• 대한수학회지
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• 제61권2호
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• pp.255-277
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• 2024

In this paper, we introduce the notion of stress-energy tensor Q of the traceless Ricci tensor for Riemannian manifolds (Mⁿ, g), and investigate harmonicity of Riemannian curvature tensor and Weyl curvature tensor when (M, g) satisfies some geometric structure such as critical point equation or vacuum static equation for smooth functions.

• Steel and Composite Structures
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• 제26권6호
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.579-584
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• 2003

Solenoid type magnetic actuator is the device, which could translate the electromagnetic energy to mechanical force. The force generated by magnetic flux, could be calculated by Maxwell stress tensor method. Maxwell stress tensor method is influenced by the magnetic flux path. Thus, magnetic force could be improved by modification of the iron case, which is the route of the magnetic flux. Modified design is obtained by parameter optimization using by Response surface methodology.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.169-179
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• 2021

In this paper, we extend the definition of p-harmonic maps between two Riemannian manifolds. We prove a Liouville type theorem for generalized p-harmonic maps. We present some new properties for the generalized stress p-energy tensor. We also prove that every generalized p-harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a homothetic vector field satisfying some condition is constant.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.715-730
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• 2015

In this note, we extend the definition of harmonic and biharmonic maps via the variation of energy and bienergy between two Riemannian manifolds. In particular we present some new properties for the generalized stress energy tensor and the divergence of the generalized stress bienergy.

• Bulletin of the Korean Chemical Society
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• 제7권3호
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• pp.204-210
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• 1986

It is shown that the linear stability coincides with the thermodynamic stability in the case of stress tensor evolution for simple dense fluids even if the constitutive (evolution) equation for the stress tensor is nolinear. The domain of coincidence can be defined in the space of parameters appearing in the constitutive equation and we find the domain is confined in an elliptical cone in a three-dimensional parameter space. The corresponding state theory in rheology of simple dense fluids is also further examined. The validity of the idea is strengthened by the examination.

• Geomechanics and Engineering
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• 제19권5호
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• pp.369-381
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• 2019

The objective of this paper is to study the two dimensional deformation in transversely isotropic thermoelastic medium without energy dissipation due to time harmonic sources using new modified couple stress theory, a continuum theory capable to predict the size effects at micro/nano scale. The couple stress constitutive relationships have been introduced for transversely isotropic thermoelastic medium, in which the curvature tensor is asymmetric and the couple stress moment tensor is symmetric. Fourier transform technique is applied to obtain the solutions of the governing equations. Assuming the deformation to be harmonically time-dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed sources have been considered to show the utility of the solution obtained. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of angular frequency are depicted graphically on the resulted quantities.

• Structural Engineering and Mechanics
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• 제76권1호
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• pp.17-26
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• 2020

The objective of this paper is to study the deformation in transversely isotropic thermoelastic solid using new modified couple stress theory subjected to ramp-type thermal source and without energy dissipation. This theory contains three material length scale parameters which can determine the size effects. The couple stress constitutive relationships are introduced for transversely isotropic thermoelastic solid, in which the curvature (rotation gradient) tensor is asymmetric and the couple stress moment tensor is symmetric. Laplace and Fourier transform technique is applied to obtain the solutions of the governing equations. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of length scale parameters are depicted graphically on the resulted quantities. Numerical results show that the proposed model can capture the scale effects of microstructures.

• 전산구조공학
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• 제10권4호
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• pp.131-142
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• 1997

본 논문에서는 4차 손상유효 tensor를 이용하여 유한 탄소성변형에 대한 운동학적인 손상해석이 소개된다. 이는 뼈대구조에서의 연속체 손상역학의 유효응력개념을 통하여 이루어진다. 소규모 변형율상태에만 적용할 수 있는 등가변형율 혹은 에너지법과는 달리 제안된 운동학적인 방법은 유효변형율과 유한변형율에 적용할 수 있는 소규모 변형상태에 있어서의 손상탄소성변형율 사이의 관계를 제공한다. 이는 실제 형상과 가상의 유효형상 모두에 대한 변형장의 운동학을 직접 고려하여 수행된다. 이 방법은 등가변형율이나 변형율 에너지 경우처럼 소규모 변형율에 한정되지 않으며, 유한변형율에 대한 에너지등가의 가정과 일치함을 보여준다. 본 논문에서는 손상이 탄소성영역에서 운동학적으로 표현되며, 손상유효 tensor는 2차 손상 tensor를 통해 손상을 운동학적 측정값이 항으로 특징지워진다.

• 지질공학
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• 제21권4호
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• pp.295-304
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• 2011

방사성폐기물처분장 주변 암반의 수많은 불확실성을 이해하기 위해서는 무결암에서 발생하는 균열의 성장과 거동 분석은 필수이다. 이에 본 연구에서는 처분장과 유사한 지질적 구조적 특성을 지닌 한국원자력연구원 내에 위치한 지하처분연구시설에서 채취한 화강암 시료를 이용하여 균열의 성장과 이에 따른 손상도를 AE parameter와 모멘트텐서해석법을 이용하여 분석하였다. 시료의 균열개시 균열결합 균열손상응력은 최대강도의 0.45배, 0.73배, 0.84배인 것으로 나타났다. 모벤트텐서해석법을 이용한 결과 응력 초기에는 인장균열의 발달이 우세하였으나 응력 수준이 증가함에 따라 전단균열이 발달하였다. 또한 시료에 균열손상응력 이상의 응력이 가해지면 파괴면을 중심으로 불안정한 전단균열이 발생하였으며 이는 파괴에 직접적인 역할을 하는 것으로 해석되었다.