• Structural Engineering and Mechanics
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• 제42권3호
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• pp.313-334
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• 2012

This paper examines the problem of a penny-shaped crack in a thermoporoelastic body. On the basis of the recently developed general solutions for thermoporoelasticity, appropriate potentials are suggested and the governing equations are solved in view of the similarity to those for pure elasticity. Exact and closed form fundamental solutions are expressed in terms of elementary functions. The singularity behavior is then discussed. The present solutions are compared with those in literature and an excellent agreement is achieved. Numerical calculations are performed to show the influence of the material parameters upon the distribution of the thermoporoelastic field. Due to its ideal property, the present solution is a natural benchmark to various numerical codes and simplified analyses.

• Earthquakes and Structures
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• 제13권5호
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• pp.465-471
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• 2017

This work derives a generalized time fractional differential equation governing wave propagation in a radially vibrating non-classical cylindrical medium. The cylinder is made of a transversely isotropic hyperelastic John's material which obeys frequency-dependent power law attenuation. Employing the definition of the conformable fractional derivative, the solution of the obtained generalized time fractional wave equation is expressed in terms of product of Bessel functions in spatial and temporal variables; and the resulting wave is characterized by the presence of peakons, the appearance of which fade in density as the order of fractional derivative approaches 2. It is obtained that the transversely isotropic structure of the material of the cylinder increases the wave speed and introduces an additional term in the wave equation. Further, it is observed that the law relating the non-zero components of the Cauchy stress tensor in the cylinder under consideration generalizes the hypothesis of plane strain in classical elasticity theory. This study reinforces the view that fractional derivative is suitable for modeling anomalous wave propagation in media.

• Structural Engineering and Mechanics
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• 제23권2호
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• pp.115-127
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• 2006

The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.

• Structural Engineering and Mechanics
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• 제19권4호
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• pp.441-457
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• 2005

An analytical method is presented to solve the problem of transient wave propagation in a transversely isotropic piezoelectric hollow sphere subjected to thermal shock and electric excitation. Exact expressions for the transient responses of displacements, stresses, electric displacement and electric potentials in the piezoelectric hollow sphere are obtained by means of Hankel transform, Laplace transform, and inverse transforms. Using Hermite non-linear interpolation method solves Volterra integral equation of the second kind involved in the exact expression, which is caused by interaction between thermo-elastic field and thermo-electric field. Thus, an analytical solution for the problem of transient wave propagation in a transversely isotropic piezoelectric hollow sphere is obtained. Finally, some numerical results are carried out, and may be used as a reference to solve other transient coupled problems of thermo-electro-elasticity.

• Advances in materials Research
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• 제9권4호
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• pp.289-309
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• 2020

The aim of the present investigation is to examine the propagation of plane harmonic waves in transversely isotropic homogeneous magneto visco thermoelastic rotating medium with fractional order heat transfer and two temperature. It is found that, for two dimensional assumed model, there exist three types of coupled longitudinal waves (quasi-longitudinal, quasi-transverse and quasi-thermal) in frequency domain. phase velocities, specific loss, penetration depth, attenuation coefficients of various reflected waves are computed and depicted graphically. The effects of viscosity and fractional order parameter by varying different values are represented graphically.

• Coupled systems mechanics
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• 제12권3호
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• pp.261-276
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• 2023

This article is an application of new modified couple stress thermoelasticity without energy dissipation in association with two-temperature theory. The upper and lower surfaces of the plate are subjected to an axisymmetric heat supply. The solution is found by using Laplace and Hankel transform techniques. The analytical expressions of displacement components, conductive temperature, stress components and couple stress are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect of two temperature is shown on the various components.

• Coupled systems mechanics
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• 제8권4호
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• pp.299-313
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• 2019

The paper represents computer modeling of the deformed state of physically nonlinear transversally isotropic bodies with hole. In order to describe the anisotropy of the mechanical properties of transversally-isotropic materials a structurally phenomenological model has been used. This model allows representing the initial material in the form of the coupled isotropic materials: the basic material (binder) considered from the positions of continuum mechanics and the fiber material oriented along the anisotropy direction of the original material. It is assumed that the fibers perceive only the axial tensile-compression forces and are deformed together with the base material. To solve the problems of the theory of plasticity, simplified theories of small elastoplastic deformation have been used for a transversely-isotropic body, developed by B.E. Pobedrya. A simplified theory allows applying the theory of small elastoplastic deformations to solve specific applied problems, since in this case the fibrous medium is replaced by an equivalent transversely isotropic medium with effective mechanical parameters. The essence of simplification is that with simple stretching of composite in direction of the transversal isotropy axis and in direction perpendicular to it, plastic deformations do not arise. As a result, the intensity of stresses and deformations both along the principal axis of the transversal isotropy and along the perpendicular plane of isotropy is determined separately. The representation of the fibrous composite in the form of a homogeneous anisotropic material with effective mechanical parameters allows for a sufficiently accurate calculation of stresses and strains. The calculation is carried out under different loading conditions, keeping in mind that both sizes characterizing the fibrous material fiber thickness and the gap between the fibers-are several orders smaller than the radius of the hole. Based on the simplified theory and the finite element method, a computer model of nonlinear deformation of fibrous composites is constructed. For carrying out computational experiments, a specialized software package was developed. The effect of hole configuration on the distribution of deformation and stress fields in the vicinity of concentrators was investigated.

• Composites Research
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• 제30권3호
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• pp.193-201
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• 2017

탄소나노튜브와 폴리에스터 계면 간 그래프팅이 나노복합재의 역학적 거동과 하중전달에 미치는 영향을 고찰하기 위해 분자동역학 전산모사를 수행하고 그 결과를 Mori-Tanaka 모델 예측해와 비교하였다. 각 방향으로의 인장과 전단 전산모사를 통해 응력-변형률 선도를 도출한 후, 가교 유무에 따른 탄성거동 변화를 관찰하였다. 또한 가로등방성 강성행렬을 방향 평균하여 나노튜브가 랜덤분포하는 경우의 등방성 영률과 전단계수를 구하였다. 그 결과 가로방향 영률과 전단계수는 그래프팅 가공에 의해 향상되었으나, 길이방향 영률의 경우 나노튜브의 물성감소로 인해 오히려 물성이 저하되었다. 나노튜브의 랜덤분포를 고려한 예측 결과에서는 그래프팅 가공에 의해 물성이 약간 감소하였다.

• 터널과지하공간
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• 제10권2호
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• pp.165-172
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• 2000

이방성 암반의 역학적 거동은 해당 암반의 이방성 각도에 따라 다양한 거동을 하게 되므로 터널이나 지하구조물들이 이방성 암반 내에 위치하는 경우, 이러한 특성을 고려한 설계 및 시공이 이루어져야 할 것이다. 따라서 본 연구에서는 먼저, 실내시험을 통하여 편마구조에 대한 역학적 특성을 규명하고 실내시험으로부터 구한 강도특성들을 이용하여 시험편 모델에 대한 유한차분해석을 수행하였으며, 시험편의 파괴메커니즘에 대한 수치해석적 분석을 수행하였다. 본 연구의 결과를 요약하면, 1)비교적 경암에 속하는 화강편마암임에도 불구하고, 퇴적층리나 불연속면을 가진 이방성 모델의 시험결과와 동일하게 편마구조의 각도변화에 따라 파괴강도의 경향을 뚜렷하게 구분할 수 있었으며, 전단강도시험을 제외하고 일반적으로 $\beta$:60$^{\circ}$에서 가장 적은 강도치를 나타내었다. 2) 횡등방성 모델을 이용하여 시험편에 대한 유한차분해석을 수행한 결과, 편마구조의 각도에 따라 응력분포 및 변형특성이 변화함을 알 수 있었다.

• 터널과지하공간
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• 제11권1호
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• pp.72-78
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• 2001

평면 이방성 암석의 시추 코아를 이용하여 일회의 단축압축시험만으로 이방성 탄성계수를 구하는 방법이 김호영에 의하여 제시되었으나 실험을 통하여 검정한 결과, 한 방향의 포아송비 v$_2$만을 사용하여 탄성계수를 구하는 방법에 문제가 있음이 발견되었다. 본 연구에서는 두 가지의 포아송비, v$_{12}$와 v$_{21}$을 사용하여 이방성 탄성계수를 계산하는 식을 유도하였고, 이방성의 각이 30$^{\circ}$와 65$^{\circ}$인 2개의 시편에 대하여 이방성 탄성계수를 측정하였다. 이방성 탄성계수는 이방성의 각에 따라 다른 식을 사용하여야 되며, 이방성 각이 45$^{\circ}$이하인 경우 v$_{21}$을, 이방성 각이 45$^{\circ}$이상인 경우에는 v$_{12}$를 이용하여 탄성계수를 계산하여야 할 것으로 사료된다.