqueness of the weak solution of the model; the proof is based on results for second order evolution variational inequalities with a time-dependent hemivariational inequality in Banach spaces.